带负顾客和不耐烦顾客的离散时间Geo/G/1重试排队

A discrete-time Geo/G/1 retrial queue with negative customers and impatient customers

考虑了一个带负顾客和不耐烦顾客且重试时间为一般分布的离散时间Geo/G/1重试排队系统.负顾客带走一个正在服务的顾客,而对重试组中的顾客无影响.正顾客到达系统若遇服务器忙则可能进入重试组也可能离开系统.通过对此排队系统的嵌入马氏链进行分析,得到了重试组队长和系统队长的概率母函数.进而得到了一系列重要的排队指标.此外,还推导出了系统的稳态存在条件.以及对无负顾客和不耐烦顾客时的待例进行了分析.最后通过几个具体的数值实例演示了一些参数对系统关键性能指标的影响.

We consider a discrete-time Geo/G/1 retrial queue with negative customers and general retrial times. Negative customers will make the customer being in service lost but has no effect to the orbit. When the server is busy, the arriving positive customers either enter the orbit or leave the system. We analyze the Markov chain underlying the considered queueing system. The system state distribution as well as the orbit size and the system size distributions are obtained in terms of their generating functions. These generating functions yield exact expressions for some important performance measures. Besides, the stability condition of the system is derived. Further, the special case of no negative customers and no impatient customers is discussed. Finally, some numerical examples are provided to illustrate the impact of several parameters on some crucial performance characteristics of the system.