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

Most practical queueing systems have dependencies between arrival and service patterns. This paper considers a simple queueing system with interarrival and service times having bivariate exponential distribution. With the marginal distributions of both interarrival and service times fixed, it studies the effect of the dependency, which is defined as the correlation coefficient between the interarrival and service times, on the system performance. The paper shows 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.