Tandem Queueing Model Research Articles

Tandem queues with deterministic service times

In this paper we consider a tandem queueing model for a sequence of multiplexers at the edge of an ATM network. All queues of the tandem queueing model have unit service times. Each successive queue receives the output of the previous queue plus some external arrivals. For the case of two queues in series, we study the end-to-end delay of a cell (customer) arriving at the first queue, and the covariance of its delays at both queues. The joint queue length process at all queues is studied in detail for the 2-queue and 3-queue cases, and we outline an approach to the case of an arbitrary number of queues in series.

A statistical approximation for queueing measures in a decision support system

We show that while we have found closed form, albeit unwieldy, expressions for a tandem queueing model with finite queue lengths and proportional service, the measures computed can be reduced to more manageable expressions. This is advantageous for placing models of this type in the model base of a decision support system where manageable, good approximate values will suffice.

Tandem Queues with Planned Inventories

This paper explores a natural generalization of the classic tandem-queue model, designed specifically to represent make- to-stock production processes. In such systems, intermediate and finished goods can be produced and stored in advance of demand. We consider the simplest version of the model, where demand is a Poisson process, and the unit production times are exponentially distributed. We propose and test a tractable approximation scheme. The approximation appears to be quite accurate.

Scheduling service in tandem queues attended by a single server

Consider a tandem queue model with a single server who can switch instantaneously from one queue to another. Customers arrive according to a Poisson process with rate λ . The amount of service required by each customer at the ith queue is an exponentially distributed random variable with rate μi. Whenever two or more customers are in the system, the decision as to which customer should be served first depends on the optimzation criterion. In this system all server allocation policies in the finite set of work conserving deterministic policies have the same expected first passage times (makespan) to empty the system of customers from any initial state. However, a unique policy maximizes the first passage probability of empty-ing the system before the number of customers exceeds K, for any value of K, and it stochastically minimizes (he number of customers in the system at any time t > 0 . This policy always assigns the server to the non empty queue closest to the exit

A cyclic service tandem queueing model with parallel queues in the first stage

This paper presents an analysis for the steady state of a two-stage tandem queueing model served by a single server, in which the first stage has two queues in parallel. Generating functions are obtained for two joint queue length distributions, one at the instant just after service completion and the other at an arbitrary instant, using a solution of a functional equation with two variables and the rate conservation principle in the theory of piecewise Markov process. The Laplace-Stieltjes transforms are also derived for some sojourn time distributions. Some numerical resultsfor mean waiting times and mean total sojourn times are presented.

Performance evaluation of data communication systems

This paper is a tutorial and a survey of analytical methods in the evaluation of data communication networks. The major mathematical methods are Markov chains applied to discrete time systems and queueing theory. Emphasis is placed on the applications of the mathematical tools. The discussion follows the framework of the layered architecture. In the section on data link control, rigorous as well as engineering approaches are highlighted. In this area, models of great accuracy have been developed. In the path-control or routing layer, the major model is provided by Kleinrock's delay analysis of packet networks. Finite buffer pools still pose many problems. The method of the homogeneous network is introduced, a method which reduces complexity originating from the network topology in favor of more realistic protocol features. This thought is expanded into the layer of end-to-end protocols where the tandem-queue model is introduced and its application to the flow-control problem discussed.

On a tandem queueing model with identical service times at both counters, I

This paper considers a queueing system consisting of two single-server queues in series, in which the service times of an arbitrary customer at both queues are identical. Customers arrive at the first queue according to a Poisson process. Of this model, which is of importance in modern network design, a rather complete analysis will be given. The results include necessary and sufficient conditions for stationarity of the tandem system, expressions for the joint stationary distributions of the actual waiting times at both queues and of the virtual waiting times at both queues, and explicit expressions (i.e., not in transform form) for the stationary distributions of the sojourn times and of the actual and virtual waiting times at the second queue. In Part II (pp. 644–659) these results will be used to obtain asymptotic and numerical results, which will provide more insight into the general phenomenon of tandem queueing with correlated service times at the consecutive queues.

On a tandem queueing model with identical service times at both counters, II

This paper is devoted to the practical implications of the theoretical results obtained in Part I [1] for queueing systems consisting of two single-server queues in series in which the service times of an arbitrary customer at both queues are identical. For this purpose some tables and graphs are included. A comparison is made—mainly by numerical and asymptotic techniques—between the following two phenomena: (i) the queueing behaviour at the second counter of the two-stage tandem queue and (ii) the queueing behaviour at a single-server queue with the same offered (Poisson) traffic as the first counter and the same service-time distribution as the second counter. This comparison makes it possible to assess the influence of the first counter on the queueing behaviour at the second counter. In particular we note that placing the first counter in front of the second counter in heavy traffic significantly reduces both the mean and variance of the total time spent in the second system.

On a tandem queueing model with identical service times at both counters, II

This paper is devoted to the practical implications of the theoretical results obtained in Part I [1] for queueing systems consisting of two single-server queues in series in which the service times of an arbitrary customer at both queues are identical. For this purpose some tables and graphs are included. A comparison is made—mainly by numerical and asymptotic techniques—between the following two phenomena: (i) the queueing behaviour at the second counter of the two-stage tandem queue and (ii) the queueing behaviour at a single-server queue with the same offered (Poisson) traffic as the first counter and the same service-time distribution as the second counter. This comparison makes it possible to assess the influence of the first counter on the queueing behaviour at the second counter. In particular we note that placing the first counter in front of the second counter in heavy traffic significantly reduces both the mean and variance of the total time spent in the second system.

On a tandem queueing model with identical service times at both counters, I

This paper considers a queueing system consisting of two single-server queues in series, in which the service times of an arbitrary customer at both queues are identical. Customers arrive at the first queue according to a Poisson process.Of this model, which is of importance in modern network design, a rather complete analysis will be given. The results include necessary and sufficient conditions for stationarity of the tandem system, expressions for the joint stationary distributions of the actual waiting times at both queues and of the virtual waiting times at both queues, and explicit expressions (i.e., not in transform form) for the stationary distributions of the sojourn times and of the actual and virtual waiting times at the second queue.In Part II (pp. 644–659) these results will be used to obtain asymptotic and numerical results, which will provide more insight into the general phenomenon of tandem queueing with correlated service times at the consecutive queues.