In this paper ,we discuss the Geom/G/1 queue with Bernoulli feedback and server setup/closedown times.We derive the probability generating function (PGF) of the steady-state queue length immediately after a service completion by the embedded Markov chain and the PGF of the queue length immediately after an arbitrary slot boundary .We also get the PGF of the stationary waiting times under first ...

We analyze a multiserver queue with a discrete autoregressive process of order 1 (DAR(1)) as an input. DAR(1) is a good mathematical model for VBR-coded teleconference traffic. Based on matrix analytic methods and the theory of Markov regenerative processes, we obtain the stationary distributions of the system size and the waiting time of an arbitrary packet. Numerical examples illustrate the q...

This paper presents the analysis of a finite buffer renewal input queue wherein the customers can decide either to join the queue with a probability or to balk. The service process is Markovian service process (MSP ) governed by an underlyingm-state Markov chain. Employing the supplementary variable and embedded Markov chain techniques, the steadystate system length distributions at pre-arrival...

Using constructive, sample-path arguments, we derive a variety of transform-free results about queue lengths and waiting times for the M/G/1/K queue. In classical analyses of M/G/1/K, it is typical to work with Markov processes obtained by defining the “state” of the system at a time epoch to be the number of customers present and, as supplementary information, the remaining service time of the...

Resequencing of customers during the service process results in hard to analyze delay distributions. A set of models with various service and resequencing policies have been analyzed already for memoryless arrival, service and resequencing processes with an intensive use of transform domain descriptions. In case of Markov modulated arrival, service and resequencing processes those methods are n...

We consider the estimation of arrival and service rates for queues based on queue length data collected at successive, not necessarily equally spaced, time points. In particular, we consider the M/M/c queue, for c large, but application of the method to the repairman problem is almost identical, and the general approach presented should extend to other queue types. The estimation procedure make...

We consider a model consisting of two fluid queues driven by the same background continuous-time Markov chain, such that the rates of change of the fluid in the second queue depend on whether the first queue is empty or not. We analyse this tandem model using operator-analytic methods.

A novel approach for obtaining the response time in a discrete-time tandem-queue with blocking is presented. The approach constructs a Markov chain based on the age of the leading customer in the first queue. We also provide a stability condition and carry out several numerical examples. © 2004 Elsevier B.V. All rights reserved.