We study a discrete-time deterministic server queue with infinite buffer and with packet arrivals that depend on a multidimensional Markov process. Using the generating functions approach we give a means for obtaining the boundary conditions vector for the case where the value zero is a multiple eigenvalue of the problem. We also derive recursive form expressions for the direct determination of...

We consider a discrete-time multi-server queue for which the moments of the stationary queue length can be expressed in terms of series over the zeros in the closed unit disk of a queue-specific characteristic function. In many important cases these zeros can be considered to be located on a queue-specific curve, called generalized Szegö curve. By adopting a special parametrization of these Sze...

Congestion control in the Available Bit Rate (ABR) class of Asynchronous Transfer Mode (ATM) networks poses interesting challenges due to the presence of delays, magnitude and rate constraints on the inputs and additive disturbances. In this paper, we consider a discrete-time fixed-structure controller for an ATM/ABR switch, also modeled in discrete-time, and solve a robust tracking control pro...

We consider finiteand infinite-capacity queues with discrete-time batch Markovian arrival processes (D-BMAP) under the assumption of the Late Arrival System with Delayed Access as well as the Early Arrival System. Using simple arguments such as the balance equation, “rate in = rate out,” we derive relationships among the stationary queue lengths at arrival, at departure, and at random epochs. S...

This paper presents a novel methodology for approximating the queue length (the number of customers in the system) distributions of time-varying non-Markovian manyserver queues (e.g., Gt/Gt/nt queues), where the number of servers (nt) is large. Our methodology consists of two steps. The first step uses phase-type distributions to approximate the general inter-arrival and service times, thus gen...

This paper considers the Stochastic Queue Center problem, which seeks to locate a single facility with a center-type objective in an M/G/1 queue operating environment. The objective function that we consider is to minimize a positive weighted linear function of the square of the average response time and the variance of the response time to a call. The Stochastic Queue Center problem is discuss...