负顾客的M/G/1排队系统

M/G/1 Queuing System of Negative Customers

主要探讨了两类负顾客的M/G/1排队系统,一类是先到先服务(FCFS),另一类是后到先服务(LCFS).特别地,负顾客抵消排队系统中的中间顾客(RCM).由补充变量法和状态转移方程分析得到瞬态队长L-Z变换和稳态队长概率母函数表达式,并且发现此类排队系统完全取决于队长为2的概率.

M/G/1 queuing system for two types of negative customers is discussed. One is that those who first come are first served (FCFS). The other is that those who come late are first served (LCFS). Especially, the negative customers remove those in the middle of the queuing systme. With the methods of supplementary variables and the analysis of state transition function, L-Z transformation of transient queue length and the expression of probability generating function of steady-state queue length are obtained. It is also found that this type of queuing system depends completely on the probability that the queue length is 2.