Geo/Geo/1 Working Vacation Queue with Npolicy and Negative Customers

This paper is on the basis of a Geom/Geom/1 queue with multiple working vacations，in addition to negative customers，N policy and set up time.This is a new model.The results obtained the improvement of the conclusions in previous literatures.The working vacation policy means that the servers continue to serve at a lower rate rather than stop service during the vacation，which can not only reduce the loss that the impatient customers leaves the queue because of waiting in a long time，but also improve the economical efficiency.Negative customers need not accept service；remove positive customers only one by one at the head when they are served，which obeys RCH policy.An embedded Markov chain is used to obtain the state transferring probability matrix.Using quasi birth and death process and matrix geometric solution method，the paper gains concise expressions of the steady state distributions for queue length * and obtains the result of stochastic decomposition of the queue length *. (* Indicates a formula, please see the full text)