We consider a family of multidimensional diffusion processes that arise as heavy traffic approximations for open queueing networks. More precisely, the diffusion processes considered here arise as approximate models of open queueing networks with homogeneous customer populations, which means that customers occupying any given node or station of the network are essentially indistinguishable from one another. The classical queueing network model of J. R. Jackson fits this description, as do other more general types of systems, but multiclass network models do not.The objectives of this paper are (a) to explain in concrete terms how one approximates a conventional queueing model or a real physical system by a corresponding Brownian model, and (b) to state and prove some new results regarding stationary distributions of such Brownian models. The part of the paper aimed at objective (a) is largely a recapitulation of previous work on weak convegence theorems, with the emphasis placed on modeling intuition. Wit...

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Brownian Models of Open Queueing Networks with Homogeneous Customer Populations

The fairness problems suffered by distributed-queue-dual-bus (DQDB) networks that span metropolitan areas are examined in detail. The problems arise because the network control information is subject to propagation delays that are much longer than the transmission time of a data segment. A rate control procedure is proposed that requires only a minor modification of the current DQDB protocol. In order to guarantee that a node acquires only 90% of the available slots, every time it inserts nine data segments into its local queue it inserts one extra request slot into its transmission queue. This lets an extra idle slot go by that was not requested by any downstream node. >

Improving the fairness of distributed-queue-dual-bus networks

Bandwidth balancing is a procedure that gradually achieves a fair allocation of bandwidth among simultaneous file transfers on a distributed-queue dual-bus (DQDB) network. Bandwidth balancing was originally designed for traffic of a single priority level. Three ways are demonstrated to extend this procedure to multi-priority traffic. >

Fair access of multi-priority traffic to distributed-queue dual-bus networks

We present an approximate performance study of the DQDB medium access protocol. The aim of the queuing analysis described in this paper is to provide close-form solutions, which should be easy to evaluate but deliver sufficiently accurate performance measures describing major behaviors of the protocol. The analysis is based on a decomposition of the medium access delay, using the technique of embedded models. The non-isochronous station-to-station traffic matrix, which consists of traffic streams assumed as Poisson, can be chosen arbitrarily. A percentage of preassigned isochronous traffic in the system is taken into account. It is shown by comparison with simulation results that the approximation technique developed in this paper is appropriate for a wide range of protocol parameters. The efficient analysis method also shows various protocol properties, which have been partly discovered in the literature by means of simulations.

Approximate performance analysis of the DQDB access protocol

A journey through the DQDB network literature

Clocked schedules represent an important method of task scheduling for computer systems with real-time applications. In this paper we consider a generalized class of clocked schedule that includes those used in many stored program control switching systems. Key performance measures for this class are discussed, and an analytic approximation method for analyzing certain of these measures is given. This approximation method is most applicable in evaluating long-term delays. (A companion paper by Doshi addresses short-term delays for systems with extremely time-critical tasks.) Comparisons are made with exact numerical results (obtained using the method presented in a companion paper by Ackroyd), detailed simulation models, and field data.

Approximate analysis of a generalized clocked schedule

In this paper we discuss new visual modeling and analysis tools and techniques as well as some concepts and approaches to the design and implementation of communication protocols. The example chosen here is the IEEE 802.6 MAN DQDB protocol. Concepts of fairness are introduced, preliminary evaluations are given and proposals for improvement are made.

Visual modeling and analysis with application to IEEE 802.6 DQDB protocol

Performance analysis modeling can provide the means of ensuring cost-effective engineering and operation of manufacturing lines. This article presents the basic concepts of performance analysis modeling and illustrates its application to the design, engineering and operation of manufacturing systems. A particularly versatile tool for performance analysis of manufacturing systems, the Performance Analysis Workstation, is also discussed. Finally, comments on future trends in performance analysis modeling are given.

Performance analysis modeling for manufacturing systems

Performance modeling and analysis provide an important means to ensure the cost-effective design and engineering of communications and computer systems, as well as services based on such systems Appropriate use of performance modeling and analysis techniques can provide quantitative insight into system performance that would otherwise be difficult, expensive, or even impossible to obtain

An introduction to performance modeling and analysis

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Approximate analysis of a generalized clocked schedule

Visual modeling and analysis with application to IEEE 802.6 DQDB protocol

Performance analysis modeling for manufacturing systems

An introduction to performance modeling and analysis