Monotone effect of dependency between interarrival and service times in a simple queueing system

Authors:
Xiuli Chao
Affiliations:
Division of Industrial and Management Engineering, Department of Mechanical and Industrial Engineering, New Jersey Institute of Technology, Newark, NJ 07102, USA
Venue:
Operations Research Letters
Year:
1995

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Abstract

Most practical queueing systems have dependencies between arrival and service patterns. In this paper we consider a simple queueing system with interarrival and service times having bivariate exponential distribution. With the marginal distributions of both interarrival and service times fixed, we study the effect of the dependency, which is defined as the correlation coefficient between the interarrival and service times, on the system performance. We show that the customer waiting time is monotonically decreasing in the dependency in increasing convex ordering sense. This result is consistent with the numerical findings reported in the literature.