Analysis of Asymmetric Single-Buffer Polling and Priority Systems without Switchover Times * 253 Tetsuya Takine Department of Applied Mathematics and Physics, Faculty of Engineerin~ Kyoto University, Kyoto 606, Japan Hideaki Takagi IBM Research, Tokyo Research Laboratory, Sanbancho YS Buildin& 5-11 Sanban-cho, Chiyoda-ku, Tokyo 102, Japan Yutaka Takahashi and Toshiharu Hasegawa Department of Applied Mathematics and Physics, Faculty of Engineerin~ Kyoto University, Kyoto 606, Japan Received April 1989 Revised March 1990 All previous works on single-buffer polling systems assume a nonzero time for a server to switch stations. In this paper, we consider similar systems with zero switchover times. The performance measures in symmetric systems of this type correspond to those in a well-known machine interference problem. Assuming that the stochastic characteristics vary from station to station, we provide an analysis of imbedded Markov chains to calculate the performance measures. In particular, we derive the state transition probabilities for systems with an arbitrary number of stations. Our approach is also applied to non-preemptive priority systems and systems with a mixture of polling and priority scheduling. Furthermore, we obtain the Laplace-Stieltjes transforms of the probability distribution function of waiting time for both polling and priority systems. Keywords: Performance Evaluation, Finite-population Queues, Polling Models, Priority Queues, Token Ring with Priorities. 1. Introduction In the performance evaluation of computer and communication systems, the assumption of single buffers has been widely used to model the process for generating service requests (called messages hereafter) at each user (called a station). In single-buffer models, we assume that a new message is generated by each station at an exponentially distributed time after the service to the previous message has been completed. Examples include a classic machine interference problem [8], a model of TSS (time sharing Tetsuya Takine was born in Kyoto, Japan, on November 28, 1961. He received the B. Eng., M. Eng., and Dr. Eng. degrees in applied mathematics and physics from Kyoto University, Kyoto, Japan, in 1984, 1986 and 1989, respectively. Since April 1989, he has been an Assistant Professor in the Department of Applied Mathematics and Physics, Kyoto University. His research interests include queueing theory and performance analysis of computer/communication systems. * This research was supported in part by a Grant-in-Aids (01580027) for general Scientific Research of the Ministry of Education, Science and Culture of Japan. North-Holland Performance Evaluation 11 (1990) 253-264 0166-5316/90/$03.50 © 1990 - Elsevier Science Publishers B.V. (North-Holland)