We present a non-equilibrium analysis and control approach for the Active Queue Management (AQM) problem in communication networks. Using simplified fluid models we carry out a bifurcation study of the complex dynamic queue behavior to show that non-equilibrium methods are essential for analysis and optimization in the AQM problem. We investigate an ergodic theoretic framework for stochastic mo...

We propose a new queueing model named the acquisition queue. It differs from conventional queueing models in that the server not only serves customers, but also performs acquisition of new customers. The server has to divide its energy between both activities. The number of newly acquired customers is uncertain, and the effect of the server’s acquisition efforts can only be seen after some fixe...

We propose a method to approximate the transient performance measures of a discrete time queueing system via a steady state analysis. The main idea is to approximate the system state at time slot t or on the n-th arrival—depending on whether we are studying the transient queue length or waiting time distribution—by the system state after a negative binomially distributed number of slots or arri...

We consider a class of two-queue polling systems with exhaustive service, where the order in which the server visits the queues is governed by a discrete-time Markov chain. For this model, we derive an expression for the probability generating function of the joint queue length distribution at polling epochs. Based on these results, we obtain explicit expressions for the Laplace-Stieltjes trans...

We consider a system consisting of two not necessarily identical exponential servers having a common Poisson arrival process. Upon arrival, customers inspect the first queue and join it if it is shorter than some threshold n. Otherwise, they join the second queue. This model was dealt with, among others, by Altman et al. (2004). We first derive an explicit expression for the Laplace-Stieltjes t...

Abstract In this paper, a new discrete-time GeomX /G/1 queue model with multiple vacations is analyzed. The Probability Generating Function (P.G.F.) of the queue length is obtained by using the method of an embedded Markov chain, and the mean of the queue length is obtained by using L’Hospital rule. Then the P.G.F. of the busy period is derived, and the probabilities for the system being in a b...

In this paper, we analyze a leaky bucket (LB) scheme with queue length dependent arrival rates. In other words, if the queue length exceeds an appropriate threshold value on buffer, the arrivals need to be controlled. In ATM networks, if the congestion occurs, the input traffics must be controlled (reduced) for congestion resolution. By the bursty and correlated properties of traffics, the arri...