Research On Steady State Performance Of Two-server Queuing Systems With Bernoulli Vacation Schedule

Queueing system with vacations has wide applications in communication system,transportation system, computer and storage system. Bernoulli vacation policy is a typicalvacation policy. It is applied not only in the daily life, but also in the wirelesscommunication system, strobe control system, computer technology and public services.The thesis considers the Bernoulli vacation policy with two servers in queuing system.Firstly, the steady-state probability of the Bernoulli vacation policy with twodifferent servers in queuing system is studied. By using quasi birth and death process andthe matrix-geometric solution, the transition rate matrix and the stability condition areobtained, and the steady-state probability vectors are analyzed by block matrix. Theiterative expressions of the steady-state probability vectors are obtained, and numericalanalysis is given.Secondly, the distribution of the length of the queue under the Bernoulli vacationpolicy with two different servers in queuing system is studied. On the basis of thematrix-geometric solution of the steady-state probability, the expressions of the average ofthe length of the queue and the probability distribution of busy servers are obtained. Somespecial situations are discussed. In the case that only one server can take a vacation, thenthe steady state indicators are given. Under the significance of the average length of thequeue, the different vacation policies are considered, and some comparative results areobtained by numerical analysis.Finally, the average of busy period and waiting time of the two different serversvacation queuing system with Bernoulli vacation policy are studied. The average of busyperiod is obtained by quasi birth and death process, the analysis of transition probabilityand Laplace-Stieltjes (LS) transform. A new quasi birth and death process is defined bythe introduction of absorbing state, then the LS transform of the distribution of waitingtime and the expression of average waiting time are given.