Geo/Geo/1Queue Model With Working Vacation And Negative Customer

Working vacation queue system has got much attention and become a research focussince Servi and Finn firstly introduced working vacation policy. The working vacationpolicy means that the servers continue to serve at a lower rate rather than stop serviceduring the vacation, which can not only reduce the loss that the impatient customers leavesthe queue because of waiting in a long time, but also improve the economical efficiency.The research on working vacation not only develops the theory of classical stochasticservice system, but also expands the foreground for the application of the queue theory inmany high-tech fields. At the same time, literatures regarding queueing models incorpora-ting negative customers are extensively discussed by researchers worldwide. In our life,negative customers are pretty common phenomenon. Therefore, to study the queueingsystem with working vacation and negative customers has very important practicalapplication and theoretical significanceIn this theory, a Geo/Geo/1queue with multiple working vacations in whichcustomers are either “positive” or “negative” is studied, negative customers need notaccept service and remove positive customers only one by one at the head when they areserved, which is called RCH-policy. In addition to N-policy.The results obtained improvethe conclusions in previous literatures. In this paper, we consider Geo/Geo/1varied queuewith multiple working vacations and negative customers. The organization of the papertakes three parts as follows：Firstly, this paper deals with a Geom/Geom/1queue system with multiple workingvacations in which customers are either “positive” or “negative”, in addition to N-policy.The embedded Markov chain method is used to obtain the state transferring probabilitymatrix. Using matrix-geometric solution method, the paper gains concise expressions ofthe steady state distributions for queue length and conditional waiting time and obtain theresult of stochastic decomposition of the queue length and waiting time.Secondly, this paper deals with a Geo/Geo/1queue with multiple working vacationsin which customers are either "positive "or "negative", in addition to set-up time. An embedded Markov chain is used to obtain the state transferring probability matrix, Weobtain the generating function of queue length and waiting time and gain the conciseexpressions of stochastic decomposition of the queue length and waiting time.Finally, the numerical results of the model are presented, which straightlydemonstrates the effect of different system parameters on the steady-state queue lengthand waiting time in this paper.