We consider a multi-class multi-server retrial queueing system. Customers of each class arrive from outside the system according to a Poisson process. The service times for each class of customers are assumed to be exponentially distributed with service rates depending on both the customers’ class and the servers. We define the offered load and provide stability and instability conditions for this retrial queueing system. The stability result can be obtained by introducing artificial primitive processes and using the fluid limit approach.

中文翻译：

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服务时间取决于类别和服务器的多类多服务器重试排队系统的稳定性

我们考虑一个多类多服务器重试排队系统。根据泊松过程，每个类别的客户从系统外部到达。假设每一类客户的服务时间与取决于客户类别和服务器的服务费率呈指数分布。我们定义了提供的负载，并为这个重试排队系统提供了稳定性和不稳定性条件。稳定性结果可以通过引入人工原始过程和使用流体极限方法来获得。