有一般服务运作和休假时间的排队系统

Queueing system with general operation and vacation time

考虑一个有一般服务运作和休假时间的M/M/1排队系统.这时服务是非空竭的,也就是说服务员可能在系统有顾客的情形下进入休假.服务员的运作时间和休假时间都为一般分布,且相互独立.使用补充变量的方法,求解出系统稳态队长的母函数.在求解过程中遇到的未知函数p0(x),可利用第一类Fredholm积分方程的数值解来确定.最后给出了系统稳态平均队长.

An M/M/1 queueing system with general operation and vacation time is considered.The server is nonexhaustive,that is to say,server may be in vacation when the system is not empty.The probability generating function of queue length under stability is obtained by supplementing variables,where, p\-0(x) may be found numerically by solving first kind Fredholm integral equation.At last,the expected value of queue length is obtained.