M/M/1 Queueing System with Delayed Controlled Vacation
An M/M/1 queue with delayed vacation is studied. If the server
has been idle for a period of time (called the delay time), the
server begins an exponentially distributed vacation which is repeated
as long as the number of customers in the system remains less than some
number K. For the cases of exponential and deterministic delay time,
exact expressions for the steady state probability
distribution are obtained, together with associated performance measures.
System optimization is also considered; values of K are given which
minimize the average total cost per unit time, and it is shown that
the optimal delay period is either 0 (no delay) or infinite (no vacation),
in case of Poisson arrivals.
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