M/G/1Queuing System With Bernoulli Feedback And Working Vacations

Working vacation queue has become a research focus since Servi and Finn firstlyintroduced the working vacation queue. The character of working vacation queue is that,the server continues to work with a lower speed, but not completely stop service duringthe vacation time, which can reduce the loss and dissatisfaction from customers, but alsoimprove the operating efficiency. The research on working vacation queue not onlyinfused the energy and viability for the development of the theory of classical stochasticservice system, but also expanded the foreground for the application of the queue theory inthe various up-to-date technical fields, such as, optical fiber communication, stochasticnetwork, computer system and manufacturing system.In this thesis, a continuous time M/G/1queueing system with working vacation isconsidered. Based on the classical M/G/1queueing system, set-up time and Bernoulli feedback are introduced. The results obtained expand and improve the conclusions in previousliteratures and enrich the contents of the queueing system.Firstly, the development history and current state of queueing theory and vacationqueue be described, their applications in the up-to-date technical fields are also introduced.Furthermore, Markov chain and the M/G/1-type matrix queue be introduced simply, aconcise review about the study methods of M/G/1queue with set-up time is given, whichprovide a preparation for our model analysis in theory.Secondly, we discuss the M/G/1queue with multiple working vacations and set-uptime. By using M/G/1-type structure matrix method, the distribution of the stationaryqueue length and waiting time are derived, the corresponding stochastic decompositionresults are also obtained. Furthermore, some numerical examples of the model are gainedby MATLAB software and the feasibility of application of the model we studied is proved.Subsequently, the M/G/1single working vacation queue with set-up time be studied.By exercising matrix-geometric solution method, we obtain the distribution of thestationary queue length and waiting time, the corresponding stochastic decompositionresults are also obtained. The theory results of working vacation are enriched. Finally, various numerical examples are presented to compare the two differentmodel and the system optimization is facilitated.