Perturbation analysis of waiting times in the G/G/1 queue

Authors:
Haralambie Leahu;Bernd Heidergott;Arie Hordijk
Affiliations:
Vrije Universiteit Amsterdam, Amsterdam, Netherlands;Vrije Universiteit Amsterdam, Amsterdam, Netherlands;Leiden University, Leiden, Netherlands
Venue:
Discrete Event Dynamic Systems
Year:
2013

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Abstract

This paper is devoted to perturbation analysis of the stationary distribution of waiting times in the G/G/1 queue with a parameter-dependent service time distribution. We provide sufficient conditions under which the stationary distribution is Lipschitz continuous and we explicitly compute the Lipschitz constant. Thereby, we provide bounds on the effect of a (finite) perturbation of the service time distribution on the stationary waiting time. The case of infinitesimal perturbations (read, derivatives) is treated as well.