Balking and reneging in m/g/s systems exact analysis and approximations

Authors:
Liqiang Liu;Vidyadhar g. Kulkarni
Affiliations:
Department of statistics and operations researchuniversity of north carolinachapel hill, nc 27599–3180 e-mail: vkulkarni@email.unc.edu;Department of statistics and operations researchuniversity of north carolinachapel hill, nc 27599–3180 e-mail: vkulkarni@email.unc.edu
Venue:
Probability in the Engineering and Informational Sciences
Year:
2008

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Abstract

We consider the virtual queuing time (vqt, also known as work-in-system, or virtual-delay) process in an M/G/s queue with impatient customers. We focus on the vqt-based balking model and relate it to reneging behavior of impatient customers in terms of the steady-state distribution of the vqt process. We construct a single-server system, analyze its operating characteristics, and use them to approximate the multiserver system. We give both analytical results and numerical examples. We conduct simulation to assess the accuracy of the approximation.