Analysis of the Discrete - Time GI / Geom ( n ) / 1 / N Queue

Keywords-Discre tet ime, Finite buffer, Geometric, Queue, State dependent. 1. I N T R O D U C T I O N In recent years, there has been a growing interest in the analysis of discrete-time queues due to their applications in communica t ion systems and other related areas. This can be judged by the fact t ha t two books [1,2] have recently come out. Also, various special issues of some journals have been exclusively devoted to discrete-time queues and their applications [3]. In the pas t few years, not only have a large number of articles on various aspects of discrete-t ime queues a l ready appeared in the literature, but they still continue to do so. One of the main reasons for the analysis of discrete-time queues is tha t continuous-t ime queueing models cannot accura te ly give the performance measures of discrete-time queueing models in which basic units are digital such as machine cycle t ime or bits and packets. Further, t hough discrete-t ime queues can be used to derive continuous-t ime results, the reverse is generally not t rue [2, p. v]. In fact, much of the impor tance of discrete-time queues stems from the fact tha t they can be used in the The authors are grateful to H. Lee, RMC, for his help in the preparation of this paper. They are also thankful to NSERC for supporting this research. The third author acknowledges with thanks the financial support provided by the Department of Industrial Engineering, University of Toronto and other services provided by the Department of Mathematics and Computer Science, Royal Military College of Canada, Kingston, Ontario. Typeset by . A ~ T E X