Abstract:
We consider a queueing system $M|G|1$ with possible vacations in server
operations for principal customers (for example, if a server is leased).
A cost optimization problem is solved. As control parameters, we use the
probability $\alpha$ of the vacation and its duration. Under fairly general
assumptions about the system behavior during vacations, we show that the
optimal value of the probability $\alpha$ is either 0 or 1. We also give
necessary and sufficient conditions for a vacation to be carried out, i.e.,
$\alpha=1$. With constant vacation durations, we find conditions such that
$\alpha=1$, and the vacation duration is optimal. Two examples are
considered. In the first example, the revenue from the vacation is a linear
function of its duration, and, in the second example, the revenue is
a quadratic function.
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