Far East Journal of Theoretical Statistics
Volume 20, Issue 2, Pages 151 - 162
(November 2006)
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G. H. Shahkar (Iran) and A. Badamchi Zadeh (Iran)
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Abstract: We analyze a single server queue with Poisson input, k
phases of heterogeneous service with Bernoulli schedule and a general vacation
time. In this model the server provides k phases of heterogeneous service
one after the other to the arriving customers. As soon as the service of a
customer is complete, the server may take a vacation with probability q
or else with probability
may continue to serve the next customer, if any (or may remain idle, in case
there is no customer in the system).
The vacation times are assumed to be general. We obtain steady state
probability generating function for queue size distributions at a random epoch
as well as at a departure epoch. Next, we derive the mean queue size and
expected busy period. |
Keywords and phrases: queue,
k phases of heterogeneous service, Bernoulli schedule, generalized
vacation time, queue size, waiting time and busy period. |
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