The Pointwise Stationary Approximation for Mt/Mt/s Queues Is Asymptotically Correct As the Rates Increase
验证了Green等人的猜想：对于具有正弦到达率的多服务台马尔可夫队列，当服务率和到达率增加且瞬时业务强度固定时，点态平稳近似（PSA）在长期平均性能指标上是渐近正确的。
Green, Kolesar and Svoronos (in press) and Green and Kolesar (in press) use numerical methods to investigate the behavior of multiserver Markov queues with a Poisson arrival process having a sinusoidal arrival rate. For this model they propose an approximation for long-run average performance measures called the pointwise stationary approximation (PSA), which consists of an appropriate weighted average of the performance measure that would result at each point in time if the system were stationary with the arrival rate that applies at that point in time. In this paper we verify their conjecture that PSA is asymptotically correct as the service and arrival rates increase with the instantaneous traffic intensity held fixed (corresponding to long arrival rate cycles). We actually establish both pointwise and average versions of this result for general time-dependent birth-and-death processes.