Queues with Markovian arrival and service processes, i.e., MAP/MAP/1 queues, have been useful in the analysis of computer and communication systems and di erent representations for their stationary sojourn time and queue length distribution have been derived. More speci cally, the class of MAP/MAP/1 queues lies at the intersection of the class of QBD queues and the class of semi-Markovian queue...

We consider a bulk service G I / M / l queue with service rates depending on service batch size. If there are n customers waiting at the completion of service, min(n, I\) customers enter service. We show that the queue size and the service batch size at points of arrivals form an embedded Markov chain and the steady-state probabilities of this Markov chain have the matrix geometric form. We des...

We consider a basic cold standby system attended by a single repairman. The system satisfies the usual conditions (i.i.d. random variables, perfect repair, instantaneous and perfect switch, queueing). The operative unit has a constant failure rate and an arbitrary repair time distribution. We analyse the idle time of the repairman during the survival time of the system. Finally, as an example, ...

This thesis is based on some applications of Markov chains and decision processes for performance analysis ofcongestion avoidance algorithms and power control. First, we study the behaviour of the window size of an MIMDcongestion control algorithm when subject to different loss processes. We show that the logarithm of the embeddedwindow size follows an additive recursive equation, w...

We consider a single-server queueing system with Poisson arrivals and general service times. While the server is up, it is subject to breakdowns according to a Poisson process. When the server breaks down, we may either repair the server immediately or postpone the repair until some future point in time. The operating costs of the system include customer holding costs, repair costs and running ...

Lin & Kumar [2] introduced a control model with a single queue and two heterogeneous servers. They showed, using policy iteration, that the slower server should only be used if the queue length is above a certain level, i.e., the optimal policy is of threshold type. In this note we give a simple iterative proof of this result. AMS Subject Classification (1991): 90B22, 90C40

Queueing network models have proven to be very useful in the analysis of communication systems. The departure process of a queue in a queueing network is of special interest because it is the arrival process to other queues in the network. For high speed networks, correlation and burstiness are very important factors for system performance and thus the smooth Bernoulli process is no longer a go...

This paper presents an algorithmic procedure to calculate the queue length and delay distribution of customers in a discrete time D-MAP/PH/1 queue, where the service time distribution of a customer depends on the inter-arrival time between himself and his predecessor. Setting up a Markov chain that keeps track of the contents of such a queue will result in a state space explosion as the inter-a...

AblJract Two queues are fed by independent, time-homogeneous Poisson arrival processes. One server is available to handle both. All service-durations, in both queues, are 'drawn independently from the sarpe distril?uUon. A ~etup time is. incurred whenever the server moves (switches) from one queue to the other. We prove that in order to minimize the sum of discounted setup charges and holding c...