René David

An Efficient Algorithm for Analysis of Transfer Lines With Unreliable Machines and Finite Buffers

Abstract In a recent paper [3], Gershwin proposed a decomposition method for the approximate analysis of transfer lines with unreliable machines and finite buffers. The method is based on a decomposition of the line into a set of two-machine lines. It leads to a set of equations which are solved using an iterative algorithm. Experimental results have shown that this technique is very accurate. However, it may happen that the algorithm fails to converge. In this paper, we propose to replace the original set of equations by an equivalent one, which is again solved using an iterative procedure. This new algorithm is simpler than the previous one, and its computational complexity is lower. Moreover, on all examples we tested, the algorithm always converged.

Modeling and Analysis of Assembly Systems with Unreliable Machines and Finite Buffers

Abstract An assembly line is a tree-structured manufacturing system in which some machines perform assembly operations. In this paper, we consider assembly lines with the following features: every operation is performed in a fixed amount of time, machines are unreliable, and buffers have finite capacity. Usually, the times to failures of machines are much larger than the processing times. This allows us to approximate the behavior of these systems by a continuous flow model. The behavior of this model is then analyzed using a decomposition technique which is an extension of an earlier technique proposed in the case of transfer lines. An efficient algorithm for calculating performance measures such as production rate and average buffer levels is derived. Experimental results are provided showing mat this approximate method is quite accurate.

A unified modeling of Kanban systems using petri nets

The success of some Just In Time (JIT) systems has led to a growing interest in Kanban systems, which provide a way to implement a JIT control policy. Much work has recently been devoted to this problem, and especially many models have been developed to evaluate the performance of such systems. In this article, we focus our attention of these existing models. Each author uses his/her own representation, which is not formal in most cases, and so it is often difficult to understand the proposed model and to compare it with others. In this article, we show that Petri nets are well suited to provide a unified modeling of Kanban systems. We first propose a basic model, then show that most models encountered in the literature can easily be represented by a Petri net model. Once such a formal model is obtained, it can then be used to analyze the behavior of the system, both qualitatively and quantitatively. Some preliminary results pertaining to the quantitative analysis are presented at the end of the article.

Delay fault testing: choosing between random SIC and random MIC test sequences

The combination of higher quality requirements and sensitivity of high performance circuits to delay defects has led to an increasing emphasis on delay testing of VLSI circuits. In this context, it has been proven that Single Input Change (SIC) test sequences are more effective than classical Multiple Input Change (MIC) test sequences when a high robust delay fault coverage is targeted. In this paper, we show that random SIC (RSIC) test sequences achieve a higher fault coverage than random MIC (RMIC) test sequences when both robust and non-robust tests are under consideration. Experimental results given in this paper are based on a software generation of RSIC test sequences that can be easily generated in this case. For a built-in self-test (BIST) purpose, hardware generated RSIC sequences have to be used. This kind of generation will be shortly discussed at the end of the paper.

A new approach of test confidence estimation

Two measures of test confidence in tested circuits are presented. One takes into account all circuits tested and appears to be a novel measure that is of interest to circuit manufacturers. The other measure, which has already been introduced, takes into account only those circuits that have passed the test and is of interest to the circuit user. Both measures are functions of the same variable, called faulty circuit coverage, which quantifies the confidence in the test sequence. This variable is rather difficult to compute. Therefore a novel approach to approximate the faulty circuit coverage, based on a partition of the prescribed set of faults, is proposed.<<ETX>>

Asymptotic continuous Petri nets: an efficient approximation of discrete event systems

Two continuous Petri net (CPN) models involving time are defined. They differ by the calculation of the instantaneous firing speeds of the transitions. Both can be used to approximate a timed Petri net. The first model considers constant firing speeds (constant-speed CPN, CCPN). It is very easy to simulate. The second model considers firing speeds depending on the marking (variable speed CPN, VCPN). It provides a better approximation, but its simulation is longer because the markings and speeds are given by differential equations. The authors introduce a third model, which has the advantages of the two preceding ones. This model represents the asymptotic behavior of the VCPN. Their precision is similar. It is as easy to simulate as the CCPN.<<ETX>>

Asymptotic continuous Petri nets

A Petri net is basically a discrete model. However, continuous Petri nets, such that the markings are real numbers have been defined. Two continuous Petri net models involving time have been drawn up. They differ by the calculation of the instantaneous firing speeds of the transitions. Both can be used to approximate a timed Petri net. The former considers constant firing speeds (CCPN) and is very easy to simulate (few events have to be considered, even when it approximates a timed Petri net with many reachable markings). The latter considers firing speeds depending on the marking (VCPN). Although it provides a better approximation, its simulation is longer because the markings and speeds are given by differential equations. This paper introduces a third model (ACPN) which presents the advantages of the two preceding ones. In most cases, this model represents the asymptotic behavior of the VCPN. Then their precisions are similar. Since the firing speeds of the ACPN are constant, it is as easy to simulate as the CCPN.

RANDOM TESTING OF THE DATA PROCESSING SECTION OF A MICROPROCESSOR

The principle of random testing is as follows : a random input sequence is applied s imultaneously to both a circuit under test and a reference circuit. The outputs are compared. In t he case of microprocessors, we apply a sequence of random instructions with random data. The research aim is to calculate the test length (i.e. the number of instructions) for given instruction probabilities. The paper deals with the faults in the data processing section, which is modeled by a qraph containing registers and operators. We consider functional level fault models in registers and operators. We use the notion of Minimal Detectinq Transition Sequences (MDTS) .

Modeling of Production Systems by Continuous Petri Nets

Continuous Petri Nets (continuous-PN) have been introduced to avoid the explosion of the number of reachable states in a classical Petri Net, when this net contains a great number of tokens. This is the case of production systems, particularly a flexible manufacturing system. In a continuous-PN, the marking of a place is represented by a real number and with each transition is associated a maximum firing speed. Two kinds of modelling of manufacturing systems by continuous-PN are presented in this paper. The first one gives good results when the system is saturated (many parts). The second one works well even if the system is not saturated.

Bases of Petri Nets

The main users of Petri nets are computer and automatic control scientists. However, this tool is sufficiently general to model phenomena of extremely varying types.