The Batch Arival Discrete Time Queue With Vacation And Set-Up And Close-Down Time

Queuing theory is an important component of operational research, originated in the early 20th century Danish mathematician, electrical engineers Erlang(A.K.Erlang) telephone conversation. Leave queue is an extension of classical queuing theory and development, initially by Levy and Yechiali(1975) study, and the reality of life in supporting work, maintenance strategy, machine malfunctions, start-up time, the Round Robin services, traffic congestion, priority such issues evoked on vacation queue research. At a certain point in time and with batch arrival queuing system in life and production can be found everywhere. Customers in this paper will arrive at discrete time and a multiple or single vacation queue system with batch arrival and set-up and close-down time will be researched. The model is of some theoretical and practical significance.The paper gives a basic assumption of the study model, by means of imbedded Markov chain, this thesis offers transition probability matrix of the system and further deduces the steady-state queue length and other corresponding steady state quota, thus stabling the theory of stochastic decomposition of the steady-state queue length and giving the special example of the model.Firstly, the paper studies the Geom/G/1 queue with multiple(single) vacation and server set-up and close-down time. We derive the generating function and the stochastic decomposition of the steady state queue length and waiting time distributions.Secondly, we extend the model above, we study the Geom X/ G /1 queue with multiple(single) vacation and server set-up and close-down time. We describe the model, by means of the embedded markov chain and transition probability matrix we get the stationary distributions for queue length and waiting time and their stochastic decomposition results.Finally, we give the special example of the model to prove the corresponding stochastic decomposition theorem.