Shortest Expected Delay Routing for Erland Servers (Condensed Version of 93-38)

摘要

The queueing problem with Poisson arrivals and two identical parallel Erlangservers is analyzed for the case of shortest expected delay routing. The problem may be represented as a random walk on the integer grid in the first quadrant of the plane. The approach presented in the paper directly solves the equilibrium equations. It is shown that the equilibrium distribution of the random walk can be written as an infinite linear combination of products. The results can be used for an efficient computation of performance criteria, such as the waiting time distribution and the moments of the waiting time and the queue lengths.