Benoit Trouillet

Formal approach of fms cyclic scheduling

This correspondence is related to the determination of both control and scheduling of flexible manufacturing systems under cyclic command. Different approaches can be found in the literature, but we focus on those which respect the optimal throughput while minimizing the work in process. So, we recall methods of performance evaluation developed during the last 20 years. The last part is devoted to a new approach of cyclic scheduling using a Petri net. This method uses algebraic tools (dioids) developed for the study of marked graphs. In this way, the problem of the scheduling is progressively transformed into a problem of the search of solution(s) on a system of equations

Fair Queuing Model for EDCA to Optimize QoS in Ad-Hoc Wireless Network

This study aims to develop and optimize the Quality of Service (QoS) with fairness in multi-hop wireless adhoc networks. IEEE802.11e (EDCA) standard is concerned to support QoS in wireless adhoc networks. Thereby, EDCA differentiates and classifies the packets in Access Categories depending on their priorities. However, it cannot guarantee strict QoS required by real-time and multimedia services without proper network control mechanisms. And also, the unfairness of bandwidth sharing ,because of the hidden and exposed terminals problems, leads to degrade the guarantee services. Our proposition (FQ-EDCA) is to enhance the QoS of EDCA by implementing a Fair Queuing scheduling technique and improving the architecture of EDCA scheme. FQ-EDCA is proved and analyzed by experimental simulations for many topologies like (star, chain, tree, ...). Thus, the bandwidth is distributed fairly between all the source nodes. As a consequence, these nodes can access the channel fairly to transmit their flows with respect to EDCA specifications of Access Categories (AC) priorities. And also, the delay of flows of the same priorities is minimized and nearly fixed for all the source nodes. This leads to minimize the Jitter also. Therefore, the services guarantees of QoS is enhanced.

Routing Fairness Model for QoS Optimization in Wireless Network

This study aims to develop and optimize the Quality of Service (QoS) with fairness in wireless ad hoc networks. We will discuss the conception and the mechanisms that are specified by IEEE802.11e (EDCA) standard which is concerned to QoS in wireless adhoc networks. IEEE802.11e (EDCA) enhances the original standard by enhancing the distributed coordination function (DCF). DCF consists in deferring the channel access in ad hoc mode. Thereby, EDCA differentiates and classifies the packets in access categories depending on their priorities. However, there are many propositions that develop the QoS in ad hoc mode. They are based on control access channel such as Multiple Access Collision Avoidance with Contention Window optimization (MACAW). This model is enhanced with (RAMAC) to access channel fairly by differentiating the routed and owned packets in routing nodes. Our proposition (F-EDCA) is to enhance and develop QoS of EDCA in adhoc networks by implementing the principles of RAMAC. Thus, the transmitted queued packets in routing nodes will be differentiated depending on their priorities (EDCA specifications) and their type (Owned or Routed packet) to apply fairness in routing nodes.

Cyclic scheduling problems with assemblies: an approach based to the search of an initial marking in a marked graph

This paper deals with the scheduling of shared resources in cyclic problem. This scheduling problem is solved by transforming a Petri net with conflicts into a marked graph. Then the marked graph can be analysed thanks to the (min,+) dioid.

Transformation of the cyclic scheduling problem of a large class of FMS into the search of an optimized initial marking of a linearizable weighted T-system

We show that Petri net is a pertinent model to compute analytically the cyclic scheduling of flexible manufacturing system (FMS) with shared non-preemptive resources and assembly or disassembly of multiple components. The proposed method is based on two techniques: 1) the linearization of Petri net conflicts on resources; and 2) the linearization of weighted T-system will give a deterministic marked graph if a specific condition of normalization of the transitions is satisfied. We show that it is possible to compute the best cyclic scheduling in p steps with respect to the cycle time by means of an optimal (min,+) set of linear equations. By using (max,+) algebra it is possible to discriminate among the candidate solutions, the solutions giving the minimum time cycle.

TWO APPROACHES TO THE CYCLIC SCHEDULING WITH ASSEMBLY

Abstract This paper concerns the domain of Flexible Manufacturing Systems (FMS) and focuses on the scheduling problems encountered in these systems. We have chosen the cyclic behaviour to study this problem, to reduce its complexity. This cyclic scheduling problem, whose complexity is NP-hard in the general case, aims at optimize the cycle time (CT) with a minimal WIP(Work In Process). In this context, We present two resolution approaches. In the first step, a genetic approach is proposed to find a schedule which can reach the optimal production rate while minimizing the WIP. In the second step, after a Petri net model of the cyclic scheduling problem has been given, we describe a formal approach of the cyclic scheduling problem based on dioid algebra. Finally we conclude with a comparison of the two approaches.

Petri Net Model and Mathematical Resolution for Cross Docking

Abstract In this paper, we consider a truck dock assignment problem. The constaints are: the number of trucks exceeds the number of docks available and we evaluate the time constaint in the cross docks with the use of resources. The goal is to minimize the penality cost, we are not able to unload all trucks for thre main reason: • the number of trucks exceeds the number of docks available • the time windows of trucks cannot permit the transhipment • there are no sufficient resources or capacity in the cross dock to process the cargo. We will combine an existing model in Miao et al. [2009] to abstract the truck docks assignment and a model from a Petri net study of the internal cross dock with resources. The main idea is to integrate more details, like resource and operational time based on the number of pallets. And this is possible using a Petri net approach with a mathematical tool. Then the final IP model is solved with ILOG CPLEX Solver.

FQ-EDCA: An extension of EDCA to improve fairness in ad-hoc wireless network

IEEE802.11e (EDCA) standard is concerned to support QoS in wireless ad-hoc networks [4]. However, EDCA cannot control traffic when there is a congestion to guarantee QoS required by real-time and multimedia applications. Therefore, the ill-behaved sources consume the most of bandwidth allowed. That leads to some of source nodes (i.e. Out-ranged nodes) suffer from the lack of bandwidth and unfairness. So, without a proper control mechanism, this leads to degrade the guarantee services. Our proposition (FQ-EDCA) is a Fairness Queuing model for EDCA. This paper aims to evaluate its scalability and its robustness. It enhances the QoS of EDCA by implementing a hierarchical scheduling techniques and improving the architecture of EDCA scheme. Thereby, the traffic is regulated between the source nodes. Thus, the bandwidth is distributed fairly between all the source nodes. As a consequence, these nodes can transmit their packets fairly with respect to the EDCA specifications. Moreover, the end-to-end delay of packets for the flows of the same priorities is bounded (i.e. for outranged source nodes). Therefore, the services guarantees of QoS is enhanced by FQ-EDCA, which is proved and analyzed by experimental simulations for large scale topologies.

A Formal Approach for Timed Weighted T-Systems

This paper is a consequence of further works which deal with the linear character of weighted T-systems in dioids like (max ,+) or (min ,+). Our objective is to propose an algebraic point of vue this kind of Petri nets. The deterministic property permits to propose a mathematical abstraction of the Petri net behavior and the possibility to evaluate some properties on the system of equations. And the next result decline the possibility to transform the weighted T-systems in a marked graph.

On the Linearization of Weighted T-Systems

This paper deals with the possibility to study the behavior of a large class of Petri net: weighted T-systems (WTS). We recall recent results which propose to linearize WTS on a marked graph (MG), in order to obtain a model which can be analyzed using tropical algebra like (max, +) or (min, +). In the last part, we present a transformation to extend the previous results. The idea is to introduce synchronization in the model, this kind of transition enrich the model and gives the opportunity to apply the different results