The Discrete Time Queueing With Multiple Vacation And Batch Arrive

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 multiple vacation bulk reached with the queuing system start-up time in life and production can be found everywhere. Customers in this paper will arrive at discrete time and batch multiple vacation leave with start-up time queuing for research. On this model and the results of analysis of this model in other yet to be seen in the literature.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 module.The full text is divided into four chapters. The first chapter of topics related with the basic knowledge, and recalling the history of the queue on vacation, pay attention to the development of the status quo, thesis research also indicates that the use value.The second chapter of the study model is the basic assumption that customers using embedded in the Markov chain leave moment, the system is given step transition probability matrix, and introduced the classic GeomX/G/1 leave queuing model, the model for the analysis behind the relevant indicators were prepared. Foster invoked the third chapter criteria of the model system analysis conditions for the existence of steady-state distribution, the use of embedded Markov chain step transition probability matrix, derived from the start-up time with multiple vacation GeomX/G/1 queuing system captain of the steady-state distribution and several customers waiting for the distribution to prove that the corresponding stochastic decomposition theorem.The fourth chapter derived steady-state model of some relevant indicators also discussed the steady-state model of steady-state distribution and waiting time waiting for the additional time delay...