Study For Optional Services And Optimization Strategy Of Continuous Time Vacation Queue

In the1970s, vacation queue system as an extension of the classical queueing systemsolves the problems when the system behavior changes with the state parameter. Someproblems can not be solved only by classical queueing system. In the vacation queuesystem, service station can not receive customers according to some strategy. The researchof it helped the systems save the service facilities, and optimize the service design, andmake the control of the system have more flexible space. What’s more, with thedevelopment of economic, competitions in market becomes more and more intense.People have more requires and choices of goods and services, so as to the profits andbenefit. Therefore the introduction and research of different strategies of vacation queuesystem become more and more important.In this theory, we focus on the classical continuous time vacation queue with differentstrategies, such as: second optional service, working vacation, N-policy, optimal servicestrategy. The organization of the paper takes three parts as follows：Firstly, this paper deals with the M/M/1queue model with multiple vacations andsecond optional service. By introducing a two-dimensional Markov chain, analyzing theconditions of the model, we get its QBD, and by using matrix-geometric method, we getthe probability distributions of the stationary indices. Moreover, we derive the stochasticdecomposition results of the queue length and conditional waiting time.Secondly, this paper deals with an M/M/1working vacation queue with secondoptional service and N-policy, using the QBD and matrix-geometric method, we get themain parameters of the statement. We also prove the conditional stochastic decompositionstructures of queue length and waiting time, gain the distributions of the additional queuelength and additional delay. We present the numerical example to describe the changetendency of performance indices with parameters.Finally, we consider the optimal strategy of the service company’s profit whichsystem is based on the M/M/c queue with vacation, in the competitive market environment.By studying the core factors such as: the customers’ expected waiting time, optimalwaiting time, the service capacity cost and so on, we obtained the optimal profit function, and research the difference of the function depending on the functional form of parameters.Then by compared the results, we get the optimization strategy.All the researches of the models are based on the reality. These results of researchesin our real life have important theoretical significance and practical application value.