Bulk Queuing Process Of Markov Skeleton Process Approach

In this thesis, we discuss one special type of queuing process—Bulkqueue, which is also called GI^(X)/G^(Y)/1 queuing process.Bulk queue is one special type of queuing system, in whichcustomers arrive in groups of random size by a server in batches ofrandom size. In practical problems, we often encounter this queuingprocess. For example, in the bus station, the passengers arrive in groupsand leave in batches, so the number of passenger waiting for the bus atthe station is a Bulk queue.The tool we use to solve the problem is Markov Skeleton Process,which is firstly put forward by Prof. Hou zhenting and his colleagues in1997.The process contains many extant classical stochastic processmodels, such as Markov process, semi-Markov process, piecewisedeterministic Markov process etc. They have important value in theoryand application. Prof. Hou zhenting and his colleagues have successfullysolved a series of classical difficult problems of transient distribution,steady-state distribution, ergodicity in queuing system, meanwhile posedmany new problems and new thoughts. Recently, the theory has gotcomplemented and perfected.In the queuing theory, the Markov Skeleton Process theory hasalready demonstrated its effectiveness and superiority than the other.Many difficult issues have been well settled. For example, the transient distribution of queue length and waiting time of GI^X/G^Y/n queuingsystem, and the transient distribution of queue length of queuingnetworks. With its increasingly intensive application in the queue theory,the Markov Skeleton Process theory will play a greater role in facilitatingthe development of queue theory.In this thesis, we obtain the transient distribution of queue length ofbulk queuing system. And for a special case (Y≡1, which is also wrote asGI^X/G/1 queuing process), we give a further discussion, and obtain itstransient distribution of queue length, steady-state distribution, ergodicityand the existence conditions.