In this paper we establish asymptotics for the basic steady-state distributions in a large class of single-server queues. We consider the waiting time, the workload (virtual waiting time) and the steady-state queue lengths at an arbitrary time, just before an arrival and just after a departure. We start by establishing asymptotics for steady-state distributions of Markov chains of M/GI/1 type. ...

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...

Vacation queueing models have wide range of application in several areas including computer-communication, and manufacturing systems. A finite-butTer single-server queue with renewal input and multiple exponential vacations has been analysed by Karaesmen and Gupta (1996). In this paper we extend the analysis to cover the batch arrivals. i.e. we consider a batch alTiva! single-server queue with ...

Devices can now be powered wirelessly by Access Points (APs). However, an AP cannot transmit frequently to charge devices as it may starve other nearby APs operating on the same channel. Consequently, there is a need to schedule the transmissions of APs to ensure their data queues remain short whilst charging energy-harvesting devices. We present a finite-horizon Markov Decision Process (MDP) t...

In this paper we demonstrate how tree-like processes can be used to analyze a general class of priority queues with three service classes, creating a new methodology to study priority queues. The key result is that the operation of a 3-class priority queue can be mimicked by means of an alternate system that is composed of a single stack and queue. The evolution of this alternate system is redu...

This paper explores the variations in mean queue length for stationary arrival processes with the same mean and autocorrelation functions, or equivalently, the same mean and power spectrum. Three types of processes, namely, two-state Markov-modulated Poisson processes, periodic-sequence modulated Poisson processes and processes generated by randomly filtering a white noise process, are investig...

A nite-buuered banyan network analysis technique designed to model networks at high traac loads is presented. The technique specially models two states of the network queues: queue empty and queue congested (roughly, zero or one slots free). A congested queue tends to stay congested because packets bound for the queue accumulate in the previous stage. The expected duration of this state is comp...

We consider a system of parallel queues with dedicated arrival streams. At each decision epoch a decisionmaker can move customers from one queue to another. The cost for moving customers consists of a fixed cost and a linear, variable cost dependent on the number of customers moved. There are also linear holding costs that may depend on the queue in which customers are stored. Under very mild a...

A new queue, referred to here as the HetSigma queue, in the Markovian framework, is proposed in order to model nodes in modern telecommunication networks. The queue has many of the necessary ingredients, such as joint (or individual) Markov modulation of the arrival and service processes, superposition of K CPP (compound Poisson process) streams of (positive) customer arrivals, and a CPP of neg...

We consider a queue with finite buffer where the buffer size limits the amount of work that can be stored in the queue. The arrival process is a Poisson or a Markov modulated Poisson process. The service times (packet lengths) are iid with a general distribution. Our queue models the systems in the Internet more realistically than the usual M/GI/1/K queue which restricts the number of packets i...