Single Vacation Mmpp (2) / G / 1 Queuing System

In this paper, the MMPP(2)/G/1 queuing system with exhaustive service and single vacation is researched, that is, customers arrive according to an Markov-modulated Poisson process with two states. The queuing systems with vacation that customers arrive according to Poisson process have been extensive studied, but the systems with customers arrive according to an Markov-modulated Poisson process with two states, that is MMPP(2)/G/1 queuing system with single vacation, have not been studied in open literatures.The whole thesis includes three chapters. In the first chapter, the development history of the queue theory, the vacation queue theory, and the research status of MMPP were shown. In the second chapter, the basis of theoretical knowledge of the queue theory were introduced which would be used in this paper. In the third chapter, the MMPP(2)/G/1 queuing system with single vacation was studied. With regarding customer immediate leaving and retarding numbers customers in the system as top of observation, the Markov chain imbedded in which the customer arrived and its transition probability matrix were given. Then, the generating function of the queue length was obtained by analysing the queuing system. And the mean queue length was given by the character of the generating function. The mean waiting time, the mean staying time, and the average amount of customers being served in the period of MMPP(2)/G/1 queuing system with single vacation were obtained by LST theory. And the period of queuing system is further analyzed.