Analysis Of Queueing Systems With Working Vacation And Markovian Arrival Process

In this thesis, we study the queue with Markovian arrival process and some working vacation policies, which include the policy of working vacations and vacation interruption, the single working vacation and the variant of multiple working vacations. The thesis is organized as follows.In chapter 2, an M/G/1 queue with working vacations and vacation interruption is analyzed. The necessary and sufficient condition for the stability of the system is derived. We obtain the queue length distribution and service status at an arbitrary epoch under steady state conditions by using the method of a supplementary variable and the matrix-analytic method. Further, we provide the Laplace-Stieltjes transform (LST) of the stationary waiting time. Finally, numerical examples are presented.In chapter 3, we discuss an M/G/1 queue with single working vacation. Using the method of supplementary variable and the matrix-analytic method, we obtain the queue length distribution and service status at the arbitrary epoch under the steady state conditions. Further, we derive expected busy period and expected busy cycle. Finally, several special cases are presented.In chapter 4, we analyze the GI/M/1/N queue with a variant of multiple working vacations. We analyze the Markov chain underlying the considered queueing system and obtain the transition probabilities. We obtain the queue length distribution at pre-arrival and arbitrary epochs with the method of supplementary variable and the embedded Markov chain technique. Finally, several performance measures and numerical results are obtained when the parameterH=1.In chapter 5, we consider the MAP/G/1 queue with working vacations and vacation interruption. We obtain the queue length distribution with the method of supplementary variable, combined with the RG-factorization and censoring technique. We also obtain the system size distribution at pre-arrival epoch and the LST of waiting time.In chapter 6, we discuss the BMAP/G/1 retrial queue with feedback and starting failures. If an arriving customer finds the server busy or down, the customer leaves the service area and enters the orbit and makes a retrial at a later time.When a customer is served completely, he will decide either to join the orbit again for another service with probability p or to leave the system forever with probabilityq=1-p. We obtain the queue length distribution with the method of supplementary variable, combined with the RG-factorization and censoring technique. The mean length of the system busy period of our model is obtained by the theory of regenerative process.