Asymptotic behavior of the loss probability for an M/G/1/N queue with vacations

TL;DR

This paper investigates the asymptotic behavior of loss probabilities in an M/G/1/N queue with server vacations, providing exact rates for different traffic intensities and extending results to related queue models.

Contribution

It offers new asymptotic results for loss probabilities in M/G/1/N queues with vacations and extends these findings to the dual GI/M/1/N model.

Findings

Derived exact asymptotic rates for loss probability under various traffic intensities.

Extended asymptotic results to the standard M/G/1/N queue without vacations.

Provided asymptotic properties for the dual GI/M/1/N queue model.

Abstract

In this paper, asymptotic properties of the loss probability are considered for an M/G/1/N queue with server vacations and exhaustive service discipline, denoted by an M/G/1/N -(V, E)-queue. Exact asymptotic rates of the loss probability are obtained for the cases in which the traffic intensity is smaller than, equal to and greater than one, respectively. When the vacation time is zero, the model considered degenerates to the standard M/G/1/N queue. For this standard queueing model, our analysis provides new or extended asymptotic results for the loss probability. In terms of the duality relationship between the M/G/1/N and GI/M/1/N queues, we also provide asymptotic properties for the standard GI/M/1/N model.