Tandem queues with non-stationary arrivals.

We consider a network of K queues in tandem labeled Q1,Q2, .., QK. The arrivals to Q1 form a non-homogeneous Poisson process whose intensity is periodic. We conjecture that asymptotically the arrival process Aj to Qj, j = 1, 2, .., K is cycle stationary. In addition, we conjecture that asymptotically as j gets larger, the arrival process at the jth queue gets closer to a stationary point process. Hence, the queue performance measures become more stationary as j increases. We perform Monte-Carlo simulations and design statistical tests whose results support the conjecture.