Attendant Multiple Vacation N-policy M / G (a, B) / 1 Queuing System

Queue system with vacations is an important model of queue theory. In this paper, we introduced the theoretical and practical situation about queue system with vacation and queue system with repairable service station all over the world. Basing on the work of the M/G/1 queue system with N-policy and multiple vacation, two threshold values a and b are proposed. The problem of the M/G (a, b)/1 queue system with N-policy and multiple vacation is studied.In this paper, the methods of supplementary variable, direct probability and renewal process are adopted to study the M/G (a, b)/1 queue system with N-policy and multiple vacation, the results show that: 1. The expression of general function of queue length at arbitrary time t for equilibrium case2. Mean queue length of system3. Expected length of idle period4. Expected length of busy periodFinally, a cost model of the system is constructed. The numericalsolution for a particular case of the model is also presented.