Abstract
A class of discrete-timeM/G/1 queues, including both round robin and last come first served service, in which customers are subject to permutations is considered. These time slotted queues, analogous to the symmetric queues of Kelly, are analyzed by examination of the time reversed process. Product form stationary distributions are found for a type of doubly stochastic server of Schassberger [5] and for a Bernoulli arrival process queue model of Henderson and Taylor [2].
Similar content being viewed by others
References
H. Daduna and R. Schassberger, A discrete-time round robin queue with Bernoulli input and general arithmetic service time distributions, Acta Inf. 15 (1981) 251–263.
W. Henderson and P.G. Taylor, Insensitivity in discrete-time queues with a moving server, Queueing Syst. 11 (1992) 273–297.
F.P. Kelly,Reversibility and Stochastic Networks (Wiley, New York, 1979).
S.M. Ross,Stochastic Processes (Wiley, New York, 1983).
R. Schassberger, The doubly stochastic server: A time sharing model, Zeits. Oper. Res. 25 (1981) 179–189.
H. Takagi,Analysis of Polling Systems (MIT Press, Cambridge, MA, 1986).
H. Takagi, Queueing analysis of polling models, ACM Comp. Surveys 20 (1988) 5–28.
R.D. Yates, High speed round robin queueing networks, PhD thesis, MIT Dept. of Electrical Engineering and Computer Science (1990).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Yates, R.D. Analysis of discrete time queues via the reversed process. Queueing Syst 18, 107–116 (1994). https://doi.org/10.1007/BF01158776
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01158776