Abstract We study three non-equivalent queueing models in continuous time that each generalise the classical M/M/1 queue a different way. Inter-event times all are Mittag-Leffler distributed, which is heavy tail distribution with no moments. For of we answer question being at zero infinitely often (the ‘recurrence’ regime) or not transient regime). Aside from this question, analytical propertie...

We study a model of a polling system, that is, a collection of d queues with a single server that switches from queue to queue. The service time distribution and arrival rates change randomly every time a queue is emptied. This model is mapped to a mathematically equivalent model of a random walk with random choice of transition probabilities, a model which is of independent interest. All our r...

We assess the performance of a discrete-time queueing system with train arrivals. Arrivals at the queue stem from a number of active sessions, each generating a packet in a slot with fixed probability q. Since an exact analysis is not feasible for q 6= 1, we rely on Taylor-series expansions around q = 0 of the joint probability generating functions of the number of active sessions and the queue...

The performance evaluation of many complex manufacturing, communication and computer systems has been made possible by modeling them as queueing systems. Many approximations used in queueing theory have been drawn from the behavior of queues in light and heavy tra c conditions. In this paper, we propose a new approximation technique, which combines the light and heavy tra c characteristics. Thi...

We consider a two-queue polling model with switch-over times and k-limited service (serve at most ki customers during one visit period to queue i) in each queue. The major benefit of the k-limited service discipline is that it besides bounding the cycle time effectuates prioritization by assigning different service limits to different queues. System performance is studied in the heavy-traffic r...

This paper considers MAP/G/1 queueing systems under the following two situations: (1) At the end of a busy period, the server is turned off and inspects the queue length every time a customer a,rrives. When the queue length reaches a pre-specified value N , the server turns on and serves customers continuously until the system becomes empty. (2) At the end of a busy period, the server takes a s...

Fast Congestion Notification (FN) is one of the proactive queue management mechanisms that practices congestion avoidance to help avoid the beginning of congestion by marking/dropping packets before the router’s queue gets full; and exercises congestion control, when congestion avoidance fails, by increasing the rate of packet marking/dropping. Technically, FN avoids the queue overflows by cont...

Packet routing is an important problem in parallel computation since a single step of inter-processor communication can be thought of as a packet routing task. In this paper we present an optimal algorithm for packet routing on a mesh-connected computer. Two important criteria for judging a routing algorithm will be 1) its run time, i.e., the number of parallel steps it takes for the last packe...

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 two-queue polling model with switch-over times and k-limited service (serve at most k i customers during one visit period to queue i) in each queue. The major benefit of the k-limited service discipline is that it-besides bounding the cycle time-effectuates prioritization by assigning different service limits to different queues. System performance is studied in the heavy-traffic ...