We obtain the queue length probability distribution at equilibrium for a multi-server, single queue with generalised exponential (GE) service time distribution and a Markov modulated compound Poisson arrival process (MMCPP)—i.e. a Poisson point process with bulk arrivals having geometrically distributed batch size whose parameters are modulated by a Markovian arrival phase process. This arrival...

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...

Over the last two decades there has been considerable growth in digital communication systems which operate on a slotted system. In several applications, transmission of packets over the network takes place in batches of varying size, and transmission time depends upon the size of the batch. Performance modelling of these systems is usually done using discrete-time queues. In view of this, we c...

PALM-MARTINGALE CALCULUS, QUEUES WITH VACATIONS, BATCH MARKOVIAN ARRIVAL PROCESSES,SERVER SET-UP Using Palm-martingale calculus, we derive the workload characteristic function and queue length moment generating function for the BMAP IGl/1 . queue with server vacations. In the queueing system under study, the server may start a vacation at the completion of a service or at the arrival of a custo...

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...

In this paper we study a Geo/T-IPH/1 queue model, where T-IPH denotes the discrete time phase type distribution defined on a birth-and-death process with countably many states. The queue model can be described by a quasi-birth-anddeath (QBD) process with countably phases. Using the operator-geometric solution method, we first give the expression of the operator and the joint stationary distribu...

The loss probability of a queueing system provides in many cases insuucient information for performance evaluation, for example, of le transfer retransmission protocols and real-time applications with signal reconstruction. This paper evaluates and characterizes the correlation between packet losses for three queu-eing systems in discrete time that are motivated by BISDN applications. In the rs...