Prescriptive Analytics for Queue Optimization: An Optimization-based Paradigm for Modelling Queues

60 Pages Posted: 20 Jun 2018 Last revised: 5 Feb 2024

See all articles by Chaithanya Bandi

Chaithanya Bandi

Northwestern University - Kellogg School of Management

Gar Goei Loke

Durham University Business School

Peng Wang

Singapore University of Social Sciences

Taozeng Zhu

Dongbei University of Finance and Economics

Date Written: June 5, 2018

Abstract

Queueing networks occur in many contexts, leading to the need to control and optimize aspects of the network, such as routing of jobs and capacity control. Queuing theory, as it stands, is focused on the analysis of the stochastic properties of a network, leveraging upon them to perform optimization. These methods of analysis are bespoke for the network and rapidly grow in theoretical complexity with network size, with the researcher indispensable in the process. These factors impede the wider use of its techniques in the automation-driven business world. In this paper, we present a fundamentally novel approach to queueing, with the goal of creating a unified framework to solve optimization problems in queueing networks for a large class of queueing problems, that would lend itself to a tractable package that is accessible to business users, untrained in queueing theory. We do so by proposing a novel set of primitives for modelling queues, founded on optimization principles, leaving the correlated stochastics of queues to be resolved as a constrained problem. We also introduce a new state variable, what we call present delay that tracks waiting time at each node. This allows much of the dynamics to decompose into a linear form, which improves tractability. Finally, we handle the stochastics by leveraging emergent techniques in robust optimization that achieves tractable solutions in stochastic optimization formulations. Our final model is one that can solve any connected network of GI/GI/. queues in polynomial time.

Keywords: Optimal Control, Queueing networks, Delay constraints, Fluid models, Diffusion limits, Convex Optimization, Robust Optimization

JEL Classification: C44, C61

Suggested Citation

Bandi, Chaithanya and Loke, Gar Goei and Wang, Peng and Zhu, Taozeng, Prescriptive Analytics for Queue Optimization: An Optimization-based Paradigm for Modelling Queues (June 5, 2018). Available at SSRN: https://ssrn.com/abstract=3190874 or http://dx.doi.org/10.2139/ssrn.3190874

Chaithanya Bandi

Northwestern University - Kellogg School of Management ( email )

2001 Sheridan Road
Evanston, IL 60208
United States

Gar Goei Loke (Contact Author)

Durham University Business School ( email )

Mill Hill Lane
Durham, DH1 3LB
United Kingdom

Peng Wang

Singapore University of Social Sciences ( email )

461 Clementi Road
599491
Singapore
83583856 (Phone)

Taozeng Zhu

Dongbei University of Finance and Economics ( email )

Dalian
China

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