On interchangeability for exponential single-server queues in tandem

Abstract

Consider two exponential single-server queues in tandem and suppose that service rates of customer n are λ n and μ n respectively. In this note, a simple and direct proof is given of the fact that the departure process from the tandem queue is statistically unaffected when the service rates are interchanged if λ n – μn is independent of n. The proof is based only on the memoryless property of exponential distributions.