Queueing theory

Summary

Queueing theory is the mathematical study of waiting lines, or queues. A queueing model is constructed so that queue lengths and waiting time can be predicted. Queueing theory is generally considered a branch of operations research because the results are often used when making business decisions about the resources needed to provide a service. Queueing theory has its origins in research by Agner Krarup Erlang, who created models to describe the system of incoming calls at the Copenhagen Telephone Exchange Company. These ideas have since seen applications in telecommunication, traffic engineering, computing, project management, and particularly industrial engineering, where they are applied in the design of factories, shops, offices, and hospitals. Spelling The spelling "queueing" over "queuing" is typically encountered in the academic research field. In fact, one of the flagship journals of the field is Queueing Systems. Single

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Self-Synchronizing Properties of CSMA Wireless Multi-hop Networks

Olivier Dousse, Patrick Thiran, Kuang Xu

We show that CSMA is able to spontaneously synchronize transmissions in a wireless network with constant-size packets, and that this property can be used to devise efficient synchronized CSMA scheduling mechanisms without message passing. Using tools from queuing theory, we prove that for any connected wireless networks with arbitrary interference constraints, it is possible to implement self-synchronizing TDMA schedules without any explicit message passing or clock synchronization besides transmitting the original data packets, and the interaction can be fully local in that each node decides when to transmit next only by overhearing its neighbors’ transmissions. We also provide a necessary and sufficient condition on the emergence of self-synchronization for a given TDMA schedule, and prove that such conditions for self-synchronization can be checked in a finite number of steps for a finite network topology.

2010

QOBJ modeling - A new approach in discrete event simulation

This paper deals with a new discrete event simulation modeling concept, called qobj, which comes from two well-known paradigms: objects and queuing networks. The first provides important conceptual tools for model organization, while the second one allows for nice visualization of models' internal state and processes. Thanks to the integration of these two paradigms, the qobj concept allows the suppression of several dichotomies characterizing current simulation modeling approaches. For instance, qobj allows the description of system elements which are both mobile and able to do processing, and allows the dynamic instantiation of static and mobile elements during simulation. The design of lift group models for an industrial project illustrates the main features of the qobj concept.

Springer Verlag1998

Describing network congestion and blocking with an analytic queueing network model

Michel Bierlaire, Carolina Osorio Pizano

In a network with capacity constraints congestion effects such as bottlenecks, spillbacks and gridlocks can be observed. These can be described with a queueing network model. The main challenge of such an approach lies in adequately capturing the between-queue correlation, which explains these congestion effects as well as their overall network impact. We present an analytic queueing network model, with finite capacity queues, where structural parameters are used to capture the between-queue correlation. We describe the methods validation versus both pre-existing methods and simulation runs. The method is then applied to study patient flow within a set of hospital units of the Geneva University Hospitals. In this context the main source of congestion is known as bed blocking. The model has allowed us to identify three main sources of bed blocking and to quantify their impact upon the different hospital units.

2007