Bruno Baynat

A product-form approximation method for general closed queueing networks with several classes of customers

Abstract This paper presents a new method for obtaining approximate solutions of general closed queueing networks with several classes of customers. The idea is to associate with each class of customers, a single-class closed queueing network with load-dependent exponential service stations. For each single-class network associated with a particular class of customers, the interactions with the customers belonging to other classes are taken into account in the estimation of the load-dependent service rates. These parameters are obtained by analyzing each station in isolation under the assumption that the arrival process of each class is a state-dependent Markovian process. An iterative algorithm is used to determine the unknown parameters. The main computational charge of the method is due to the analysis of the stations in isolation. A class aggregation technique is proposed that significantly reduces the complexity of these analyses. Although the principle of the method is fairly general, in this paper we only consider queueing networks with general service time distributions and either FIFO or priority disciplines. Numerical results are provided that show that this method is fairly accurate, even when the class aggregation technique is used.

Determining Inventory Levels in a CONWIP Controlled Job Shop

We extend the concept of CONWIP control to a job shop setting, in which multiple products with distinct routings compete for the same set of resources. The problem is to determine the fixed overall WIP level and its allocation to product types (WIP mix) to meet a uniformly high customer service requirement for each product type. We formulate an optimization problem for an open queuing network model in which customer orders pull completed products from the system. Then, assuming heavy demand, we derive a throughput target for each product type in a closed queuing network and provide a simple heuristic to find a minimum total WJP and WIP mix that will achieve an operating throughput close to this target. In numerical examples, the WIP mix suggested by this approach achieves the customer service requirement with a relatively low total WIP

A unified view of product-form approximation techniques for general closed queueing networks

Abstract Two major approximate techniques have been proposed for the analysis of general closed queueing networks, namely the aggregation method and Maries method. The idea of the aggregation technique is to replace a subsystem (a subnetwork) by a flow equivalent single-server with load-dependent service rates. The parameters of the equivalent server are obtained by analyzing the subsystem in isolation as a closed system with different populations. The idea of Maries method is also to replace a subsystem by an equivalent exponential service station with load-dependent service rates. However, in this case, the parameters of the equivalent server are obtained by analyzing the subsystem in isolation under a load-dependent Poisson arrival process. Moreover, in Maries case, the procedure is iterative. In this paper we provide a general and unified view of these two methods. The contributions of this paper are the following. We first show that their common principle is to partition the network into a set of subsystems and then to define an equivalent product-form network. To each subsystem is associated a load-dependent exponential station in the equivalent network. We define a set of rules in order to partition any general closed network with various features such as general service time distributions, pupulation constraints, finite buffers, state-dependent routing. We then show that the aggregation method and Maries method are two ways of obtaining the parameters of the equivalent network associated with a given partition. Finally, we provide a discussion pertaining to the comparison of the two methods with respect to their accuracy and computational complexity.

Retouched bloom filters: allowing networked applications to trade off selected false positives against false negatives

Where distributed agents must share voluminous set membership information, Bloom filters provide a compact, though lossy, way for them to do so. Numerous recent networking papers have examined the trade-offs between the bandwidth consumed by the transmission of Bloom filters, and the error rate, which takes the form of false positives, and which rises the more the filters are compressed. In this paper, we introduce the retouched Bloom filter (RBF), an extension that makes the Bloom filter more flexible by permitting the removal of selected false positives at the expense of generating random false negatives. We analytically show that RBFs created through a random process maintain an overall error rate, expressed as a combination of the false positive rate and the false negative rate, that is equal to the false positive rate of the corresponding Bloom filters. We further provide some simple heuristics that decrease the false positive rate more than than the corresponding increase in the false negative rate, when creating RBFs. Finally, we demonstrate the advantages of an RBF over a Bloom filter in a distributed network topology measurement application, where information about large stop sets must be shared among route tracing monitors.

A Multi-class Approximation Technique for the Analysis of Kanban-Like Control Systems

Analytical methods have been proposed in the literature for performance evaluation of kanban control systems. Among them, the method presented by Di Mascolo and colleagues appears to be of special interest since it can handle manufacturing stages consisting of any number of machines and it is fairly accurate. This paper presents a new way of deriving the analytical method presented by Di Mascolo et al. The approach is to see the queueing network of the kanban control system as a multiclass queueing network in which each kanban loop is represented by a class of customers. This allows one to use the general technique proposed in Baynat and Dallery for analysing multiclass queueing network using product-form approximation methods. In terms of equations, the new method is equivalent to that previously presented. However, the computational algorithm is much more efficient since it avoids the two levels of iterations involved in the original algorithm. Another major advantage of the new method over that originally proposed is that it provides a general framework for the analysis of more general kanban systems. Indeed, it is shown in this paper how this approach can easily be extended in order to handle kanban systems with multiple consumers and multiple suppliers, kanban-controlled assembly systems and generalized kanban systems.

Approximate techniques for general closed queueing networks with subnetworks having population constraints

Abstract We consider closed queueing networks with general service times and subnetworks having population constraints. Each such subnetwork consists of a subset of stations of the original network. The population constraint of a subnetwork prescribes that the total number of customers that can be simultaneously present inside the subnetwork is limited to a fixed value called the capacity of the subnetwork. A customer who wants to enter the subnetwork while it is full has to wait in an external queue. As soon as a customer leaves the subnetwork, the first-in-line customer is allowed to enter the subnetwork. We apply and compare two approximate techniques for analyzing such networks, namely the aggregation technique and Maries method. We emphasize the similarities and differences between these two techniques. Finally, we compare their accuracy.

An Efficient Analytical Model for the Dimensioning of WiMAX Networks

This paper tackles the challenging task of developing a simple and accurate analytical model for performance evaluation of WiMAX networks. The need for accurate and fast-computing tools is of primary importance to face complex and exhaustive dimensioning issues for this promising access technology. In this paper, we present a generic Markovian model developed for three usual scheduling policies (slot sharing fairness, throughput fairness and opportunistic scheduling) that provides closed-form expressions for all the required performance parameters at a click speed. This model is compared in depth with realistic simulations that show its accuracy and robustness regarding the different modeling assumptions. Finally, the speed of our analytical tool allows us to carry on dimensioning studies that require several thousands of evaluations, which would not be tractable with any simulation tool.

Production capacity of flexible manufacturing systems with fixed production ratios

Determining the production capacity of flexible manufacturing systems is a very important issue in the design of such systems. We propose an approach for determining the production capacity (i.e., the maximum production rate) of a flexible manufacturing system with several part types, dedicated pallets, and fixed production ratios among the different part types. We show that the problem reduces to the determination of a single parameter for which we propose an iterative procedure. Simulation or approximate analytical techniques can be used as the building block performance evaluation technique in the iterative procedure.

An efficient analytical model for WiMAX networks with multiple traffic profiles

In this paper, we present a simple and accurate analytical model for performance evaluation of WiMAX networks with multiple traffic profiles. This very promising access technology has been designed to support numerous kinds of applications having different traffic characteristics. The need for accurate and fast-computing tools is thus of primary importance to face complex dimensioning issues that integrate this traffic profile diversity. Our product-form queueing model provides closed-form expressions giving all the required performance parameters for each traffic profile at a click speed. The model is compared with extensive simulations that show its accuracy and robustness. Finally, the speed of our analytical tool allows us to carry on a preliminary performance study.

Towards an Erlang-like law for GPRS/EDGE network engineering

A model for GPRS/EDGE network engineering is developed in order to obtain an Erlang-like law. It is based on a discrete-time Markov chain. It captures the main features of the GPRS/EDGE radio resource allocation and assumes an ON/OFF traffic (infinite sessions with geometric distributions of ON/OFF sizes) performed by a finite number of users over the cell. The Markov chain is simplified by Taylor series expansion and a simple and accurate Erlang-like law is obtained.