On Niu's Conjecture for Two-Station Tandem Queues

Abstract

In this paper, we prove a long standing conjecture in queueing theory made by Niu (1980): in a two-station tandem queueing system with constant service time (c) at station 1, the stationary average waiting time at station 2 is nonincreasing in c. Two very different proofs are provided: one for the general case and one for a special case in which the arrival process is Poisson and the service time at station 2 is exponential.