Stability of Parallel Queueing Systems with Coupled Service Rates
Stability of Parallel Queueing Systems with Coupled Service Rates
复制标题
耦合服务率并行排队系统的稳定性
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
Lasse Leskelä
中科院分区：
文献类型：
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作者：
S. Borst;M. Jonckheere;Lasse Leskelä
本文考虑了一个由独立到达流供给的并行排队系统，其中每个队列的服务率取决于所有队列中的顾客数。基于多类生灭过程的随机单调性和边缘漂移性质，得到了系统稳定的充分必要条件。这些条件产生一个尖锐的表征系统的稳定性，每个队列的服务率是减少在其他队列中的客户数量，并具有统一的限制，队列长度趋于无穷大。结果示出的应用程序中的稳定区域可能是非凸的。
This paper considers a parallel system of queues fed by independent arrival streams, where the service rate of each queue depends on the number of customers in all of the queues. Necessary and sufficient conditions for the stability of the system are derived, based on stochastic monotonicity and marginal drift properties of multiclass birth and death processes. These conditions yield a sharp characterization of stability for systems where the service rate of each queue is decreasing in the number of customers in other queues, and has uniform limits as the queue lengths tend to infinity. The results are illustrated with applications where the stability region may be nonconvex.