Stochastic Monotonicity of the Output Process of Parallel Queues.

Abstract

This paper considers the output process of a system of K DOT /M/I queues in parallel with Bernoulli routing of jobs upon arrival. It is shown that the output process is stochastically increasing as the routing probabilities approach 1/K in a certain sense. The proof crucially depends on the fact that the absolute value of a simple random walk is a time-homogeneous birth and death process.