International audience

In this article, we emphasize on one hand the importance of quantifying the shortage cost in order to measure the optimal parameters for any selected inventory policy and thus enhance the performance of the supply chain and on the other hand the complexity of doing so. Then, we provide a detailed literature review of the existing various models for quantifying the shortage cost in an inventory management context along with a classification of this literature under three categories: Theoretical descriptive models, empirical approaches and simulation based models. Finally, we point out some gaps in this literature such as the lack of continuity of research in this field and the absence of generic fairly easy to apply but accurate methods and we suggest a few future perspectives.

The need to guarantee quality-of-service (QoS) to multimedia applications leads to a tight integration between the routing and forwarding functions in the Internet. multiprotocol label switching tries to provide a global solution for this integration. In this context, multipoint-to-point (m2p) networks appear as a key architecture since they provide a cheaper way to connect edge nodes than point-to-point connections. M2p networks have been mainly studied for their load balancing ability. In this paper, we go a step further: we propose and evaluate a traffic management scheme that provides deterministic QoS guarantees for multimedia sources in an m2p network. We first derive an accurate upper bound on the end-to-end delay in an m2p architecture based on the concept of additivity. Broadly speaking, an m2p network is additive if the maximum end-to-end delay is equal to the sum of local maximum delays. We then introduce two admission control algorithms for additive networks: a centralized algorithm and a distributed algorithm and discuss their complexity and their scalability.

International audience

In this paper, we study quantitative as well as qualitative properties of Fork-Join Queuing Networks with Blocking (FJQN/Bs). Specifically, we prove results regarding the equivalence of the behavior of a FJQN/B and that of its duals and a strongly connected marked graph. In addition, we obtain general conditions that must be satisfied by the service times to guarantee the existence of a long-term throughput and its independence on the initial configuration. We also establish conditions under which the reverse of a FJQN/B has the same throughput as the original network. By combining the equivalence result for duals and the reversibility result, we establish a symmetry property for the throughput of a FJQN/B. Last, we establish that the throughput is a concave function of the buffer sizes and the initial marking, provided that the service times are mutually independent random variables belonging to the class of PERT distributions that includes the Erlang distributions. This last result coupled with the symmetry property can be used to identify the initial configuration that maximizes the long-term throughput in closed series-parallel networks.

The authors consider closed queuing networks with general service times and subnetworks having population constraints. Each such subnetwork consist of a subset of stations of the original network. The population constraint of a subnetwork prescribes that the total number of customers than can be simultaneously present inside the subnetwork is limited to a fixed value, called the capacity of the subnetwork. A customer wanting to enter a subnetwork while it is full must wait in an external queue. As soon as a customer leaves the subnetwork, the first customer in line is allowed to enter the subnetwork. Such queuing networks with population constraints are of interest for modeling and analysis of manufacturing systems. Two approximate techniques for analyzing such networks, namely the aggregation technique and the method of R. Marie (1979, 1980), are compared.>

The authors discuss the performance evaluation of a closed transfer line with a limited number of pallets. They consider a system consisting of machines separated by buffers of limited capacity. Each machine has a constant processing time and is prone to failures. A continuous flow model is used to describe the behavior of such a system. This model is analyzed by a decomposition method which is an extension of a method developed for open transfer lines. The constraint of the population is taken into account by imposing the condition that the sum of the average queue lengths is equal to the number of pallets of the closed line. Numerical examples show the accuracy of the method.>

The authors consider a multiclass open queueing network with class-dependent window flow control; that is, the total number of jobs of each class that may be present in the network cannot exceed a given value. A job that arrives at the network during the time that the current number of jobs of the same class is equal to the population constraint, is forced to wait in an external queue. A method is presented for obtaining an approximate solution of such a queueing network. The method is based on the use of an equivalent closed queuing network model, which is analyzed using an approximate product-form solution technique. The performance parameters of the original open queueing network are easily derived from the equivalent closed queueing network. Numerical results show that this method is fairly accurate.>

We study a class of queueing networks in which a number of subnetworks have a limited global capacity, i.e. the total number of customers present in the subnetwork cannot exceed a fixed value. We show that under a condition called "global reversible routing", the system has the so-called product-form solution. We then derive an algorithm to predict the performance of the system. Though the result is of interest for any kind of queueing systems, such as Computer systems and communication networks, we emphasize the flexible manufacturing system application. We show that our model is especially well suited to handle a flexible manufacturing system consisting of cells, where each cell is composed of a set of work stations and a local storage area.

We introduce the concept of approximate disaggregation which enables us to replace a station by a subnetwork, i.e. a set of stations, such that the performance of the derived network is close to the performance of the initial network. We use this concept to disaggregate any multiple-server station into a set single-server stations. Using two different disaggregations, we are able to bound the performance of the initial network by the performance of a “lower” and an “upper” network each consisting of single-server stations, whose performance can in turn be bounded by the Balanced Job Bounds (or other known bounds). Several examples show the useful information provided by these bounds at a very low cost: for Κ stations and Ν customers, the computational complexity here is Ο(Κ) which is significantly less than the Ο(ΚΝ2) operations required for exact solution. Indeed, despite the multiple server stations, the computational complexity of our bounds is the same as that of Balanced Job Bounds.