Friday, 11:00 - 11:25 h, Room: MA 004

 

Nataly Youssef
Robust queueing theory

Coauthors: Chaithanya Bandi, Dimitris Bertsimas

 

Abstract:
We propose an approach for studying queueing systems by employing robust optimization as opposed to stochastic analysis. While traditional queueing theory relies on Kolmogorov's axioms and models arrivals and services as renewal processes, we use the limiting laws of probability as the axioms of our methodology and model the queueing primitives by uncertainty sets. We begin by analyzing the performance of single-class multi-server queues and obtain closed form expressions for the waiting times with heavy-tailed arrival and service processes; expressions that are not available under traditional queueing theory. We develop an exact calculus for analyzing a network of queues based on the following key principle: (a) the departure, (b) the superposition, and (c) the thinning of arrival processes have the same uncertainty set representation as the original arrival processes. We also derive closed form expressions for the transient behavior of single class queues and feed-forward networks. We show that our approach (a) yields accurate results in comparison to simulations for large scale queueing networks, and (b) is to a large extent insensitive to network size and traffic intensity.

 

Talk 2 of the invited session Fri.1.MA 004
"A robust optimization approach to stochastic analysis" [...]
Cluster 20
"Robust optimization" [...]

 

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