Jackson networks with unlimited supply of work

Weiss, Gideon

doi:10.1017/s0021900200000863

Cited by 36 publications

(1 citation statement)

References 7 publications

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“…It complements recent work on queueing systems where some of the servers are always busy [12]. Additionally, this analysis is not dependent on the distributions of arrivals or duration of treatment.…”

Section: Methods: Mathematical Modelsupporting

confidence: 58%

A Mathematical Modelling Approach for Systems Where the Servers Are Almost Always Busy

Pagel

Richards

Utley

2012

Computational and Mathematical Methods in Medicine

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The design and implementation of new configurations of mental health services to meet local needs is a challenging problem. In the UK, services for common mental health disorders such as anxiety and depression are an example of a system running near or at capacity, in that it is extremely rare for the queue size for any given mode of treatment to fall to zero. In this paper we describe a mathematical model that can be applied in such circumstances. The model provides a simple way of estimating the mean and variance of the number of patients that would be treated within a given period of time given a particular configuration of services as defined by the number of appointments allocated to different modes of treatment and the referral patterns to and between different modes of treatment. The model has been used by service planners to explore the impact of different options on throughput, clinical outcomes, queue sizes, and waiting times. We also discuss the potential for using the model in conjunction with optimisation techniques to inform service design and its applicability to other contexts.

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Section: Methods: Mathematical Modelsupporting

confidence: 58%

A Mathematical Modelling Approach for Systems Where the Servers Are Almost Always Busy

Pagel

Richards

Utley

2012

Computational and Mathematical Methods in Medicine

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Analysis of Jackson networks with infinite supply and unreliable nodes

et al. 2017

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Jackson networks are versatile models for analyzing complex networks. In this paper we study generalized Jackson networks with single-server stations, where nodes may have an infinite supply of work. We allow simultaneous breakdown of servers and consider group repair strategies. We establish the existence of a steadystate distribution of the queue-length vector at stable nodes for different types of failure regimes. In steady state the distribution of the failure/repair regime and of the queuelength vector at stable nodes decouples in a product-form way. We provide closed-form solutions for the classical performance measures such as throughput or mean sojourn time at a station.

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Scheduling and Control of Queueing Networks

Weiss

2021

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Applications of queueing network models have multiplied in the last generation, including scheduling of large manufacturing systems, control of patient flow in health systems, load balancing in cloud computing, and matching in ride sharing. These problems are too large and complex for exact solution, but their scale allows approximation. This book is the first comprehensive treatment of fluid scaling, diffusion scaling, and many-server scaling in a single text presented at a level suitable for graduate students. Fluid scaling is used to verify stability, in particular treating max weight policies, and to study optimal control of transient queueing networks. Diffusion scaling is used to control systems in balanced heavy traffic, by solving for optimal scheduling, admission control, and routing in Brownian networks. Many-server scaling is studied in the quality and efficiency driven Halfin–Whitt regime and applied to load balancing in the supermarket model and to bipartite matching in ride-sharing applications.

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Jackson networks with unlimited supply of work

Cited by 36 publications

References 7 publications

A Mathematical Modelling Approach for Systems Where the Servers Are Almost Always Busy

A Mathematical Modelling Approach for Systems Where the Servers Are Almost Always Busy

Analysis of Jackson networks with infinite supply and unreliable nodes

Scheduling and Control of Queueing Networks

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