The paper studies a multiserver retrial queueing system with $m$ servers.Arrival process is a point process with strictly stationary and ergodicincrements. A customer arriving to the system occupies one of the free servers.If upon arrival all servers are busy, then the customer goes to the secondaryqueue, orbit, and after some random time retries more and more to occupy aserver. A service time of each customer is exponentially distributed randomvariable with parameter $\mu_1$. A time between retrials is exponentiallydistributed with parameter $\mu_2$ for each customer. Using a martingaleapproach the paper provides an analysis of this system. The paper establishesthe stability condition and studies a behavior of the limiting queue-lengthdistributions as $\mu_2$ increases to infinity. As $\mu_2\to\infty$, the paperalso proves the convergence of appropriate queue-length distributions to thoseof the associated `usual' multiserver queueing system without retrials. Analgorithm for numerical solution of the equations, associated with the limitingqueue-length distribution of retrial systems, is provided.
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机译：本文研究了具有$ m $个服务器的多服务器重试排队系统。到达过程是一个具有固定和遍历增量的点过程。到达系统的客户占用了其中一台空闲服务器。如果到达时所有服务器都处于繁忙状态，则该客户进入次要队列，进入轨道，并且经过一段时间的随机重试后越来越多地占用服务器。每个客户的服务时间以参数$ \ mu_1 $呈指数分布。重试之间的时间与每个客户的参数$ \ mu_2 $呈指数分布。本文使用a方法提供了对该系统的分析。本文建立了稳定性条件，并研究了随着$ \ mu_2 $增加到无穷大，限制队列长度分布的行为。作为$ \ mu_2 \ to \ infty $，本文还证明了适当的队列长度分布与相关的“常规”多服务器排队系统的收敛，而无需重试。提供了与重试系统的限制队列长度分布相关的方程式数值解的算法。
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