35 A Decomposition Approach to Modelling High Service Time Variability * John Zahorjan, Edward D. Lazowska and Richard L. Garner Department of Computer Science, University of Washington, Seattle, WA 98195, U.S.A. Received 2 November 1981 Revised 14 June 1982 The predictive ability of queueing network models can be greatly enhanced if these models include the effects of system characteristics such as high service time variability and simulta- neous resource possession, which violate the assumptions re- quired for their efficient exact solution. In this paper we present a new approximate solution technique for queueing networks that include Coxian servers to represent resources at which customers have high service time variability. Our ap- proach is unique in several respects: it is based directly on the theory of near-complete decomposability, it is non-iterative (performance measures for the queueing network of interest are expressed as linear combinations of the performance measures of a set of separable queueing networks), and it is conceptually and computationally simple. Kevword~: Performance Modeling, Queueing Network Mod- els, Approximate Solution Technique, Coxian Distribution. Near-Complete Decomposability. 1. Introduction Separable queueing networks [2], those for which exact solutions can be obtained by relatively effi- cient means and for which approximate solutions can be obtained with excellent accuracy and ef- ficiency, have met with great success in modelling the performance of computer systems. This success has been achieved despite the fact that most com- puter systems include characteristics that violate the assumptions required for separability, char- acteristics such as the simultaneous or overlapped possession of several resources by a customer, first-come-first-served scheduling in the presence of high service time variability, priority scheduling, and others. There are many reasons for this success. It often happens that the characteristic violating the separability assumptions has a negligible effect on the performance of the system. Ignoring such a characteristic in formulating a model will have a negligible effect on accuracy. For example, al- though a resource may be scheduled first-come- first-served, the variability in service times may be small enough or the load on the resource light John Zahorjan received a Sc.B. in Ap- plied Mathematics from Brown Uni- versity in 1975 and a Ph.D. in Com- puter Science from the University of Toronto in 1980. He is currently an Assistant Professor of Computer Sci~ ence at the University of Washington, where his research interests are in the area of performance modeling of com- puter and computer communication systems. * This research was supported in part by the National Science Foundation under Grants No. MCS-8003344 and MCS- 8104879. North-Holland Publishing Company Performance Evaluation 3 (1983) 35-5,1 0166-5316/83/0000-0000/$03.00 © 1983 North-Holland Edward D. Lazowska received an A.B. from Brown University in 1972 and a Ph.D. in Computer Science from the University of Toronto in 1977. He has been on the faculty of the Department of Computer Science at the University of Washington since that time. His research interests fall within the gen- eral area of computer systems: modell- ing and analysis, design and imple- mentation, distributed systems. Richard L. Garner received a B.A. in Mathematics from Washington State University in 1973. After working in industry for several years he entered the University of Washington, where he received his Ph.D. in Computer Sci- ence in 1982, His research work was involved with the application of de- composition approaches to the analy- sis of queueing network models of computer systems. He is currently op- erating Richard L. Garner & Associ- ates in the Seattle area.