服务中断渐近可忽略的G/M/n/m+M模型的高负荷极限

Heavy-traffic Limits for G/M/n/m + M Queueing Models with Symptotically Negligible Service Interruptions

为更切合实际,本文将G/M/n+M队列扩展到有限等待空间,在等待空间有限的情况下考虑服务中断对队列系统的影响.假设服务中断是渐近可忽略的,应用鞅和连续映射定理,得到了队长过程的FCLT,其极限是有跳跃的随机积分方程的分段唯一解.结果表明服务中断的影响是由刻画队长过程极限的跳跃来体现的,即在等待空间有限的情况下也能得到类似结论.

For the practical purpose, this paper extends G/M/n＋M queue to the finite-capacity case and discusses the service interruptions’ effect to the queuing system when the capacity is finite. Assuming that the service interruptions are asymptotically negligible, by applying the martingale and continuous mapping theorem, we obtain the FCLT for the queue-length process, where the limit is characterized as the pathwise unique solution to a stochastic integral equation with jumps. The results indicate that the effects of service interruptions are reflected by the jumps which scaled the queue-length process limits, in other words, we can derive the similar conclusions in the finite-capacity case.