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Analysis of multi-level queueing systems with servers breakdown by using recursive solution technique

机译：递归求解技术分析服务器故障的多级排队系统

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摘要

In this paper we construct a multi-level queueing model that alternates between three modes of an operation system. The service times have followed an Erlang type K distribution with parameter μ. Customers arrive in batches according to a time-homogeneous compound Poisson process with mean rate λ for the batches. Our aim is to give a recursive scheme for the solution of the steady state equations. Next we derive some important measures of performance which may affect the efficiency of the system under consideration such as the expected waiting time per customer, the expected number of customers who arrive to a full system. The expected number of customers will also be calculated. Finally, we can also calculate the efficiency measures of the system by using the recursive results through an example.
机译：在本文中，我们构造了一个在操作系统的三种模式之间交替的多级排队模型。服务时间遵循带有参数μ的Erlang类型K分布。客户根据时间均匀的复合Poisson过程分批到达，批次的平均比率为λ。我们的目的是为稳态方程的求解提供一个递归方案。接下来，我们得出一些重要的性能指标，这些指标可能会影响所考虑系统的效率，例如每个客户的预期等待时间，到达完整系统的预期客户数量。还将计算预期的客户数量。最后，我们还可以通过一个示例，使用递归结果来计算系统的效率度量。

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