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Modelling and analysis using Q-GERT networks
3~
Book reviews
variety o f ~ t s t h a may be measured, such as reliability, maintainability, complexity, portability, robustness, effectiveness. There is no dear line in these chapters, sometimes costs figure centrally, sometimes the ,amber of bugs. Two subjects are of interest. One is the author's idea of weasuring the progress towards program reliability by artificially inserting bugs(he calls this "bebugging"). If the tests reveal x original andy artificial bugs, wherey is z% of the known artificial ones then one may assume (at least Glib does) that the number x represents z% of the original bugs (the idea was proposed by the author in earlier publications in 1975). Another interesting concept introduced in this part is the "contract for software portability", which implies that a consultant software house will undertake to convert a system for a maximum price of, say 5% (if the portability is stated to be 95%), of the original programming/debugging cost to any standard environment of major manufacture. The concept of "complexity" is linked ~o the number of decision boxes, which seerr~ssomewhat restzictive in that I F . . . THEN . . . ElSE . . . FI nests, especially when combined with GOTO's provide complexity of a nature whi,:h is dif. fer~nt from D O . . . WHILE. ~. OD or D O . . . UNTIL • . . OD blocks. The second part is somewhat more structured than the first one. It consists of an introduction and chapters concerning the following "metrics": reliability, flexibility, structure, performance, :esource, diverse. It is in these pages (pp. 129-218) that Gilb addresses students in particu!~, hoping that practioners will "at least scan the contents for later re¢~,rence". Many of the measures proposed wiJ appear somewhat arbitrary and they certainly do not form a "system". Nevertheless, there ~s much sense in them and they certainly demonstrate that quantification of an undoubtedly relevant natzlre is possible in virtually every dimension of the many one comes across in practical work. The only question remaining is whether future forms of programming will posses these dimensions very much. The system, such as it is, may already be dated. Not surprisingly perhaps. It originated in 1972. However, the same applies to meny other approaches in programming. Part [ was added when a reviewer of the early version (essentially Part II as it stood in 1975) said that he liked what he saw but remained sceptical about the practical application. This reviwer's scepsis concerns the new material added. It provides many attractive trees, but now the wood is almost totally
unrecognisable. Fortunately. Tom Glib likes to write. Before long he will have reviewed things himself and concluded that modernisation is possible and desirable. Those to which he dedicated this book probably will rem-,~inunconvinced, but he has already provided more than mere thought provoke~. He should continue.
A.A. VERRIIN STUART University of Leiden Leiden, The Netherlands
A. ALAN B. PRISKER, Modelling and Analysis using Q-GERT Networks, Wiley, New York, 470 pages, £ 13.15/$ 22.25. Q-GERT is a simulation technique involving the graphical representation of systems in network form with provision for queues. (Eence: Graphical Evaluation and Review Technique with Queues). The network approach adopts an activity-on-branch philos. ophy, the activities thus incurring the processing times or delays, with a range of node types to provide the necessary system structure. The constructed networl:, coded in the specified manner, forms the input data to the Q-GERT Analysis Program - a tomputer program which initiates and controls the flow of transactions through the network with the necessa~/random variate sampling and information collection. Q-GERT is part of ~_nevolving family of packages sten~ning from the first GERT research at the RAND Corporation in the mid 1960s. It also has a family rehtio~ship with GASP-II and a conceptual (and computer coding) resemblance to GPSS. Interpretation of a Q-GERT computer model, i.e. the coded input to the Analysis Program, r e l y re. quires reference to the corresponding network model. Since there is now in the computer field a significant argument that transparent code is of high value in program debugging and maintenance and flow.charts are of less value than once thought, this may be a significant burden; particularly since the Q-GERT approach is an intricate one with many node and activity constructs and parameters. It is surprising that, since the formulation work of this approach to modelling consists of constructing the network, nothing is made of manual use of that network; at least in preliminary studies or small systems. T~e
Book reviews computer program required is not detailed in the book, it has to be acquired separately (at a cost). The 470 page book is very well put together. It adopts a hierarchical structure taking the student through levels of increasing sophistication with numerous case studies and exercises but includes easily accessed reference material. Its explanations are clear and careful, even painstaking, and its references (alphabetic by author) quite extensive. In summary, a well written book but one which should be regarded as an input manual to a consultant's computer package.
B.W. HOLLOCKS British Steel Corporation Sheffield, U.K.
EGINHARD J. MUTH, Transform Methods with
Applications to Engineering and Operations Research, Prentice-Hall, Englewood Cliffs, N J, 1977, xi + 372 pages, $ 29.65. The book provides a thorough elementary introduction to transform methods. After an introductory chapter on the theory of complex numbers, the author defines the Laplace transform. A number of results about these transforms and techniques for obtaining transforms are treated. The next chapter on the inverse Laplace transform is almost completely devoted to the method of partial fraction decomposi. tion. Then in Chapter 5 a number of applications to the theory of ordinary differential equations, with examples from mechanical and electrical engineering and economics are given. This chapter contains also applications to integral equations and probab~ty theory. In the remaining part of the book a similar treatment of the z.transform is given. The book has a limited scope. Only Laplace and z-transforms are treated and that only at an elementary level. The treatment is very careful and transparent. There are many examples and exercises. Therefore, the book will be very useful in elementary cGur,~¢$.
M.L.J. HAUTUS Eindhoven University o f Technology, Eindhoven The Netherlands
385
HAROLD EXTON, Hypergeometric Integrals. Wiley, New York, 1973, S 15.00. The hypergeometric function began_ life as a power series which had as special cases many of the common (elementary and not so elementary) functions ,f mathematics and mathematical physics. Naturally, this was extended to the concept of the generalized hypergeometric function which was then investigated on its own account and also for its applications. This book is in two parts. Seven chapters comprise the first part and these give the general theory of integrals and transforms of hypergeometric functions together with examples of their uses in statistics and in mathematical physics. The second part consists of about one hundi'ed pages of tables of formulae and fifty pages of computer programs (in FORTRAN) for the evaluation of integrals. This book wiLl probably be useful in a variety of sciences. HoweveL the ootential user should always be on the lookout for misprints, for in a casual run through the book a few minor ones were noticed. (Even the Bateman project with its large number of helpers could not avoid them and corrections appeared regularly in Mathematics of Computation for many years.) Contents. Part One. Chapter 1. Hypergeometric functions of one or more variables. Integrals of Euler type. 3. Definite integrals and repeated integrals. 4. Contour Integrals. 5. lnf'mite Integrals. 6. Multiple Integrals. 7. Applications. Pa~ Two. A. Tables of Hypergeometric Integrals. B. Computer Programs. Selected Bibliography. .
D. KERSHAW University o f Lancaster Lancaster, U.K.
Book reviews
variety o f ~ t s t h a may be measured, such as reliability, maintainability, complexity, portability, robustness, effectiveness. There is no dear line in these chapters, sometimes costs figure centrally, sometimes the ,amber of bugs. Two subjects are of interest. One is the author's idea of weasuring the progress towards program reliability by artificially inserting bugs(he calls this "bebugging"). If the tests reveal x original andy artificial bugs, wherey is z% of the known artificial ones then one may assume (at least Glib does) that the number x represents z% of the original bugs (the idea was proposed by the author in earlier publications in 1975). Another interesting concept introduced in this part is the "contract for software portability", which implies that a consultant software house will undertake to convert a system for a maximum price of, say 5% (if the portability is stated to be 95%), of the original programming/debugging cost to any standard environment of major manufacture. The concept of "complexity" is linked ~o the number of decision boxes, which seerr~ssomewhat restzictive in that I F . . . THEN . . . ElSE . . . FI nests, especially when combined with GOTO's provide complexity of a nature whi,:h is dif. fer~nt from D O . . . WHILE. ~. OD or D O . . . UNTIL • . . OD blocks. The second part is somewhat more structured than the first one. It consists of an introduction and chapters concerning the following "metrics": reliability, flexibility, structure, performance, :esource, diverse. It is in these pages (pp. 129-218) that Gilb addresses students in particu!~, hoping that practioners will "at least scan the contents for later re¢~,rence". Many of the measures proposed wiJ appear somewhat arbitrary and they certainly do not form a "system". Nevertheless, there ~s much sense in them and they certainly demonstrate that quantification of an undoubtedly relevant natzlre is possible in virtually every dimension of the many one comes across in practical work. The only question remaining is whether future forms of programming will posses these dimensions very much. The system, such as it is, may already be dated. Not surprisingly perhaps. It originated in 1972. However, the same applies to meny other approaches in programming. Part [ was added when a reviewer of the early version (essentially Part II as it stood in 1975) said that he liked what he saw but remained sceptical about the practical application. This reviwer's scepsis concerns the new material added. It provides many attractive trees, but now the wood is almost totally
unrecognisable. Fortunately. Tom Glib likes to write. Before long he will have reviewed things himself and concluded that modernisation is possible and desirable. Those to which he dedicated this book probably will rem-,~inunconvinced, but he has already provided more than mere thought provoke~. He should continue.
A.A. VERRIIN STUART University of Leiden Leiden, The Netherlands
A. ALAN B. PRISKER, Modelling and Analysis using Q-GERT Networks, Wiley, New York, 470 pages, £ 13.15/$ 22.25. Q-GERT is a simulation technique involving the graphical representation of systems in network form with provision for queues. (Eence: Graphical Evaluation and Review Technique with Queues). The network approach adopts an activity-on-branch philos. ophy, the activities thus incurring the processing times or delays, with a range of node types to provide the necessary system structure. The constructed networl:, coded in the specified manner, forms the input data to the Q-GERT Analysis Program - a tomputer program which initiates and controls the flow of transactions through the network with the necessa~/random variate sampling and information collection. Q-GERT is part of ~_nevolving family of packages sten~ning from the first GERT research at the RAND Corporation in the mid 1960s. It also has a family rehtio~ship with GASP-II and a conceptual (and computer coding) resemblance to GPSS. Interpretation of a Q-GERT computer model, i.e. the coded input to the Analysis Program, r e l y re. quires reference to the corresponding network model. Since there is now in the computer field a significant argument that transparent code is of high value in program debugging and maintenance and flow.charts are of less value than once thought, this may be a significant burden; particularly since the Q-GERT approach is an intricate one with many node and activity constructs and parameters. It is surprising that, since the formulation work of this approach to modelling consists of constructing the network, nothing is made of manual use of that network; at least in preliminary studies or small systems. T~e
Book reviews computer program required is not detailed in the book, it has to be acquired separately (at a cost). The 470 page book is very well put together. It adopts a hierarchical structure taking the student through levels of increasing sophistication with numerous case studies and exercises but includes easily accessed reference material. Its explanations are clear and careful, even painstaking, and its references (alphabetic by author) quite extensive. In summary, a well written book but one which should be regarded as an input manual to a consultant's computer package.
B.W. HOLLOCKS British Steel Corporation Sheffield, U.K.
EGINHARD J. MUTH, Transform Methods with
Applications to Engineering and Operations Research, Prentice-Hall, Englewood Cliffs, N J, 1977, xi + 372 pages, $ 29.65. The book provides a thorough elementary introduction to transform methods. After an introductory chapter on the theory of complex numbers, the author defines the Laplace transform. A number of results about these transforms and techniques for obtaining transforms are treated. The next chapter on the inverse Laplace transform is almost completely devoted to the method of partial fraction decomposi. tion. Then in Chapter 5 a number of applications to the theory of ordinary differential equations, with examples from mechanical and electrical engineering and economics are given. This chapter contains also applications to integral equations and probab~ty theory. In the remaining part of the book a similar treatment of the z.transform is given. The book has a limited scope. Only Laplace and z-transforms are treated and that only at an elementary level. The treatment is very careful and transparent. There are many examples and exercises. Therefore, the book will be very useful in elementary cGur,~¢$.
M.L.J. HAUTUS Eindhoven University o f Technology, Eindhoven The Netherlands
385
HAROLD EXTON, Hypergeometric Integrals. Wiley, New York, 1973, S 15.00. The hypergeometric function began_ life as a power series which had as special cases many of the common (elementary and not so elementary) functions ,f mathematics and mathematical physics. Naturally, this was extended to the concept of the generalized hypergeometric function which was then investigated on its own account and also for its applications. This book is in two parts. Seven chapters comprise the first part and these give the general theory of integrals and transforms of hypergeometric functions together with examples of their uses in statistics and in mathematical physics. The second part consists of about one hundi'ed pages of tables of formulae and fifty pages of computer programs (in FORTRAN) for the evaluation of integrals. This book wiLl probably be useful in a variety of sciences. HoweveL the ootential user should always be on the lookout for misprints, for in a casual run through the book a few minor ones were noticed. (Even the Bateman project with its large number of helpers could not avoid them and corrections appeared regularly in Mathematics of Computation for many years.) Contents. Part One. Chapter 1. Hypergeometric functions of one or more variables. Integrals of Euler type. 3. Definite integrals and repeated integrals. 4. Contour Integrals. 5. lnf'mite Integrals. 6. Multiple Integrals. 7. Applications. Pa~ Two. A. Tables of Hypergeometric Integrals. B. Computer Programs. Selected Bibliography. .
D. KERSHAW University o f Lancaster Lancaster, U.K.