Analysis of an M/{Dn}/1 retrial queue

Authors:
Xiaoyong Wu;Xiaowu Ke
Affiliations:
Department of Mathematics and Statistics, University of Windsor, Windsor, Ont., Canada N9B 3P4;Department of Mathematics and Statistics, University of Windsor, Windsor, Ont., Canada N9B 3P4 and Department of Management Science, University of Windsor, Windsor, Ont., Canada N9B 3P4
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

Citing 10
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Abstract

We consider a single server retrial queueing system in which each customer (primary or retrial customer) has discrete service times taking on value D"j with probability p"j,j=1,2,..., and @?"j"="1^~p"j=1. An arriving primary customer who finds the server busy tries later. Moreover, each retrial customer has its own orbit, and the retrial customers try to enter the service independently of each other. We call this retrial queue an M/{D"n}/1 retrial queue. A necessary and sufficient condition for this system stability is given. In the steady state, we derive the joint distribution of the state of the server and the number of customers in the retrial orbits. The explicit expressions of some performance measures are given. In addition, the steady-state distribution of the waiting time is discussed.