不耐烦顾客强度为高次幂函数的M/M/C/N排队模型

M / M / C / N Queuing Model Taking Impatient Customers Strength as High Order Power Function

在现有文献中讨论具有不耐烦顾客排队模型较多,记αk为系统中排队等待服务的顾客为k个时,系统中不耐烦顾客离开系统的强度,文献[1]作者中讨论了以离开强度αk=kδ,δ≥0离开的M/M/C排队模型;文献[2]中讨论了强度ak=k2δ,δ≥0离开的M/M/1情况;文献[11]中讨论了强度为αk-k2δ,δ≥0离开的M/M/N情况;将讨论不耐烦顾客强度αk=knδ,δ≥0的多服务窗混合制M/M/C/N排队模型;特别地,当参数取特殊值时,就能得到上述文献中一系列结论。

In the existed literatures, there are many discussions on queuing model about impatient customers, αk is marked in the system as the strength which the impatient customers leave the system when the number of the customers in the system who queue to wait for the service is k. In reference [ 1 ], the author discusses the leavingM/M/C queuing model by taking leaving strength αk=kδ,δ≥0,furthermore, in reference [ 2] ,the leaving M/M/1situation is discussed when the strength αk=k2δ,δ≥0, and in reference [ 11 ], the leaving M/M/N situation isdiscussed when the strength αk=k2δ,δ≥0. This paper discusses multi-service windows mixed M/M/N queuingmodel when the impatient customers strength αk=knδ,δ≥0, especially when the author takes special value ofparameters, a series of conclusions in the above mentioned references can be obtained.