The Continuous Time Queue With Vacation And Set-up Time And Second Optional Service

Vacation queue is the expansion and development of the classic queuing theory.In 1980s,vacation queue had been developed into a study direction with distinguishing features,and formed a basic theoretical framework,whose core was stochastic decomposition.Now it has been widely used in computer systems,communication systems,manufacturing systems,electronic commerce and manufacture line etc.Queues with"the second optional service"have been widely used in manufacture and practice.A characteristic of this kind of queuing phenomenon is that all customers have to accept the first certain service,some of them will accept the second optional service with fixed probabilities after the first service,the others will leave the system directly. The M/G/1 queue system with set-up time,second optional service and vacation is discussed in this paper.Compared with the research of predecessor,we will combine the set-up time,second optional service with vacation strategy in this paper.Firstly,we comprehensively introduce the basic knowledge concerning the subject,then the M/G/1 queuing model with second optional service is considered.Using the broad sense service time and imbedded Markov chain method,the generating function of the steady state queue length,the LST of waiting time and the busy period are derived.Meanwhile,the particular case of the model is obtained.Secondly,based on the preceding chapter of model foundation,we study the M/G/1 queuing model with set-up time and second optional service and multiple(single) vacation.We explicitly describe the model respectively.By means of the broad sense service time and imbedded Markov chain method,we obtain the transition probability matrix of the system,further- more,the generating function of the steady-state queue length ,the LST of the waiting time and their stochastic decomposition results are deduced,in addition,we analyze the busy period and busy circulation of every model.And finally,the corresponding exceptions of the model are given,and the model is verified by numerical example.