Discrete-Time Retrial Queueing System With Vacation Policy And Negative Customers Arrival

The twenty-first Century is the era of information technology,the application of computer network in all areas.With the development of computer network communication technology,discrete time queueing system has also been studied.In the discrete time queueing system,the time axis is divided into equal intervals,from all events scattered time queuing sys-tem in(the customer arTival or departure)it can only happen in points.According to the time gap entrance protocol,a discrete time queuing system can be divided into three different model-si first to the system,has a direct entrance to the system,a late delayed entrance late system.The discrete time queue has been widely used in asynchronous transfer mode,ATM system and the integrated digital network B-ISDN system.This dissertation will leave research strategies and negative customers is applied to discrete time queuing model,and studied the following two discrete time retrial queue system models:(1)We consider a different arrival rate Geo/Geo/1 retrial queue with negative customers and working vacations.The server works at a lower service rate in a working vacation peri-od.Assume that the customers waiting in the orbit request for service with a constant retrial rate,Negative customers offset the customers of receiving the service.By using the quasi birth and death process and the generating function technique we get the probability generating function of the joint distribution of the customer number in the orbit and the server's state under the steady state.Moreover,some queuing performance measures such as the steady state distribu-tion of the customer number in the orbit are obtained.Furthermore,some special cases of our model are discussed.Finally,numerical examples are given to illustrate the effects of some parameters on some main performance measures of the system and the important value of the steady state queue length distribution in the system capacity optimal design.(2)We consider a Geo/G/1 retrial queue with negative customers where the retrial time has a general distribution and the server is subject to Bernoulli vacation policy.There is no waiting position in the server,and a new arriving customer finds the server is busy or at vacation,he will join the orbit to retry getting the service,if the server is free,he will accept service at once.It is assumed that negative customers offset the customers of receiving the service.The server after each service completion begins a single vacation with probability ?(0 ? ? ? 1)or begins to another service with probability ?=1-?.Employing the supplementary variable method and the generating function,the equilibrium equations of the evolution of the system are derived,and the stationary distribution of the embedded Markov chains and a series of queueing indices are obtained.Finally some numerical examples are provided to illustrate the impact of several parameters on some performance characteristics of the system.