- Added graphicx and subfigure packages. - Added dummy address for Antonia. - Capitalised all section titles correctly. - Removed Chanchani reference. - Added several figures. - Completely rewrote Ambler and Beynon-Davies sections. - Expanded description of new notation. - Expanded example section.

nigel.stanger / Publications

Browse code - Added graphicx and subfigure packages. - Added dummy address for Antonia. - Capitalised all section titles correctly. - Removed Chanchani reference. - Added several figures. - Completely rewrote Ambler and Beynon-Davies sections. - Expanded description of new notation. - Expanded example section. - Rewrote (shortened) many parts. Pillay_2005
1 parent 800adf7 commit 260b676e2e1296c9d45b2c78592317f8997004f6 nstanger authored on 2 Apr 2005

Browse code

- Added graphicx and subfigure packages.

- Added dummy address for Antonia.
- Capitalised all section titles correctly.
- Removed Chanchani reference.
- Added several figures.
- Completely rewrote Ambler and Beynon-Davies sections.
- Expanded description of new notation.
- Expanded example section.
- Rewrote (shortened) many parts.

Pillay_2005

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\documentclass{llncs} \usepackage{subfigure} \usepackage{graphicx} \title{A Graphical Notation for \\ Physical Database Modelling} \author{Antonia Pillay\inst{1} \and Nigel Stanger\inst{2}} \institute{???? Malaysia \and Department of Information Science, University of Otago, Dunedin, New Zealand \email{nstanger@infoscience.otago.ac.nz}} \begin{document} \maketitle \begin{abstract} In this paper we describe a graphical notation for physical database modelling. This notation provides database administrators (DBAs) with a means to model the physical structure of new and existing databases, thus enabling them to make more proactive and informed tuning decisions, compared to existing database monitoring tools. \end{abstract} \section{Introduction} As with most information systems, the design and implementation of a database goes through several phases, including conceptual, logical and physical modelling \cite{BeDa-P-2003}. These three phases are of particular interest, as they embody the progression from higher to lower levels of abstraction \cite{Tsic-D-1978}. Conceptual models are typically highly abstract, using techniques such as entity-relationship modelling. Logical models represent the database structure in a form that is closer to the physical representation, yet still sufficiently abstract to isolate applications from the physical representation \cite{Codd-EF-1970}, and are expressed using formalisms such as the relational model. A logical model for a database can be derived by transforming the corresponding conceptual model. Physical models represent the database structure in terms of the physical storage implementation of a specific database management system (DBMS) such as Oracle or DB2. A physical model for a database can be derived by transforming the corresponding logical model \cite{Bato-DS-1985,Conn-TM-2002}. Because of their low abstraction level, physical level database models have tended to not be expressed using graphical notations, unlike models at higher levels of abstraction. Physical level modelling, however, is equally as important as, if not \emph{more} important than the higher levels, because it is the physical level that determines the performance of a database \cite{BeDa-P-2003}. It is somewhat surprising that there have been relatively few attempts to devise a graphical physical modelling notation, because such a notation can provide several advantages \cite{Conn-TM-2002,BeDa-P-1992-PDD,Will-J-1992}: \begin{itemize} \item it can reduce complexity and thus improve understandability \cite{Tuft-ER-1997}; \item it can provide a more complete and integrated display of performance tuning techniques in a database; \item database developers can be more confident about the design decisions that they make for the performance of the database; \item database performance problems are more easily visualised using a graphical notation; and \item a specific methodology is developed and used, thus enabling developers to resolve physical performance issues more systematically. \end{itemize} These benefits are embodied in modern database performance monitoring tools, which provide higher-level visualisations of a database's internals in order to easily identify and highlight performance problems. Such tools, however, are primarily \emph{monitoring} tools rather than \emph{design} tools. They may therefore unintentionally encourage DBAs into a \emph{reactive} mode of continually ``tweaking'' the database to resolve performance issues, rather than a \emph{proactive} mode of anticipating and designing for expected usage. It may also be difficult for a DBA using such tools to gain a clear and comprehensive overview of all the tuning techniques that are in use within a particular database \cite{Core-MJ-1997-OracleDW}. In this paper we propose a graphical notation for physical database modelling. In Sect.~\ref{sec-techniques}, we provide a brief overview of commonly used physical tuning techniques. We then discuss in Sect.~\ref{sec-previous} two earlier approaches upon which our work is partially based. Sect.~\ref{sec-notation} introduces our proposed notation, and Sect.~\ref{sec-future} discusses possible future work. The paper concludes in Sect.~\ref{sec-conclusion}. \section{Physical Tuning Techniques} \label{sec-techniques} Database management is generally an I/O bound task, so the main performance bottleneck in most databases will be the speed of offline storage such as disk drives. Retrieving data from a hard disk is theoretically about six orders of magnitude slower than retrieving data from RAM\footnote{On the order of milliseconds (\(10^{-3}\)) for disk versus nanoseconds (\(10^{-9}\)) for RAM.}. The aim of any physical tuning strategy must therefore be to minimise the impact of slow storage, either by directly reducing the number of physical disk accesses required, or by parallelising access to disk in order to reduce contention. These considerations have led to the development of five general physical tuning techniques, which are implemented to various degrees by most modern mainstream DBMS products: \begin{description} \item[Indexes] reduce the number of physical disk accesses required to retrieve a specific record, most typically by building a B+-tree \cite{Knut-DE-1997-Art} based on some key value. Without any indexes, a DBMS often has little choice but to perform a sequential scan in order to locate a specific record. % A common database operation is to request a specific data record % identified by a some key value. When such a request occurs, the DBMS % must locate this record on disk (assuming that it is not already cached % elsewhere). If we assume that the records are randomly ordered with % respect to the chosen key value, then the DBMS has no option but to % perform a sequential scan of all the records, which will require on % average\(n/2b\) disk accesses, where \(n\) is the number of records and % \(b\) is the number of records per database block (the worst case is % \((n - 1)(b)\)). Sorting the records on the key value will obviously % help for searches based on that key value, but will not help for % searches based on a different key value. % % One solution is to build a separate index structure that associates key % values with their corresponding physical record. Because indexes are % stored separately, we can provide multiple indexes on different key % values for the same set of records. In addition, by choosing an % appropriate data structure for the index, we can improve the efficiency % of searching and thus reduce the number of physical disk accesses % required \cite{Roti-S-1996}. Most modern DBMSs use some variant of the % \emph{B+-tree} structure \cite{Knut-DE-1997-Art}. This structure has % average and worst case performance of (formula) and (formula), % respectively. % % Indexes are a ``pure'' disk access minimisation technique, that is, they % reduce the number of physical disk accesses required, but do not provide % any form of paralellism. B-tree indexes perform well for a wide range of % typical database queries (ref), but can suffer in high update % environments due to the need to also update the index. \item[Hashing] is a method of quickly locating specific records by passing a key value to a \emph{hash function}. This function returns the physical location of a hash bucket, which contains a pointer to the associated physical record (check). Hashing schemes typically require only a single disk access to retrieve a specific record. % Hashing is another pure disk access minimisation technique that performs % well for exact key queries on very large tables. Rather than build a % separate index structure, a key value is passed to a \emph{hash % function}. This function returns the physical location of a hash bucket, % which contains a pointer to the associated physical record (check). % Hashing schemes typically require only a single disk access to retrieve % a specific record, but perform poorly for queries that require the % retrieval of multiple records. \item[Clustering] minimises disk access by ensuring that related records (such as an order header and its associated order lines) are physically adjacent on disk. This usually means that related records will be stored in the same database block, and can thus be retrieved with a single disk access. % Clustering is a disk access minimisation technique that can be applied % when two different record types are logically related, and thus commonly % retrieved together; for example, an order header and its order lines. % Without any further optimisation, such an operation could at worst % require one disk access for the order header and one disk access for % each of its order lines. % % To improve this situation, we \emph{cluster} the two record types, so % that related physical records are physically adjacent to each other % \cite{Chan-N-2003-clustering}. This usually means that all the records % will be stored in the same database block, and can thus all be retrieved % with a single disk access. Clustering can, however, be expensive to % maintain in a high update environment. \item[Partitioning] provides parallel access paths to data by physically splitting a table into disjoint parts and placing them on separate disks. This is particularly advantageous when multiple users wish to access different subsets of a set of records, because it provides a separate physical access path to each of the partitions. % Partitioning can also reduce the number of disk accesses % required, because there are fewer records to scan in each partition % than if the table were not partitioned. % In a typical untuned database, all data will be stored on the same disk. % If the database is heavily accessed, then contention for the single I/O % channel to this disk becomes a major bottleneck. Partitioning reduces % this contention by splitting the database into disjoint partitions, each % of which is assigned to a different disk. This approach is particularly % advantageous in situations where multiple users wish to access different % subsets of a set of records, because it provides a disjoint physical % access paths to each of the partitions. This reduces I/O channel % contention and thus improves performance. Partitioning is thus primarily % an access parallelism technique. % % Partitioning can also provide some disk access minimisation benefits, % because the amount of data to be searched in each partition is smaller % than if the database were not partitioned. \item[Replication] provides parallel access paths to data by making multiple copies of the same records and placing them on separate disks. This is particularly advantageous when multiple users need to access the same sets of records, but is more complex to manage due to the need to keep replicas synchronised. % Replication is an access parallelism technique in which multiple copies % of the same records are placed on different disks, thus providing % multiple physical access paths to the same data. \end{description} These techniques are normally applied to different parts of a database to achieve different effects. In order to choose an appropriate physical tuning technique, the DBA must consider various factors that may benefit only some users of the database, or may improve the performance of the database as a whole. While most of the techniques can be combined to varying degrees, simply applying all techniques is usually not optimal, because each technique excells under different conditions. That is, what are optimal conditions for one technique may be the exact opposite for another, so the DBA needs to be able to model all the available information in order to develop an appropriate physical design. \section{Prior Physical Modelling Techniques} \label{sec-previous} To achieve an effective physical design requires a large amount of information, particularly with regard to the predicted or actual volume and usage of data within the database \cite{BeDa-P-2003}. Incorporating this information into a graphical model can provide a more concise and clearer overview of the physical aspects of a database system. In this section we briefly discuss two previous efforts at modelling such information in a graphical manner. \subsection{Agile Modeling (Ambler)} Ambler proposed a physical modelling notation based on the Unified Modeling Language (UML), as part of a larger effort to produce a ``traditional'' style data modelling profile for the UML \cite{Ambl-SW-2003-ADT,Ambl-SW-2004-ObjPrimer3}. Ambler and others have argued the need for such a profile for some time \cite{Ambl-SW-1998-BOA,Naib-EJ-2001-UMLDD}. Ambler's notation focuses on the physical modelling of relational databases. The notation uses class boxes without stereotypes to represent physical tables, while indexes are represented by class boxes with the stereotype \verb\|<<index>>\|, as illustrated in Fig.~\ref{fig-Ambler}. There appear to be no stereotypes for other physical tuning techniques such as partitioning, although these could be easily incorporated. \begin{figure} \includegraphics[width=\columnwidth,keepaspectratio]{Ambler} \caption{Ambler's physical modelling notation (adapted from \cite{Ambl-SW-2003-ADT})} \label{fig-Ambler} \end{figure} Ambler's approach suffers from two serious disadvantages. First, the notation is very limited in the types of symbol used. All physical level constructs are represented by class boxes, which in a complex diagram could make distinguishing them difficult. This limitation probably arises from the constraints on developing a new notation within the existing UML framework. Second, his approach appears to consistently confuse the logical and physical levels of abstraction: the same notations are used to represent not only physical but also logical and conceptual elements \cite{Ambl-SW-2003-ADT}. This confusion is illustrated by the inclusion of a view (a non-physical construct) in Fig.~\ref{fig-Ambler}. In summary, while Ambler's notation does graphically model the physical level of a database, the similarity of the graphical symbols and the evident confusion between the physical and logical levels diminish its usefulness. % . He states that since Unified % Modelling Language (UML) does not cover data (i.e., ER) modelling yet, % he presents the solution in this paper. Ambler has argued for some time % for the presence of data modelling in UML \cite{Ambl-SW-1998-BOA}, and % has suggested various ways that it should be done. It is enlightening to % know that Ambler is not alone in his quest for adopting an industry % standard in data modelling. Other methodologies like % \cite{Naib-EJ-2001-UMLDD} have recognized the need as well. This model % type is built on the practice of UML 2.0 of separating core methodology. % Ambler admits that the methodology that he has presented is not perfect % and it focuses on the physical modelling of a relational database. In % this model he also tries to stress style issues that according to him % are not appropriate for a proper UML profile \cite{Ambl-SW-2003-ADT}. % This model suggests that a class box without a stereotype in a physical % database design is a table. It also represents views that have % dependencies on the table structures. Tables, entities and views are all % modelled using class boxes. The class boxes that appear on the logical % and conceptual model are entities so the stereotype is optional. % Similarly, it is assumed that any class box without a stereotype on a % physical data model is a table. Ambler's methodology seems to be limited % in terms of annotations. All representations whether tables or indices % are modelled using class boxes. This representation can sometimes be % confusing and exact identification of tables and indices in the system % has to be known by the database designer. In this model, relationships % are modelled using associations that are derived from the logical data % model. He further discusses his methodology for modelling attributes and % columns, keys, constraints and triggers, stored procedures and sections. % Ambler states that requirements for something should be identified % before it is built. He states the requirements of each model, e.g., % requirements that are needed to model entities and tables, requirements % that are needed to model relationships, etc. % % An example of Ambler's notation is shown in Fig.~\ref{fig-Ambler}. % Even though a lot of detail is covered in his suggestion, Ambler's % methodology somehow seems relatively weak. It is much too general in % annotations and has no specific description. The methodology seems to % consistently confuse the logical and physical design. For example: both % are modelled using class boxes but are later explained as representing % different objects. However, this model will definitely be useful as a % stepping-stone to work towards an official UML data modelling profile. \subsection{Physical Design Using an Entity Model (Beynon-Davies)} Beynon-Davies proposed a method for analysing and modelling the physical usage patterns of a database \cite{BeDa-P-1992-PDD}. In his method, various aspects of the physical performance of a database are measured, such as the size and expected growth rates of tables (volume analysis), the volatility of tables, and the frequency of transactions (usage analysis). The data obtained from these analyses are then used to annotate a logical level entity-relationship diagram (ERD) of the database, producing what is known as a \emph{composite usage map} (see Fig.~\ref{fig-Beynon-Davies} on page~\ref{fig-Beynon-Davies} for an example). Beynon-Davies' method provides a very good mechanism for representing the usage statistics of database in a coherent manner, but is somewhat complex to execute without some form of automation. Our experience with teaching this method at undergraduate level shows that even with a relatively small database, the designer can quickly become overwhelmed by the sheer volume of usage data involved. In addition, Beynon-Davies' method does not produce any conclusions as to which physical tuning methods should be implemented---rather it provides much of the information required to enable these decisions to be made. Beynon-Davies' method is thus more a notation for summarising the physical usage patterns of a database, rather than a notation for physical modelling per se. % The closest model that demonstrates the link between conceptual, logical % and physical design work is by Beynon-Davies \cite{BeDa-P-1992-PDD}. He % suggests a method that can be used for the physical design process. The % paper defines physical modelling as ``the transformation of the logical % model into a definition of the physical model suitable for a specific % software/hardware configuration'' \cite{BeDa-P-1992-PDD}. % % According to Beynon-Davies one of the first steps that must be taken to % move from logical to physical database design is to establish estimates % of the average and maximum number of instances per entity (volume % analysis). Volatility analysis is represented in the same way. Similar % to volume analysis, volatility analysis cannot be used as a measure if a % table is continually growing. It is most effective if the size of the % table is static. Figure 9 summarizes Beynon-Davies's final modelling % method; he does not model all the individual annotations but generalizes % the entity relationship diagrams into a general model. % % It is understandable that the reason behind this generalization is to % minimize complexity and since individual annotations are developed in % the beginning, references can be made to them if needed. This might be % effective for small systems that have a limited number of tables. % However, for medium to large-scale projects, Beynon-Davies suggests that % a systematic analysis of volatility and usage should be done. This % analysis would constitute a map of the database application that would % be maintained by the DBA. This meets the objective of providing an % overview of all the performance tuning techniques and data in place. \section{A New Physical Notation} \label{sec-notation} Both of the notations discussed in the previous sections are limited in their ability to graphically model the physical level of a database. Ambler's notation lacks clarity and is thus potentially confusing, while Beynon-Davies' notation only summarises the physical usage patterns of a database rather than providing an actual physical level database model. We have therefore adopted aspects from both approaches to devise a graphical notation that enables database designers to graphically model the common physical database tuning techniques discussed in Sect.~\ref{sec-techniques}. The notations that we have adopted for this notation are shown in Fig.~\ref{fig-notation}. Some of these are adapted from other notations, while some we have created ourselves. The symbols have been chosen so as to be as intuitive as possible, while not being so complex as to produce a cluttered and confusing diagram. Physical models may be developed using this notation either with or without a prior Beynon-Davies style analysis. \begin{figure} \centering \subfigure[Table]{\label{fig-notation-table}\includegraphics[scale=0.9]{notation-table}} \hfill \subfigure[Indexes]{\label{fig-notation-index}\includegraphics[scale=0.9]{notation-index}} \hfill \subfigure[Hashing]{\label{fig-notation-hash}\includegraphics[scale=0.9]{notation-hash}} \\ \hfill \subfigure[Clustering]{\label{fig-notation-cluster}\includegraphics[scale=0.9]{notation-cluster}} \hfill \subfigure[Partitoning]{\label{fig-notation-partition}\includegraphics[scale=0.9]{notation-partition}} \hfill \\ \subfigure[Replication]{\label{fig-notation-replica}\includegraphics[scale=0.9]{notation-replica}} \caption{Notations for physical tuning techniques} \label{fig-notation} \end{figure} A physical table is represented by a simple box, as shown in Fig.~\ref{fig-notation-table}. This is similar to most logical and conceptual level ERD notations. Indexes are represented by a small tree-like symbol within a table, as shown in Fig.~\ref{fig-notation-index}. The index key is listed next to this symbol. Composite keys are indicated by a grouping symbol. Hashing is represented in a similar way, but uses an ``H'' symbol instead of a tree symbol (see Fig.~\ref{fig-notation-hash}). Clustering is represented by nesting one table inside another, as shown in Fig.~\ref{fig-notation-cluster} (adapted from \cite{BeDa-P-1992-PDD}). This notation is intuitive, and clearly indicates the field(s) on which the records are clustered. Partitioning is represented by splitting a table into either vertical or horizontal partitions according to the style of partitioning, as shown in Fig.~\ref{fig-notation-partition} (adapted from \cite{Silb-A-2002-4E}). Once again, the notation is intuitive, and allows the partition definitions to be easily indicated. Replication is indicated by including multiple copies of the same table, with a diagonal bar across the corner of each replica, as shown in Fig.~\ref{fig-notation-replica}. This is adapted from a similar notation used in data flow diagrams \cite{Gane-C-1979}. % The graphical notations use in this model is not complex and cluttered. % This is to enable a database designer to simplify the physical design in % a notation that will be easy to understand but comprehensive. Some of % the graphical notations use in this model was adapted from other models % and a few were modified by the author to suit the model. % % The table below illustrates some of the graphical representations that % were available to choose from. Consider the entity-relationship diagram shown in Fig.~\ref{fig-ERD}, which depicts a database for a consumer electronics manufacturer. A corresponding Beynon-Davies' composite usage map based on the fourteen most significant transactions is shown in Fig.~\ref{fig-Beynon-Davies}. The arrows represent physical access paths, while the number attached to each access path indicates the number of disk accesses per hour along that path. The diagram clearly highlights some potential performance problem areas in the database, for example: \begin{itemize} \item There are many disk accesses on the access paths between the Sale\_head/Sale\_line and the Order\_head/Order\_line tables. Since these are tables that will normally be accessed together, both could perhaps be candidates for clustering (depending on the mix of update versus read operations). \item The appear to be multiple transactions acessing the Staff table. This could imply a need for partitioning. \item There is an extremely high access rate on the Customer table. Further examination, however, reveals that this rate only occurs for a short period once per month, and that the transaction in question only requires read access. Replication of the Customer table could therefore be a suitable solution. \end{itemize} \begin{figure} \includegraphics[width=\columnwidth,keepaspectratio]{ERD} \caption{ERD of the example database} \label{fig-ERD} \end{figure} \begin{figure} \includegraphics[width=\columnwidth,keepaspectratio]{Beynon-Davies} \caption{Beynon-Davies composite usage map for the example database} \label{fig-Beynon-Davies} \end{figure} The suggestions above can be represented as a physical model using our proposed modelling notation, as shown in Fig.~\ref{fig-physical-model}. Note that we have placed indexes on all primary keys as a matter of course. \begin{figure} \caption{Physical database model for the example database} \label{fig-physical-model} \end{figure} \section{Future Research} \label{sec-future} - symbols for different types of index (reverse-key, index-organised tables, R-trees, bitmap indexes). - physical placement information, i.e., what devices partitions go on, etc. - evaluation of the notation with undergraduate students \& comparison with Beynon-Davies (preliminary results by time of publication). \section{Conclusion} \label{sec-conclusion} \bibliographystyle{splncs} \bibliography{ER2005} \end{document} \documentclass{llncs} \title{A Graphical Notation for Modelling Physical Database Structures} \author{Antonia Pillay \and Nigel Stanger} \institute{Department of Information Science, University of Otago, Dunedin, New Zealand \email{nstanger@infoscience.otago.ac.nz}} \begin{document} \maketitle \begin{abstract} In this paper we describe a graphical notation for modelling physical database structures. Such a notation will provide database administrators with a means to model the physical structures of new and existing databases, and thus enable them to make more proactive and informed tuning decisions, compared to existing database monitoring tools. \end{abstract} \section{Introduction} The design and implementation of a database system, as with most information systems, typically goes through several phases \cite{BeDa-P-2003}, including requirements analysis, conceptual modelling, logical modelling, physical modelling and implementation. Conceptual, logical and physical modelling are of particular interest here, as each represents a step in a progression from a higher to a lower level of abstraction \cite{Tsic-D-1978}. Conceptual models are typically very high-level and abstract, using techniques such as entity-relationship modelling, and are derived from the requirements. Logical level models represent the structure of a database in a form that is closer to the final physical representation, yet still sufficiently abstract to isolate application from the physical representation details (ref). Logical level models are typically derived from the corresponding conceptual models by some transformation process (ref), and use formalisms such as the relational model. Physical level models represent the structure of a database in terms of the physical storage structures provided by a specific database management system (DBMS) such as Oracle or DB2. Once again, the physical model for a database can be derived from the logical level model by some form of transformation \cite{Bato-DS-1985,Conn-TM-2002}. Because of it's low level of abstraction, modelling the physical level of a database is typically one of the last phases of implementation, and tends to be very product-specific. Consequently, physical level structures are not typically modelled using graphical notations, unlike models at the higher levels of abstraction. (refs?) Physical modelling is, however, equally as important as, if not \emph{more} important than the higher levels of modelling, because it is the physical level that has the greatest impact on the performance of a database \cite{BeDa-P-2003}. It is therefore somewhat surprising that there have been relatively few attempts to devise a graphical physical modelling notation that can be used to represent the physical structures of a database. Use of such a notation provides several advantages \cite{BeDa-P-1992-PDD,Conn-TM-2002,Will-J-1992}: \begin{itemize} \item it can reduce complexity and thus aid communication and improve understandability \cite{Tuft-ER-1997}; \item it can provide a more complete and integrated display of tables and performance tuning techniques in a database; \item database developers can be more confident about the design decisions that they make for the performance of the database; \item database performance problems are more easily visaualised using a graphical notation; and \item a specific methodology is developed and used, thus allowing the developer to resolve physical performance issues in a more systematic manner. \end{itemize} These benefits are embodied in database performance monitoring tools such as Quest's SpotLight (ref), which provides a higher-level visualisation of a database's structures in order to easily identify and highlight performance problems. Such tools, however, are primarily intended as \emph{monitoring} tools rather than as \emph{design} tools. They may therefore unintentionally encourage database administrators (DBAs) into a \emph{reactive} mode of continually ``tweaking'' the database to resolve performance issues, rather than a \emph{proactive} mode of anticipating problems, by means of prior analysis and modelling. It may also be difficult for a DBA using such tools to gain a clear and comprehensive overview of all the tuning techniques that are in use within a particular database \cite{Core-MJ-1997-OracleDW}. In this paper we propose a graphical notation for modelling the physical structures of a database system, which builds upon a methodology for physical database design proposed by Beynon-Davies \cite{BeDa-P-1992-PDD}. In Section~\ref{sec-techniques}, we provide a brief overview of current commonly used physical tuning techniques. We then proceed in Section~\ref{sec-previous} to discuss prior approaches to physical modelling and design. Section~\ref{sec-notation} introduces our proposed notation, and Section~\ref{sec-future} discusses possible future work. The paper concludes in Setion~\ref{sec-conclusion}. \section{Physical tuning techniques} \label{sec-techniques} DBMSs tend to be I/O bound, so the main bottleneck in any database system is usually the speed of offline storage such as disk drives. Retrieving data from a hard disk is theoretically about six orders of magnitude slower than retrieving the same data from RAM\footnote{On the order of milliseconds (\(10^{-3}\)) for disk versus nanoseconds (\(10^{-9}\)) for RAM.}. The ultimate aim of any physical tuning strategy is thus to minimise the impact of slow storage, either by directly reducing the number of physical disk accesses required, or by parallelising access to the disk in order to reduce contention for a limited resource. These considerations have led to the development of five general physical tuning techniques, which have been implemented to various degrees by most mainstream DBMS products: % following sections way too long --- shorten considerably \begin{description} \item[Indexes] reduce the number of physical disk accesses required to retrieve a specific record, most typically by building a B+-tree \cite{Knut-DE-1997-Art} based on some key value. Without any indexes, a DBMS often has little choice but to perform a sequential scan in order to locate a specific record. % A common database operation is to request a specific data record % identified by a some key value. When such a request occurs, the DBMS % must locate this record on disk (assuming that it is not already cached % elsewhere). If we assume that the records are randomly ordered with % respect to the chosen key value, then the DBMS has no option but to % perform a sequential scan of all the records, which will require on % average\(n/2b\) disk accesses, where \(n\) is the number of records and % \(b\) is the number of records per database block (the worst case is % \((n - 1)(b)\)). Sorting the records on the key value will obviously % help for searches based on that key value, but will not help for % searches based on a different key value. % % One solution is to build a separate index structure that associates key % values with their corresponding physical record. Because indexes are % stored separately, we can provide multiple indexes on different key % values for the same set of records. In addition, by choosing an % appropriate data structure for the index, we can improve the efficiency % of searching and thus reduce the number of physical disk accesses % required \cite{Roti-S-1996}. Most modern DBMSs use some variant of the % \emph{B+-tree} structure \cite{Knut-DE-1997-Art}. This structure has % average and worst case performance of (formula) and (formula), % respectively. % % Indexes are a ``pure'' disk access minimisation technique, that is, they % reduce the number of physical disk accesses required, but do not provide % any form of paralellism. B-tree indexes perform well for a wide range of % typical database queries (ref), but can suffer in high update % environments due to the need to also update the index. \item[Hashing] is a method of quickly locating specific records by passing a key value through a \emph{hash function}. This function returns the physical location of a hash bucket, which contains a pointer to the associated physical record (check). Hashing schemes typically require only a single disk access to retrieve a specific record. % Hashing is another pure disk access minimisation technique that performs % well for exact key queries on very large tables. Rather than build a % separate index structure, a key value is passed to a \emph{hash % function}. This function returns the physical location of a hash bucket, % which contains a pointer to the associated physical record (check). % Hashing schemes typically require only a single disk access to retrieve % a specific record, but perform poorly for queries that require the % retrieval of multiple records. \item[Clustering] minimises disk access by ensuring that related records (such as an order header and its assocaited order lines) are physically adjacent to each other on disk \cite{Chan-N-2003-clustering}. This usually means that related records will be stored in the same database block, and can thus all be retrieved with a single disk access. % Clustering is a disk access minimisation technique that can be applied % when two different record types are logically related, and thus commonly % retrieved together; for example, an order header and its order lines. % Without any further optimisation, such an operation could at worst % require one disk access for the order header and one disk access for % each of its order lines. % % To improve this situation, we \emph{cluster} the two record types, so % that related physical records are physically adjacent to each other % \cite{Chan-N-2003-clustering}. This usually means that all the records % will be stored in the same database block, and can thus all be retrieved % with a single disk access. Clustering can, however, be expensive to % maintain in a high update environment. \item[Partitioning] provides parallel access paths to data by physically splitting a table into disjoint parts and ideally placing them on separate disks. This is particularly advantageous in situations where multiple users wish to access different subsets of a set of records, because it provides a separate physical access path to each of the partitions. Partitioning can also reduce the number of disk accesses required, because the amount of data to be searched in each partition is smaller than if the table were not partitioned. % In a typical untuned database, all data will be stored on the same disk. % If the database is heavily accessed, then contention for the single I/O % channel to this disk becomes a major bottleneck. Partitioning reduces % this contention by splitting the database into disjoint partitions, each % of which is assigned to a different disk. This approach is particularly % advantageous in situations where multiple users wish to access different % subsets of a set of records, because it provides a disjoint physical % access paths to each of the partitions. This reduces I/O channel % contention and thus improves performance. Partitioning is thus primarily % an access parallelism technique. % % Partitioning can also provide some disk access minimisation benefits, % because the amount of data to be searched in each partition is smaller % than if the database were not partitioned. \item[Replication] provides parallel access to data by making multiple copies of the same records and ideally placing them on separate disks. This is particularly advantageous if multiple users need to access the same sets of records, but is more complex to manage due to the need to keep replicas synchronised. % Replication is an access parallelism technique in which multiple copies % of the same records are placed on different disks, thus providing % multiple physical access paths to the same data. \end{description} % \subsection{Discussion} The physical tuning techniques described above are normally used in different parts of the database to achieve different effects. To choose an appropriate physical tuning technique, the DBA must consider various factors that will either benefit the users of the database or improve the performance of the database as a whole. While most of the techniques can be combined to varying degrees, simply applying all techniques is usually not an optimal solution, because each technique has different conditions in which it excels. What are optimal conditions for one technique may be the exact opposite for another, so the DBA needs to be able to model all the available information in order to develop an appropriate physical design. \section{Prior physical modelling techniques} \label{sec-previous} To achieve an effective physical design requires a large amount of information, particularly with regard to the (predicted or actual) volume and usage of data within the database \cite{BeDa-P-2003}. Incorporating this information into a graphical model can provides a more concise and clearer overview of the physical aspects of a database system. In this section we discuss three previous efforts at modelling such information in a graphical manner. \subsection{Agile modeling (Ambler)} The notation suggested by Ambler \cite{Ambl-SW-2003-ADT,Ambl-SW-2004-ObjPrimer3} is a type of model that can be developed in UML using class boxes. He states that since Unified Modelling Language (UML) does not cover data (i.e., ER) modelling yet, he presents the solution in this paper. Ambler has argued for some time for the presence of data modelling in UML \cite{Ambl-SW-1998-BOA}, and has suggested various ways that it should be done. It is enlightening to know that Ambler is not alone in his quest for adopting an industry standard in data modelling. Other methodologies like \cite{Naib-EJ-2001-UMLDD} have recognized the need as well. This model type is built on the practice of UML 2.0 of separating core methodology. Ambler admits that the methodology that he has presented is not perfect and it focuses on the physical modelling of a relational database. In this model he also tries to stress style issues that according to him are not appropriate for a proper UML profile \cite{Ambl-SW-2003-ADT}. This model suggests that a class box without a stereotype in a physical database design is a table. It also represents views that have dependencies on the table structures. Tables, entities and views are all modelled using class boxes. The class boxes that appear on the logical and conceptual model are entities so the stereotype is optional. Similarly, it is assumed that any class box without a stereotype on a physical data model is a table. Ambler's methodology seems to be limited in terms of annotations. All representations whether tables or indices are modelled using class boxes. This representation can sometimes be confusing and exact identification of tables and indices in the system has to be known by the database designer. In this model, relationships are modelled using associations that are derived from the logical data model. He further discusses his methodology for modelling attributes and columns, keys, constraints and triggers, stored procedures and sections. Ambler states that requirements for something should be identified before it is built. He states the requirements of each model, e.g., requirements that are needed to model entities and tables, requirements that are needed to model relationships, etc. An example of Ambler's notation is shown in Figure~\ref{fig-Ambler}. \begin{figure} \caption{Ambler's physical model notation (adapted from \cite{Ambl-SW-2003-ADT})} \label{fig-Ambler} \end{figure} Even though a lot of detail is covered in his suggestion, Ambler's methodology somehow seems relatively weak. It is much too general in annotations and has no specific description. The methodology seems to consistently confuse the logical and physical design. For example: both are modelled using class boxes but are later explained as representing different objects. However, this model will definitely be useful as a stepping-stone to work towards an official UML data modelling profile. \subsection{Physical design using an entity model (Beynon-Davies)} The closest model that demonstrates the link between conceptual, logical and physical design work is by Beynon-Davies \cite{BeDa-P-1992-PDD}. He suggests a method that can be used for the physical design process. The paper defines physical modelling as ``the transformation of the logical model into a definition of the physical model suitable for a specific software/hardware configuration'' \cite{BeDa-P-1992-PDD}. According to Beynon-Davies one of the first steps that must be taken to move from logical to physical database design is to establish estimates of the average and maximum number of instances per entity (volume analysis). Volatility analysis is represented in the same way. Similar to volume analysis, volatility analysis cannot be used as a measure if a table is continually growing. It is most effective if the size of the table is static. Figure 9 summarizes Beynon-Davies's final modelling method; he does not model all the individual annotations but generalizes the entity relationship diagrams into a general model. It is understandable that the reason behind this generalization is to minimize complexity and since individual annotations are developed in the beginning, references can be made to them if needed. This might be effective for small systems that have a limited number of tables. However, for medium to large-scale projects, Beynon-Davies suggests that a systematic analysis of volatility and usage should be done. This analysis would constitute a map of the database application that would be maintained by the DBA. This meets the objective of providing an overview of all the performance tuning techniques and data in place. \section{A new physical notation} \label{sec-notation} In this section we discuss a new notation for graphically representing physical database models. While Ambler's notation is in many ways closer to a physical modelling notation, the evident confusion between the physical and logical levels diminishes its usefulness. Beynon-Davies' notation, on the other hand, simply adds information relevant to physical tuning to a standard entity-relationship diagram. Our experience in teaching this technique at undergraduate level is that the designer can quickly become overwhelemed by a ``mountain of numbers''. In addition, Beynon-Davies' method does not provide any conclusions as to which physical tuning methods should be implemented---rather it provides the information required in order to draw these conclusions. Beynon-Davies' method is thus more of a notation for summarising the physical usage of a database, rather than a notation for representing physical database structures. We have therefore taken Beynon-Davies' work one step further and developed a graphical notation for representing the physical database tuning techniques discussed in Section~\ref{sec-techniques}. The graphical notations use in this model is not complex and cluttered. This is to enable a database designer to simplify the physical design in a notation that will be easy to understand but comprehensive. Some of the graphical notations use in this model was adapted from other models and a few were modified by the author to suit the model. The table below illustrates some of the graphical representations that were available to choose from. Clustering is represented by nesting one entity inside another, as shown in Figure~\ref{fig-notation} (adapted from \cite{BeDa-P-1992-PDD}). This notation is intuitive, and clearly indicates the field(s) on which the records are clustered. Partitioning is represented by splitting an entity into either vertical or horizontal partitions, as shown in Figure~\ref{fig-notation} (adapted from \cite{Silb-A-2002-4E}). Once again, the notation is intuitive, and allows the partition definitions to be easily listed. Replication is indicated by including multiple copies of the same entity, with a diagonal bar across the corner of each replica (adapted from a notation used in data flow diagrams \cite{Gane-C-1979}). Indexes are represented by a small tree-like symbol within an entity. The index key is listed next to this symbol. Hashing is represented in a similar way, but using an ``H'' symbol instead of a tree symbol. \begin{figure} \caption{Graphical representations for physical structures} \label{fig-notation} \end{figure} \subsection{Example of use} Consider the entity-relationship diagram shown in Figure~\ref{fig-ERD}, which depicts a database system for a consumer electronics manufacturer. A corresponding Beynon-Davies' annotated model is shown in Figure~\ref{fig-Beynon-Davies}. Analysis of this figure enables us to draw certain conclusions about the physical characteristics of this database: \begin{itemize} \item conclusions\ldots (see 321 assignment material) \end{itemize} \begin{figure} \caption{ERD of the example database} \label{fig-ERD} \end{figure} \begin{figure} \caption{Beynon-Davies annotated model for the example database} \label{fig-Beynon-Davies} \end{figure} Figure~\ref{fig-physical-model} shows a physical model of this database system using our proposed notation. \begin{figure} \caption{Physical database model for the example database} \label{fig-physical-model} \end{figure} \section{Future research} \label{sec-future} - symbols for different types of index (reverse-key, index-organised tables, R-trees, bitmap indexes). - evaluation of the notation with undergraduate students \& comparison with Beynon-Davies (preliminary results by time of publication). \section{Conclusion} \label{sec-conclusion} \bibliographystyle{splncs} \bibliography{ER2005} \end{document}

Ignore Space Show notes View

Physical_modelling.tex

\documentclass{llncs}

\usepackage{subfigure}
\usepackage{graphicx}

\title{A Graphical Notation for \\ Physical Database Modelling}
\author{Antonia Pillay\inst{1} \and Nigel Stanger\inst{2}}
\institute{???? Malaysia \and Department of Information Science, University of Otago, Dunedin, New Zealand \email{nstanger@infoscience.otago.ac.nz}}

\begin{document}

\maketitle

\begin{abstract}
In this paper we describe a graphical notation for physical database
modelling. This notation provides database administrators (DBAs) with a
means to model the physical structure of new and existing databases,
thus enabling them to make more proactive and informed tuning decisions,
compared to existing database monitoring tools.
\end{abstract}

\section{Introduction}

As with most information systems, the design and implementation of a
database goes through several phases, including conceptual, logical and
physical modelling \cite{BeDa-P-2003}. These three phases are of
particular interest, as they embody the progression from higher to lower
levels of abstraction \cite{Tsic-D-1978}. Conceptual models are
typically highly abstract, using techniques such as entity-relationship
modelling. Logical models represent the database structure in a form
that is closer to the physical representation, yet still sufficiently
abstract to isolate applications from the physical representation
\cite{Codd-EF-1970}, and are expressed using formalisms such as the
relational model. A logical model for a database can be derived by
transforming the corresponding conceptual model.

Physical models represent the database structure in terms of the
physical storage implementation of a specific database management system
(DBMS) such as Oracle or DB2. A physical model for a database can be
derived by transforming the corresponding logical model
\cite{Bato-DS-1985,Conn-TM-2002}. Because of their low abstraction
level, physical level database models have tended to not be expressed
using graphical notations, unlike models at higher levels of
abstraction.

Physical level modelling, however, is equally as important as, if not
\emph{more} important than the higher levels, because it is the physical
level that determines the performance of a database \cite{BeDa-P-2003}.
It is somewhat surprising that there have been relatively few attempts
to devise a graphical physical modelling notation, because such a
notation can provide several advantages
\cite{Conn-TM-2002,BeDa-P-1992-PDD,Will-J-1992}:
\begin{itemize}

\item it can reduce complexity and thus improve understandability
	\cite{Tuft-ER-1997};

\item it can provide a more complete and integrated display of
	performance tuning techniques in a database;

\item database developers can be more confident about the design
	decisions that they make for the performance of the database;

\item database performance problems are more easily visualised
	using a graphical notation; and

\item a specific methodology is developed and used, thus enabling
	developers to resolve physical performance issues more
	systematically.

\end{itemize}

These benefits are embodied in modern database performance monitoring
tools, which provide higher-level visualisations of a database's
internals in order to easily identify and highlight performance
problems. Such tools, however, are primarily \emph{monitoring} tools
rather than \emph{design} tools. They may therefore unintentionally
encourage DBAs into a \emph{reactive} mode of continually ``tweaking''
the database to resolve performance issues, rather than a
\emph{proactive} mode of anticipating and designing for expected usage.
It may also be difficult for a DBA using such tools to gain a clear and
comprehensive overview of all the tuning techniques that are in use
within a particular database \cite{Core-MJ-1997-OracleDW}.

In this paper we propose a graphical notation for physical database
modelling. In Sect.~\ref{sec-techniques}, we provide a brief overview of
commonly used physical tuning techniques. We then discuss in
Sect.~\ref{sec-previous} two earlier approaches upon which our work is
partially based. Sect.~\ref{sec-notation} introduces our proposed
notation, and Sect.~\ref{sec-future} discusses possible future work. The
paper concludes in Sect.~\ref{sec-conclusion}.

\section{Physical Tuning Techniques}
\label{sec-techniques}

Database management is generally an I/O bound task, so the main
performance bottleneck in most databases will be the speed of offline
storage such as disk drives. Retrieving data from a hard disk is
theoretically about six orders of magnitude slower than retrieving data
from RAM\footnote{On the order of milliseconds (\(10^{-3}\)) for disk
versus nanoseconds (\(10^{-9}\)) for RAM.}. The aim of any physical
tuning strategy must therefore be to minimise the impact of slow
storage, either by directly reducing the number of physical disk
accesses required, or by parallelising access to disk in order to reduce
contention.

These considerations have led to the development of five general
physical tuning techniques, which are implemented to various degrees by
most modern mainstream DBMS products:

\begin{description}

\item[Indexes] reduce the number of physical disk accesses required
	to retrieve a specific record, most typically by building a B+-tree
	\cite{Knut-DE-1997-Art} based on some key value. Without any
	indexes, a DBMS often has little choice but to perform a sequential
	scan in order to locate a specific record.

% A common database operation is to request a specific data record
% identified by a some key value. When such a request occurs, the DBMS
% must locate this record on disk (assuming that it is not already cached
% elsewhere). If we assume that the records are randomly ordered with
% respect to the chosen key value, then the DBMS has no option but to
% perform a sequential scan of all the records, which will require on
% average\(n/2b\) disk accesses, where \(n\) is the number of records and
% \(b\) is the number of records per database block (the worst case is
% \((n - 1)(b)\)). Sorting the records on the key value will obviously
% help for searches based on that key value, but will not help for
% searches based on a different key value.
% 
% One solution is to build a separate index structure that associates key
% values with their corresponding physical record. Because indexes are
% stored separately, we can provide multiple indexes on different key
% values for the same set of records. In addition, by choosing an
% appropriate data structure for the index, we can improve the efficiency
% of searching and thus reduce the number of physical disk accesses
% required \cite{Roti-S-1996}. Most modern DBMSs use some variant of the
% \emph{B+-tree} structure \cite{Knut-DE-1997-Art}. This structure has
% average and worst case performance of (formula) and (formula),
% respectively.
% 
% Indexes are a ``pure'' disk access minimisation technique, that is, they
% reduce the number of physical disk accesses required, but do not provide
% any form of paralellism. B-tree indexes perform well for a wide range of
% typical database queries (ref), but can suffer in high update
% environments due to the need to also update the index.

\item[Hashing] is a method of quickly locating specific records by
	passing a key value to a \emph{hash function}. This function returns
	the physical location of a hash bucket, which contains a pointer to
	the associated physical record (check). Hashing schemes typically
	require only a single disk access to retrieve a specific record.

% Hashing is another pure disk access minimisation technique that performs
% well for exact key queries on very large tables. Rather than build a
% separate index structure, a key value is passed to a \emph{hash
% function}. This function returns the physical location of a hash bucket,
% which contains a pointer to the associated physical record (check).
% Hashing schemes typically require only a single disk access to retrieve
% a specific record, but perform poorly for queries that require the
% retrieval of multiple records.

\item[Clustering] minimises disk access by ensuring that related
	records (such as an order header and its associated order lines) are
	physically adjacent on disk. This usually means that related records
	will be stored in the same database block, and can thus be retrieved
	with a single disk access.

% Clustering is a disk access minimisation technique that can be applied
% when two different record types are logically related, and thus commonly
% retrieved together; for example, an order header and its order lines.
% Without any further optimisation, such an operation could at worst
% require one disk access for the order header and one disk access for
% each of its order lines.
% 
% To improve this situation, we \emph{cluster} the two record types, so
% that related physical records are physically adjacent to each other
% \cite{Chan-N-2003-clustering}. This usually means that all the records
% will be stored in the same database block, and can thus all be retrieved
% with a single disk access. Clustering can, however, be expensive to
% maintain in a high update environment.

\item[Partitioning] provides parallel access paths to data by
	physically splitting a table into disjoint parts and placing them on
	separate disks. This is particularly advantageous when multiple
	users wish to access different subsets of a set of records, because
	it provides a separate physical access path to each of the
	partitions.
% 	Partitioning can also reduce the number of disk accesses
% 	required, because there are fewer records to scan in each partition
% 	than if the table were not partitioned.

% In a typical untuned database, all data will be stored on the same disk.
% If the database is heavily accessed, then contention for the single I/O
% channel to this disk becomes a major bottleneck. Partitioning reduces
% this contention by splitting the database into disjoint partitions, each
% of which is assigned to a different disk. This approach is particularly
% advantageous in situations where multiple users wish to access different
% subsets of a set of records, because it provides a disjoint physical
% access paths to each of the partitions. This reduces I/O channel
% contention and thus improves performance. Partitioning is thus primarily
% an access parallelism technique.
% 
% Partitioning can also provide some disk access minimisation benefits,
% because the amount of data to be searched in each partition is smaller
% than if the database were not partitioned.

\item[Replication] provides parallel access paths to data by making
	multiple copies of the same records and placing them on separate
	disks. This is particularly advantageous when multiple users need to
	access the same sets of records, but is more complex to manage due
	to the need to keep replicas synchronised.

% Replication is an access parallelism technique in which multiple copies
% of the same records are placed on different disks, thus providing
% multiple physical access paths to the same data.

\end{description}

These techniques are normally applied to different parts of a database
to achieve different effects. In order to choose an appropriate physical
tuning technique, the DBA must consider various factors that may benefit
only some users of the database, or may improve the performance of the
database as a whole. While most of the techniques can be combined to
varying degrees, simply applying all techniques is usually not optimal,
because each technique excells under different conditions. That is, what
are optimal conditions for one technique may be the exact opposite for
another, so the DBA needs to be able to model all the available
information in order to develop an appropriate physical design.

\section{Prior Physical Modelling Techniques}
\label{sec-previous}

To achieve an effective physical design requires a large amount of
information, particularly with regard to the predicted or actual volume
and usage of data within the database \cite{BeDa-P-2003}. Incorporating
this information into a graphical model can provide a more concise and
clearer overview of the physical aspects of a database system. In this
section we briefly discuss two previous efforts at modelling such
information in a graphical manner.

\subsection{Agile Modeling (Ambler)}

Ambler proposed a physical modelling notation based on the Unified
Modeling Language (UML), as part of a larger effort to produce a
``traditional'' style data modelling profile for the UML
\cite{Ambl-SW-2003-ADT,Ambl-SW-2004-ObjPrimer3}. Ambler and others have
argued the need for such a profile for some time
\cite{Ambl-SW-1998-BOA,Naib-EJ-2001-UMLDD}.

Ambler's notation focuses on the physical modelling of relational
databases. The notation uses class boxes without stereotypes to
represent physical tables, while indexes are represented by class boxes
with the stereotype \verb|<<index>>|, as illustrated in
Fig.~\ref{fig-Ambler}. There appear to be no stereotypes for other
physical tuning techniques such as partitioning, although these could be
easily incorporated.

\begin{figure}
	\includegraphics[width=\columnwidth,keepaspectratio]{Ambler}
	\caption{Ambler's physical modelling notation (adapted from \cite{Ambl-SW-2003-ADT})}
	\label{fig-Ambler}
\end{figure}

Ambler's approach suffers from two serious disadvantages. First, the
notation is very limited in the types of symbol used. All physical
level constructs are represented by class boxes, which in a complex
diagram could make distinguishing them difficult. This limitation
probably arises from the constraints on developing a new notation within
the existing UML framework.

Second, his approach appears to consistently confuse the logical and
physical levels of abstraction: the same notations are used to represent
not only physical but also logical and conceptual elements
\cite{Ambl-SW-2003-ADT}. This confusion is illustrated by the inclusion
of a view (a non-physical construct) in Fig.~\ref{fig-Ambler}.

In summary, while Ambler's notation does graphically model the physical
level of a database, the similarity of the graphical symbols and the
evident confusion between the physical and logical levels diminish its
usefulness.

% . He states that since Unified
% Modelling Language (UML) does not cover data (i.e., ER) modelling yet,
% he presents the solution in this paper. Ambler has argued for some time
% for the presence of data modelling in UML \cite{Ambl-SW-1998-BOA}, and
% has suggested various ways that it should be done. It is enlightening to
% know that Ambler is not alone in his quest for adopting an industry
% standard in data modelling. Other methodologies like
% \cite{Naib-EJ-2001-UMLDD} have recognized the need as well. This model
% type is built on the practice of UML 2.0 of separating core methodology.
% Ambler admits that the methodology that he has presented is not perfect
% and it focuses on the physical modelling of a relational database. In
% this model he also tries to stress style issues that according to him
% are not appropriate for a proper UML profile \cite{Ambl-SW-2003-ADT}.

% This model suggests that a class box without a stereotype in a physical
% database design is a table. It also represents views that have
% dependencies on the table structures. Tables, entities and views are all
% modelled using class boxes. The class boxes that appear on the logical
% and conceptual model are entities so the stereotype is optional.
% Similarly, it is assumed that any class box without a stereotype on a
% physical data model is a table. Ambler's methodology seems to be limited
% in terms of annotations. All representations whether tables or indices
% are modelled using class boxes. This representation can sometimes be
% confusing and exact identification of tables and indices in the system
% has to be known by the database designer. In this model, relationships
% are modelled using associations that are derived from the logical data
% model. He further discusses his methodology for modelling attributes and
% columns, keys, constraints and triggers, stored procedures and sections.
% Ambler states that requirements for something should be identified
% before it is built. He states the requirements of each model, e.g.,
% requirements that are needed to model entities and tables, requirements
% that are needed to model relationships, etc.
% 
% An example of Ambler's notation is shown in Fig.~\ref{fig-Ambler}.

% Even though a lot of detail is covered in his suggestion, Ambler's
% methodology somehow seems relatively weak. It is much too general in
% annotations and has no specific description. The methodology seems to
% consistently confuse the logical and physical design. For example: both
% are modelled using class boxes but are later explained as representing
% different objects. However, this model will definitely be useful as a
% stepping-stone to work towards an official UML data modelling profile.

\subsection{Physical Design Using an Entity Model (Beynon-Davies)}

Beynon-Davies proposed a method for analysing and modelling the physical
usage patterns of a database \cite{BeDa-P-1992-PDD}. In his method,
various aspects of the physical performance of a database are measured,
such as the size and expected growth rates of tables (volume analysis),
the volatility of tables, and the frequency of transactions (usage
analysis). The data obtained from these analyses are then used to
annotate a logical level entity-relationship diagram (ERD) of the
database, producing what is known as a \emph{composite usage map} (see
Fig.~\ref{fig-Beynon-Davies} on page~\ref{fig-Beynon-Davies} for an
example).

Beynon-Davies' method provides a very good mechanism for representing
the usage statistics of database in a coherent manner, but is somewhat
complex to execute without some form of automation. Our experience with
teaching this method at undergraduate level shows that even with a
relatively small database, the designer can quickly become overwhelmed
by the sheer volume of usage data involved.

In addition, Beynon-Davies' method does not produce any conclusions as
to which physical tuning methods should be implemented---rather it
provides much of the information required to enable these decisions to
be made. Beynon-Davies' method is thus more a notation for summarising
the physical usage patterns of a database, rather than a notation for
physical modelling per se.

% The closest model that demonstrates the link between conceptual, logical
% and physical design work is by Beynon-Davies \cite{BeDa-P-1992-PDD}. He
% suggests a method that can be used for the physical design process. The
% paper defines physical modelling as ``the transformation of the logical
% model into a definition of the physical model suitable for a specific
% software/hardware configuration'' \cite{BeDa-P-1992-PDD}.
% 
% According to Beynon-Davies one of the first steps that must be taken to
% move from logical to physical database design is to establish estimates
% of the average and maximum number of instances per entity (volume
% analysis). Volatility analysis is represented in the same way. Similar
% to volume analysis, volatility analysis cannot be used as a measure if a
% table is continually growing. It is most effective if the size of the
% table is static. Figure 9 summarizes Beynon-Davies's final modelling
% method; he does not model all the individual annotations but generalizes
% the entity relationship diagrams into a general model.
% 
% It is understandable that the reason behind this generalization is to
% minimize complexity and since individual annotations are developed in
% the beginning, references can be made to them if needed. This might be
% effective for small systems that have a limited number of tables.
% However, for medium to large-scale projects, Beynon-Davies suggests that
% a systematic analysis of volatility and usage should be done. This
% analysis would constitute a map of the database application that would
% be maintained by the DBA. This meets the objective of providing an
% overview of all the performance tuning techniques and data in place.

\section{A New Physical Notation}
\label{sec-notation}

Both of the notations discussed in the previous sections are limited in
their ability to graphically model the physical level of a database.
Ambler's notation lacks clarity and is thus potentially confusing, while
Beynon-Davies' notation only summarises the physical usage patterns of a
database rather than providing an actual physical level database model.
We have therefore adopted aspects from both approaches to devise a
graphical notation that enables database designers to graphically model
the common physical database tuning techniques discussed in
Sect.~\ref{sec-techniques}.

The notations that we have adopted for this notation are shown in
Fig.~\ref{fig-notation}. Some of these are adapted from other notations,
while some we have created ourselves. The symbols have been chosen so as
to be as intuitive as possible, while not being so complex as to produce
a cluttered and confusing diagram. Physical models may be developed
using this notation either with or without a prior Beynon-Davies style
analysis.

\begin{figure}
	\centering
	\subfigure[Table]{\label{fig-notation-table}\includegraphics[scale=0.9]{notation-table}}
	\hfill
	\subfigure[Indexes]{\label{fig-notation-index}\includegraphics[scale=0.9]{notation-index}}
	\hfill
	\subfigure[Hashing]{\label{fig-notation-hash}\includegraphics[scale=0.9]{notation-hash}}	\\
	\hfill
	\subfigure[Clustering]{\label{fig-notation-cluster}\includegraphics[scale=0.9]{notation-cluster}}
	\hfill
	\subfigure[Partitoning]{\label{fig-notation-partition}\includegraphics[scale=0.9]{notation-partition}}
	\hfill	\\
	\subfigure[Replication]{\label{fig-notation-replica}\includegraphics[scale=0.9]{notation-replica}}
	\caption{Notations for physical tuning techniques}
	\label{fig-notation}
\end{figure}

A physical table is represented by a simple box, as shown in
Fig.~\ref{fig-notation-table}. This is similar to most logical and
conceptual level ERD notations.

Indexes are represented by a small tree-like symbol within a table, as
shown in Fig.~\ref{fig-notation-index}. The index key is listed next to
this symbol. Composite keys are indicated by a grouping symbol. Hashing
is represented in a similar way, but uses an ``H'' symbol instead of a
tree symbol (see Fig.~\ref{fig-notation-hash}).

Clustering is represented by nesting one table inside another, as shown
in Fig.~\ref{fig-notation-cluster} (adapted from
\cite{BeDa-P-1992-PDD}). This notation is intuitive, and clearly
indicates the field(s) on which the records are clustered.

Partitioning is represented by splitting a table into either vertical or
horizontal partitions according to the style of partitioning, as shown
in Fig.~\ref{fig-notation-partition} (adapted from
\cite{Silb-A-2002-4E}). Once again, the notation is intuitive, and
allows the partition definitions to be easily indicated.

Replication is indicated by including multiple copies of the same table,
with a diagonal bar across the corner of each replica, as shown in
Fig.~\ref{fig-notation-replica}. This is adapted from a similar notation
used in data flow diagrams \cite{Gane-C-1979}.

% The graphical notations use in this model is not complex and cluttered.
% This is to enable a database designer to simplify the physical design in
% a notation that will be easy to understand but comprehensive. Some of
% the graphical notations use in this model was adapted from other models
% and a few were modified by the author to suit the model.
% 
% The table below illustrates some of the graphical representations that
% were available to choose from.

Consider the entity-relationship diagram shown in Fig.~\ref{fig-ERD},
which depicts a database for a consumer electronics manufacturer. A
corresponding Beynon-Davies' composite usage map based on the fourteen
most significant transactions is shown in Fig.~\ref{fig-Beynon-Davies}.
The arrows represent physical access paths, while the number attached to
each access path indicates the number of disk accesses per hour along
that path. The diagram clearly highlights some potential performance
problem areas in the database, for example:
\begin{itemize}

\item There are many disk accesses on the access paths between the
	Sale\_head/Sale\_line and the Order\_head/Order\_line tables. Since
	these are tables that will normally be accessed together, both could
	perhaps be candidates for clustering (depending on the mix of update
	versus read operations).

\item The appear to be multiple transactions acessing the Staff
	table. This could imply a need for partitioning.
	
	\item There is an extremely high access rate on the Customer table.
	Further examination, however, reveals that this rate only occurs for
	a short period once per month, and that the transaction in question
	only requires read access. Replication of the Customer table could
	therefore be a suitable solution.
	
\end{itemize}

\begin{figure}
	\includegraphics[width=\columnwidth,keepaspectratio]{ERD}
	\caption{ERD of the example database}
	\label{fig-ERD}
\end{figure}

\begin{figure}
	\includegraphics[width=\columnwidth,keepaspectratio]{Beynon-Davies}
	\caption{Beynon-Davies composite usage map for the example database}
	\label{fig-Beynon-Davies}
\end{figure}

The suggestions above can be represented as a physical model using our
proposed modelling notation, as shown in Fig.~\ref{fig-physical-model}.
Note that we have placed indexes on all primary keys as a matter of
course.

\begin{figure}
	\caption{Physical database model for the example database}
	\label{fig-physical-model}
\end{figure}

\section{Future Research}
\label{sec-future}

- symbols for different types of index (reverse-key, index-organised
tables, R-trees, bitmap indexes).

- physical placement information, i.e., what devices partitions go on, etc.

- evaluation of the notation with undergraduate students \& comparison
with Beynon-Davies (preliminary results by time of publication).

\section{Conclusion}
\label{sec-conclusion}

\bibliographystyle{splncs}

\bibliography{ER2005}

\end{document}

\documentclass{llncs}

\title{A Graphical Notation for Modelling Physical Database Structures}
\author{Antonia Pillay \and Nigel Stanger}
\institute{Department of Information Science, University of Otago, Dunedin, New Zealand \email{nstanger@infoscience.otago.ac.nz}}

\begin{document}

\maketitle

\begin{abstract}
In this paper we describe a graphical notation for modelling physical
database structures. Such a notation will provide database
administrators with a means to model the physical structures of new and
existing databases, and thus enable them to make more proactive and
informed tuning decisions, compared to existing database monitoring
tools.
\end{abstract}

\section{Introduction}

The design and implementation of a database system, as with most
information systems, typically goes through several phases
\cite{BeDa-P-2003}, including requirements analysis, conceptual
modelling, logical modelling, physical modelling and implementation.
Conceptual, logical and physical modelling are of particular interest
here, as each represents a step in a progression from a higher to a
lower level of abstraction \cite{Tsic-D-1978}. Conceptual models are
typically very high-level and abstract, using techniques such as
entity-relationship modelling, and are derived from the requirements.
Logical level models represent the structure of a database in a form
that is closer to the final physical representation, yet still
sufficiently abstract to isolate application from the physical
representation details (ref). Logical level models are typically derived
from the corresponding conceptual models by some transformation process
(ref), and use formalisms such as the relational model.

Physical level models represent the structure of a database in terms of
the physical storage structures provided by a specific database
management system (DBMS) such as Oracle or DB2. Once again, the physical
model for a database can be derived from the logical level model by some
form of transformation \cite{Bato-DS-1985,Conn-TM-2002}. Because of it's
low level of abstraction, modelling the physical level of a database is
typically one of the last phases of implementation, and tends to be very
product-specific. Consequently, physical level structures are not
typically modelled using graphical notations, unlike models at the
higher levels of abstraction. (refs?)

Physical modelling is, however, equally as important as, if not
\emph{more} important than the higher levels of modelling, because it is
the physical level that has the greatest impact on the performance of a
database \cite{BeDa-P-2003}. It is therefore somewhat surprising that
there have been relatively few attempts to devise a graphical physical
modelling notation that can be used to represent the physical structures
of a database. Use of such a notation provides several advantages
\cite{BeDa-P-1992-PDD,Conn-TM-2002,Will-J-1992}:

\begin{itemize}

\item it can reduce complexity and thus aid communication and
	improve understandability \cite{Tuft-ER-1997};

\item it can provide a more complete and integrated display of
	tables and performance tuning techniques in a database;

\item database developers can be more confident about the design
	decisions that they make for the performance of the database;

\item database performance problems are more easily visaualised
	using a graphical notation; and

\item a specific methodology is developed and used, thus allowing
	the developer to resolve physical performance issues in a more
	systematic manner.

\end{itemize}

These benefits are embodied in database performance monitoring tools
such as Quest's SpotLight (ref), which provides a higher-level
visualisation of a database's structures in order to easily identify and
highlight performance problems. Such tools, however, are primarily
intended as \emph{monitoring} tools rather than as \emph{design} tools.
They may therefore unintentionally encourage database administrators
(DBAs) into a \emph{reactive} mode of continually ``tweaking'' the
database to resolve performance issues, rather than a \emph{proactive}
mode of anticipating problems, by means of prior analysis and modelling.
It may also be difficult for a DBA using such tools to gain a clear and
comprehensive overview of all the tuning techniques that are in use
within a particular database \cite{Core-MJ-1997-OracleDW}.

In this paper we propose a graphical notation for modelling the physical
structures of a database system, which builds upon a methodology for
physical database design proposed by Beynon-Davies
\cite{BeDa-P-1992-PDD}. In Section~\ref{sec-techniques}, we provide a
brief overview of current commonly used physical tuning techniques. We
then proceed in Section~\ref{sec-previous} to discuss prior approaches
to physical modelling and design. Section~\ref{sec-notation} introduces
our proposed notation, and Section~\ref{sec-future} discusses possible
future work. The paper concludes in Setion~\ref{sec-conclusion}.

\section{Physical tuning techniques}
\label{sec-techniques}

DBMSs tend to be I/O bound, so the main bottleneck in any database
system is usually the speed of offline storage such as disk drives.
Retrieving data from a hard disk is theoretically about six orders of
magnitude slower than retrieving the same data from RAM\footnote{On the
order of milliseconds (\(10^{-3}\)) for disk versus nanoseconds
(\(10^{-9}\)) for RAM.}. The ultimate aim of any physical tuning
strategy is thus to minimise the impact of slow storage, either by
directly reducing the number of physical disk accesses required, or by
parallelising access to the disk in order to reduce contention for a
limited resource.

These considerations have led to the development of five general
physical tuning techniques, which have been implemented to various
degrees by most mainstream DBMS products:

% following sections way too long --- shorten considerably

\begin{description}

\item[Indexes] reduce the number of physical disk accesses required
	to retrieve a specific record, most typically by building a B+-tree 
	\cite{Knut-DE-1997-Art} based on some key value. Without any
	indexes, a DBMS often has little choice but to perform a sequential
	scan in order to locate a specific record.

\item[Hashing] is a method of quickly locating specific records by
	passing a key value through a \emph{hash function}. This function
	returns the physical location of a hash bucket, which contains a
	pointer to the associated physical record (check). Hashing schemes
	typically require only a single disk access to retrieve a specific
	record.

\item[Clustering] minimises disk access by ensuring that related
	records (such as an order header and its assocaited order lines) are
	physically adjacent to each other on disk
	\cite{Chan-N-2003-clustering}. This usually means that related
	records will be stored in the same database block, and can thus all
	be retrieved with a single disk access.

\item[Partitioning] provides parallel access paths to data by
	physically splitting a table into disjoint parts and ideally placing
	them on separate disks. This is particularly advantageous in
	situations where multiple users wish to access different subsets of
	a set of records, because it provides a separate physical access
	path to each of the partitions. Partitioning can also reduce the
	number of disk accesses required, because the amount of data to be
	searched in each partition is smaller than if the table were not
	partitioned.

\item[Replication] provides parallel access to data by making
	multiple copies of the same records and ideally placing them on
	separate disks. This is particularly advantageous if multiple users
	need to access the same sets of records, but is more complex to
	manage due to the need to keep replicas synchronised.

% Replication is an access parallelism technique in which multiple copies
% of the same records are placed on different disks, thus providing
% multiple physical access paths to the same data.

\end{description}

% \subsection{Discussion}

The physical tuning techniques described above are normally used in
different parts of the database to achieve different effects. To choose
an appropriate physical tuning technique, the DBA must consider various
factors that will either benefit the users of the database or improve
the performance of the database as a whole. While most of the techniques
can be combined to varying degrees, simply applying all techniques is
usually not an optimal solution, because each technique has different
conditions in which it excels. What are optimal conditions for one
technique may be the exact opposite for another, so the DBA needs to be
able to model all the available information in order to develop an
appropriate physical design.

\section{Prior physical modelling techniques}
\label{sec-previous}

To achieve an effective physical design requires a large amount of
information, particularly with regard to the (predicted or actual)
volume and usage of data within the database \cite{BeDa-P-2003}.
Incorporating this information into a graphical model can provides a
more concise and clearer overview of the physical aspects of a database
system. In this section we discuss three previous efforts at modelling
such information in a graphical manner.

\subsection{Agile modeling (Ambler)}

The notation suggested by Ambler
\cite{Ambl-SW-2003-ADT,Ambl-SW-2004-ObjPrimer3} is a type of model that
can be developed in UML using class boxes. He states that since Unified
Modelling Language (UML) does not cover data (i.e., ER) modelling yet,
he presents the solution in this paper. Ambler has argued for some time
for the presence of data modelling in UML \cite{Ambl-SW-1998-BOA}, and
has suggested various ways that it should be done. It is enlightening to
know that Ambler is not alone in his quest for adopting an industry
standard in data modelling. Other methodologies like
\cite{Naib-EJ-2001-UMLDD} have recognized the need as well. This model
type is built on the practice of UML 2.0 of separating core methodology.
Ambler admits that the methodology that he has presented is not perfect
and it focuses on the physical modelling of a relational database. In
this model he also tries to stress style issues that according to him
are not appropriate for a proper UML profile \cite{Ambl-SW-2003-ADT}.

This model suggests that a class box without a stereotype in a physical
database design is a table. It also represents views that have
dependencies on the table structures. Tables, entities and views are all
modelled using class boxes. The class boxes that appear on the logical
and conceptual model are entities so the stereotype is optional.
Similarly, it is assumed that any class box without a stereotype on a
physical data model is a table. Ambler's methodology seems to be limited
in terms of annotations. All representations whether tables or indices
are modelled using class boxes. This representation can sometimes be
confusing and exact identification of tables and indices in the system
has to be known by the database designer. In this model, relationships
are modelled using associations that are derived from the logical data
model. He further discusses his methodology for modelling attributes and
columns, keys, constraints and triggers, stored procedures and sections.
Ambler states that requirements for something should be identified
before it is built. He states the requirements of each model, e.g.,
requirements that are needed to model entities and tables, requirements
that are needed to model relationships, etc.

An example of Ambler's notation is shown in Figure~\ref{fig-Ambler}.

\begin{figure}
	\caption{Ambler's physical model notation (adapted from \cite{Ambl-SW-2003-ADT})}
	\label{fig-Ambler}
\end{figure}

Even though a lot of detail is covered in his suggestion, Ambler's
methodology somehow seems relatively weak. It is much too general in
annotations and has no specific description. The methodology seems to
consistently confuse the logical and physical design. For example: both
are modelled using class boxes but are later explained as representing
different objects. However, this model will definitely be useful as a
stepping-stone to work towards an official UML data modelling profile.

\subsection{Physical design using an entity model (Beynon-Davies)}

The closest model that demonstrates the link between conceptual, logical
and physical design work is by Beynon-Davies \cite{BeDa-P-1992-PDD}. He
suggests a method that can be used for the physical design process. The
paper defines physical modelling as ``the transformation of the logical
model into a definition of the physical model suitable for a specific
software/hardware configuration'' \cite{BeDa-P-1992-PDD}.

According to Beynon-Davies one of the first steps that must be taken to
move from logical to physical database design is to establish estimates
of the average and maximum number of instances per entity (volume
analysis). Volatility analysis is represented in the same way. Similar
to volume analysis, volatility analysis cannot be used as a measure if a
table is continually growing. It is most effective if the size of the
table is static. Figure 9 summarizes Beynon-Davies's final modelling
method; he does not model all the individual annotations but generalizes
the entity relationship diagrams into a general model.

It is understandable that the reason behind this generalization is to
minimize complexity and since individual annotations are developed in
the beginning, references can be made to them if needed. This might be
effective for small systems that have a limited number of tables.
However, for medium to large-scale projects, Beynon-Davies suggests that
a systematic analysis of volatility and usage should be done. This
analysis would constitute a map of the database application that would
be maintained by the DBA. This meets the objective of providing an
overview of all the performance tuning techniques and data in place.

\section{A new physical notation}
\label{sec-notation}

In this section we discuss a new notation for graphically representing
physical database models. While Ambler's notation is in many ways closer
to a physical modelling notation, the evident confusion between the
physical and logical levels diminishes its usefulness. Beynon-Davies'
notation, on the other hand, simply adds information relevant to
physical tuning to a standard entity-relationship diagram. Our
experience in teaching this technique at undergraduate level is that the
designer can quickly become overwhelemed by a ``mountain of numbers''.
In addition, Beynon-Davies' method does not provide any conclusions as
to which physical tuning methods should be implemented---rather it
provides the information required in order to draw these conclusions.
Beynon-Davies' method is thus more of a notation for summarising the
physical usage of a database, rather than a notation for representing
physical database structures.

We have therefore taken Beynon-Davies' work one step further and
developed a graphical notation for representing the physical database
tuning techniques discussed in Section~\ref{sec-techniques}.

The graphical notations use in this model is not complex and cluttered.
This is to enable a database designer to simplify the physical design in
a notation that will be easy to understand but comprehensive. Some of
the graphical notations use in this model was adapted from other models
and a few were modified by the author to suit the model.

The table below illustrates some of the graphical representations that
were available to choose from.

Clustering is represented by nesting one entity inside another, as shown
in Figure~\ref{fig-notation} (adapted from \cite{BeDa-P-1992-PDD}). This
notation is intuitive, and clearly indicates the field(s) on which the
records are clustered.

Partitioning is represented by splitting an entity into either vertical
or horizontal partitions, as shown in Figure~\ref{fig-notation} (adapted
from \cite{Silb-A-2002-4E}). Once again, the notation is intuitive, and
allows the partition definitions to be easily listed.

Replication is indicated by including multiple copies of the same
entity, with a diagonal bar across the corner of each replica (adapted
from a notation used in data flow diagrams \cite{Gane-C-1979}).

Indexes are represented by a small tree-like symbol within an entity.
The index key is listed next to this symbol. Hashing is represented in a
similar way, but using an ``H'' symbol instead of a tree symbol.

\begin{figure}
	\caption{Graphical representations for physical structures}
	\label{fig-notation}
\end{figure}

\subsection{Example of use}

Consider the entity-relationship diagram shown in Figure~\ref{fig-ERD},
which depicts a database system for a consumer electronics manufacturer.
A corresponding Beynon-Davies' annotated model is shown in
Figure~\ref{fig-Beynon-Davies}. Analysis of this figure enables us to
draw certain conclusions about the physical characteristics of this
database:

\begin{itemize}

\item conclusions\ldots (see 321 assignment material)

\end{itemize}

\begin{figure}
	\caption{ERD of the example database}
	\label{fig-ERD}
\end{figure}

\begin{figure}
	\caption{Beynon-Davies annotated model for the example database}
	\label{fig-Beynon-Davies}
\end{figure}

Figure~\ref{fig-physical-model} shows a physical model of this database
system using our proposed notation.

\begin{figure}
	\caption{Physical database model for the example database}
	\label{fig-physical-model}
\end{figure}

\section{Future research}
\label{sec-future}

- symbols for different types of index (reverse-key, index-organised
tables, R-trees, bitmap indexes).

- evaluation of the notation with undergraduate students \& comparison
with Beynon-Davies (preliminary results by time of publication).

\section{Conclusion}
\label{sec-conclusion}

\bibliographystyle{splncs}

\bibliography{ER2005}

\end{document}

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