Exploiting Hidden Convexity for Optimal Flow Control in Queueing Networks
49 Pages Posted: 20 Jun 2018 Last revised: 25 Nov 2018
Date Written: June 5, 2018
Optimal ﬂow control in queueing networks is a challenging problem occurring in many contexts, such as data centers, cloud computing, healthcare, revenue management, and distributed networks, etc. The traditional approach has been to adopt heuristic solutions or consider inﬁnite-horizon ﬂuid or diﬀusion approximations. Motivated by emerging techniques in Robust Optimization, we propose a framework, termed Pipeline Queues, which tracks the dynamics of a queue simultaneously in terms of its queue length and waiting time. We begin by showing that the dynamics of a traditional queueing system can be equivalently modeled using this approach. Our key contribution is the uncovering of the hidden convexity resulting from our modeling approach. This leads us to tractable optimization formulations for generic ﬂow control problems of obtaining performance guarantees on average and quantiles of waiting time, under arbitrary arrival and service distributions with non-zero initial conditions. Our model is ﬂexible enough to capture partial observability and uncertainty of the initial state, as well as various constraints on the control policy.
We apply our approach to multiple examples from the literature and numerically illustrate their application. Finally, we implemented our model on a real dataset at a major hospital in India. Our proposed policies are near optimal and perform signiﬁcantly better than present heuristics.
Keywords: Optimal Control, Queueing networks, Delay constraints, Fluid models, Diﬀusion limits, Convex Optimization, Robust Optimization
JEL Classification: C44, C61
Suggested Citation: Suggested Citation