155 System Performance with User Behavior Graphs * Mafia Calzarossa Dipartimento di Informatica e Sistemistica, Universitgt di Pavia, 1-27100 Pavia, Italy Raymond Marie IRISA, Universit~ de Rennes, 35042 Rennes, France Kishor S. Trivedi Department of Computer Science, Duke University, Durham, NC 27706, USA Received November 1989 Revised April 1990 Workload characterization is known to be a difficult and yet a very important facet of performance modeling. User behavior graphs have been advocated as a practical means of workload characterization. Performance modeling with user behavior graphs is for the most part carried out using costly simulations. We present inexpensive and yet accurate analytic performance models based on user behavior graphs. Keywords: Markov Chain, Memory Constraint, Product- Form Queuing Networks, User Behavior Graph, Workload Characterization. !iiii i ii!!i M. a C, aro a receiv her toral degree in Mathematics from the University of Pavia, Pavia, Italy, in 1981. She has been with the Numerical Analysis Institute of Italian National Research Council till 1987 and a Visit- ing Scientist at the University of Cali- fornia at Berkeley and at Duke Uni- versity during 1984 and 1985. Pre- sently, she is a Professor of Computer Science at the Engineering School of the University of Pavia. Her research interests include workload characterization and performance evaluation of computer systems, parallel systems and computer networks. * This work was supported in part by the Italian National Research Council (C.N.R.) under Grant 89.00014.69, by the Italian Government under the 40% Project and by the U.K. Science and Engineering Research Council while the third author was a visiting fellow at the Computing Laboratory of the University of Newcastle upon Tyne. North-Holland Performance Evaluation 11 (1990) 155-164 I. Introduction The design of executable, artificial workload mod- els is a preliminary fundamental step for all stud- ies dealing with the performance evaluation of computer systems [6]. The workload of an interac- tive system can be adequately described by a set of user behavior graphs (ubg's); one graph for each user [7]. The basic elements of such a prob- abilistic graph are - nodes which represent different command types issued by a user - arcs representing the issuance of the next com- mand upon the completion of the current one. During a terminal session, a user interactively submits different command types according to his/her ubg. The command type to be issued next is determined by the transition probabilities of the ubg. The sojourn time in each node of the ubg is Raymond A. Marie received the Doctorat d'Ing6nieur and the Doctorat d'Etat es-Sciences Math6matiques from the University of Rennes, France, in 1973 and 1978, respectively. Since 1977, he is a Research Manager of an INRIA project. He spent the 1981- 1982 academic year as a Visiting Asso- ciate Professor at North Carolina State University, Raleigh, NC, U.S.A. Cur- rently, he is a Professor at the Com- puter Science Department of the Uni- versity of Rennes. His active research interests include performance evaluation of computer systems and reliability computation of complex systems. Kishor S. Trivedi received the B. Tech. degree from the Indian Institute of Technology (Bombay), and M.S. and Ph.D. degrees in computer science from the University of Illinois, Urba- na-Champaign. He is the author of text entitled, Probability and Statistics with Reliabil- ity, Queueing and Computer Science Applications, published by Prentice- Hall. His research interests are in computing system reliability and per- formance evaluation. He is a Professor of Computer Science and Electrical En- gineering at Duke University, Durham, NC. He has served as a Principal Investigator on various AFOSR, ARO, Burroughs, IBM, DEC, NASA, NIH, ONR, NSF, and SPC funded pro- jects and as a consultant to industry and research laboratories. He was an Editor of the IEEE Transactions on Computers from 1983-1987. 0166-5316/90/$03.50 © 1990 - Elsevier Science Publishers B.V. (North-Holland)