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Self-help Service System With Bulk Arrival

Posted on:2014-01-17Degree:MasterType:Thesis
Country:ChinaCandidate:J M YuanFull Text:PDF
GTID:2250330425470942Subject:Probability theory and mathematical statistics
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In this thesis, we consider self-help service system with bulk arrival. The single system and two systems are discussed. In the case of single system, we discuss three cases:absorbing state, steady state, and instantaneous state. Each case is investigated in detail. In the case of two systems, queue length behavior is examined and the service ratio of each system is presented. This thesis mainly includes four parts:The first chapter is the introduction. The historical background of the research problem, the research status and the main content of this paper are expounded. Markov chain is a kind of very important stochastic processes, it plays an important role in queuing theory. Queuing theory is very important and widely used in real life. In this chapter, we illustrate the development of queuing theory and the model of this thesis.In the second chapter, some knowledge needed in this thesis is summarized. Most of them are the general theory of markov process, including the basic concepts and properties of markov chain and markov transition function, the nature and significance of the Q-matrix, the nature of the Q-function and resolvent and the concept of ergodicity, which plays an important role in the later chapters.In the third chapter, the regularity of self-help service system with bulk arrival is studied. We first consider the model with absorbing state 0. Explicit expressions for the absorbing probabilities and mean absorbing times are presented. A simple conclusion is given for this criterion. If there is no absorbing state, the recurrence and ergodicity are examined. Equilibrium behavior is studied and the probability generating function of the equilibrium distribution is obtained. In addition, we also consider the existence of the process if there is instantaneous state.In the forth chapter, two self-help service systems with bulk arrival is first investigated. Customers can move from one system to another. The average time from any state to the other and service ratio of each system are obtained.
Keywords/Search Tags:Markov process, regularity, absorbent, recurrence, equilibrium distribution
PDF Full Text Request
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