A Maclaurin-series expansion approach to coupled queues with phase-type distributed service times

International audienc

A Fixed-Point Algorithm for Closed Queueing Networks

In this paper we propose a new efficient iterative scheme for solving closed queueing networks with phase-type service time distributions. The method is especially efficient and accurate in case of large numbers of nodes and large customer populations. We present the method, put it in perspective, and validate it through a large number of test scenarios. In most cases, the method provides accuracies within 5% relative error (in comparison to discrete-event simulation)

Capacity planning of prisons in the Netherlands

In this paper we describe a decision support system developed to help in assessing the need for various type of prison cells. In particular we predict the probability that a criminal has to be sent home because of a shortage of cells. The problem is modelled through a queueing network with blocking after service. We focus in particular on the new analytical method to solve this network

A tractable analytical model for large-scale congested protein synthesis networks

This paper presents an analytical model, based on finite capacity queueing network theory, to evaluate congestion in protein synthesis networks. These networks are modeled as a set of single server bufferless queues in a tandem topology. This model proposes a detailed state space formulation, which provides a fine description of congestion and contributes to a better understanding of how the protein synthesis rate is deteriorated. The model approximates the marginal stationary distributions of each queue. It consists of a system of linear and quadratic equations that can be decoupled. The numerical performance of this method is evaluated for networks with up to 100,000 queues, considering scenarios with various levels of congestion. It is a computationally efficient and scalable method that is suitable to evaluate congestion for large-scale networks. Additionally, this paper generalizes the concept of blocking: blocking events can be triggered by an arbitrary set of queues. This generalization allows for a variety of blocking phenomena to be modeled.Swiss National Science Foundation (Grant 205320-117581

A tight bound on the throughput of queueing networks with blocking

In this paper, we present a bounding methodology that allows to compute a tight lower bound on the cycle time of fork--join queueing networks with blocking and with general service time distributions. The methodology relies on two ideas. First, probability masses fitting (PMF) discretizes the service time distributions so that the evolution of the modified network can be modelled by a Markov chain. The PMF discretization is simple: the probability masses on regular intervals are computed and aggregated on a single value in the orresponding interval. Second, we take advantage of the concept of critical path, i.e. the sequence of jobs that covers a sample run. We show that the critical path can be computed with the discretized distributions and that the same sequence of jobs offers a lower bound on the original cycle time. The tightness of the bound is shown on computational experiments. Finally, we discuss the extension to split--and--merge networks and approximate estimations of the cycle time.queueing networks, blocking, throughput, bound, probability masses fitting, critical path.

Threshold queueing describes the fundamental diagram of uninterrupted traffic

Queueing due to congestion is an important aspect of road traffic. This paper provides a brief overview of queueing models for traffic and a novel threshold queue that captures the main aspects of the empirical shape of the fundamental diagram. Our numerical results characterises the sources of variation that influence the shape of the fundamental diagram

Approximations for fork/join systems with inputs from multi-server stations.

Fork/join stations are commonly used to model synchronization constraints in queuing network models of computer and manufacturing systems. This paper presents an exact analysis of a fork/join station in a closed queuing network with inputs from multi-server stations with two-phase Coxian service distributions. The underlying queue length process is analyzed exactly to determine performance measures such as through put, and distributions of the queue length at the fork/join station. By choosing suitable parameters for the two-phase Coxian distributions, the effect of variability in inputs on system performance is studied. The study reveals that for several system configurations, analysis of the simpler system with exponential inputs provides efficient approximations for performance measures. Both, the exact analysis and the simple approximations of fork/join systems constitute useful building blocks for developing efficient methods for analyzing large queuing networks with fork/join stations.queueing; fork/join; synchronization; assembly systems; closed queuing networks;

Manufacturing flow line systems: a review of models and analytical results

The most important models and results of the manufacturing flow line literature are described. These include the major classes of models (asynchronous, synchronous, and continuous); the major features (blocking, processing times, failures and repairs); the major properties (conservation of flow, flow rate-idle time, reversibility, and others); and the relationships among different models. Exact and approximate methods for obtaining quantitative measures of performance are also reviewed. The exact methods are appropriate for small systems. The approximate methods, which are the only means available for large systems, are generally based on decomposition, and make use of the exact methods for small systems. Extensions are briefly discussed. Directions for future research are suggested.National Science Foundation (U.S.) (Grant DDM-8914277