Analysis of the loss probability in the M/G/1+G queue

We consider the loss probability in the stationary M/G/1+G queue, i.e., the stationary M/G/1 queue with impatient customers whose impatience times are generally distributed. It is known that the loss probability is given in terms of the probability density function v(x) of the virtual waiting time and that v(x) is given by a formal series solution of a Volterra integral equation. In this paper, we show that the series solution of v(x) can be interpreted as the probability density function of a random sum of dependent random variables and we reveal its dependency structure through the analysis of a last-come first-served, preemptive-resume M/G/1 queue with workload-dependent loss. Furthermore, based on this observation, we show some properties of the loss probability.

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