Prescriptive Analytics for Queue Optimization: An Optimization-based Paradigm for Modelling Queues
60 Pages Posted: 20 Jun 2018 Last revised: 5 Feb 2024
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: Suggested Citation