Large Tandem Queueing Networks with Blocking

Projet MCRSystems consisting of many queues in series have been considered by Glynn and Whitt (1991) and Baccelli, Borovkov and Mairesse (2000). We extend their results to apply to situations where the queues have finite capacity and so various types of «blocking» can occur. The models correspond to max-plus type recursions, of simple form but in infinitely many dimensions; they are related to «percolation» problems of finding paths of maximum weight through a two-dimensional lattice with random weights at the vertices. Topics treated include: laws of large numbers for the speed of customers progressing through the system; stationary behaviour for systems with external arrival processes; functional laws of large numbers describing the behaviour of the «front of the wave» progressing through a system which starts empty; stochastic orderings for waiting times of customers at successive queues. Several open problems are noted

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.

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

Arrival first queueing networks with applications in kanban production systems

In this paper we introduce a new class of queueing networks called {\it arrival first networks}. We characterise its transition rates and derive the relationship between arrival rules, linear partial balance equations, and product form stationary distributions. This model is motivated by production systems operating under a kanban protocol. In contrast with the conventional {\em departure first networks}, where a transition is initiated by service completion of items at the originating nodes that are subsequently routed to the destination nodes (push system), in an arrival first network a transition is initiated by the destination nodes of the items and subsequently those items are processed at and removed from the originating nodes (pull system). These are similar to the push and pull systems in manufacturing systems