Some effects of nonstationarity on multiserver Markovian queueing systems

The authors examine the effects of nonstationarity on the performance of multiserver queueing systems with exponential service times and sinusoidal Poisson input streams. The present primary objective is to determine when and how a stationary model may be used as an approximation for a nonstationary system. The authors focus on a particular question: How nonstationary can an arrival process be before a simple stationary approximation fails? The present analysis reveals that stationary models can seriously underestimate delays when the actual system is only modestly nonstationary. Other findings include confirmation and elaboration of S.M. Ross’s conjecture that expected delays increase with nonstationarity, and the identification of easily computed and tight lower and upper bounds for expected delay and the probability of delay. These empirical results are based on a series of computer experiments in which the differential equations governing system behavior are solved numerically.