Priority queue and its applications to traffic control

Abstract

Retrial queueing system (or queue with repeated calls, queue with returning customers) is characterized by a feature that if the arriving customers find all servers busy, then the blocked customers leave the system temporarily and reattempt their requests after a random amount of time. Due to the retrial phenomena, it has many applications in telephone switching systems, computer system and networks, and wireless telecommunication. Priority schemes are necessary to satisfy the Quality of Services(QoS) of multiple classes of traffic. For lower loss, Push-Out priority is implemented and for shorter delay, HOL priority is implemented in this thesis. We investigate the M/M/c retrial queues with geometric loss and feedback, and the $MMPP_1$, $MMPP_2/G_1$, $G_2/1/$ with wixed Push-Out and HOL scheme. We obtain the analytic solution of queue length distribution and loss probabilities. In Chapter 1, we introduce the queueing system, the retrial queue and the priority queue. We explain the $MMPP$ which is the input traffic of our model, and explain the types of traffic modeling and some schemes of traffic control in Asynchronous Transfer Mode(ATM) networks. In Chapter 2, we study the M/M/c retrial queues where the number of reattempts is restricted to one time. We find the joint distribution of the number of busy servers and the number of customers in the retrial group in steady state for c=1, 2. We also obtain the expected number of busy servers, the expected number of customers in the retrial group and the loss probability. In Chapter 3, we study the M/M/c retrial queue with geometric loss and feedback. We obtain the steady state probability distribution of queue lengths. In Chapter 4, we analyze the $MMPP_1, MMPP_2/G_1, G_2/1/K+1$ queue with mixed Push-Out and HOL scheme. By the method of the classical imbedded Markov chain and the semi-Markov process, we obtain the queue length distribution of the imbedded Markov chain at the service completion point, that of the se...