Queueing theory, the set of probabilistic techniques that study waiting lines or queues, is a fundamental tool to analyze the performance of modern telecommunication networks. In this talk, we present the results of the performance analysis of two queueing systems.

We consider a game where users share the capacity of a single server. The allocated capacity to a user is directly proportional to its payment. Each user wants to minimize its payment while ensuring a certain quality of service. Due to lack of analytical expressions for the underlying queuing discipline, we are able to give the solution of the game only under some assumptions. For the general case, we develop an approximation based on a heavy-traffic result and we validate the accuracy of the approximation numerically.

We consider a parallel-server system with homogeneous servers where incoming tasks are dispatched by a single dispatcher that implements a size-based policy such that the servers are equally loaded. We analyze the economies of scale when we scale up the number of servers and the arrival rate proportionately. We consider two continuous service time distributions, uniform and Bounded Pareto, and a discrete distribution with two values. We show that the performance degradation is small for uniformly distributed job sizes, but that for Bounded Pareto and two points distributions it can be unbounded.

References

• Doncel, J., Ayesta, U., Brun, O., & Prabhu, B. (2014). A resource-sharing game with relative priorities. Performance Evaluation, 79, 287-305.
• Doncel, J., Aalto, S., & Ayesta, U. (2017). Economies of Scale in Parallel-Server Systems. In IEEE Infocom 2017.
• Hassin, R. (2016). Rational queueing. CRC press.
• Hassin, R., & Haviv, M. (2003). To queue or not to queue: Equilibrium behavior in queueing systems (Vol. 59). Springer Science & Business Media.
• Harchol-Balter, M. (2013). Performance modeling and design of computer systems: queueing theory in action. Cambridge University Press.
• Harchol-Balter, M., Crovella, M. E., & Murta, C. D. (1999). On choosing a task assignment policy for a distributed server system. Journal of Parallel and Distributed Computing, 59(2), 204-228.

About Josu Doncel

Josu Doncel is currently assistant professor at the University of the Basque Country, where he obtained the Industrial Engineering Degree in 2007, the B.Sc. in Mathematics in 2010 and, in 2011, the MS degree in Applied Mathematics and Statistics. In 2015, he received the PhD degree from Université de Toulouse (France).  He has previously held research positions at LAAS-CNRS (France), INRIA Grenoble (France) and BCAM-Basque Center for Applied Mathematics (Spain) and teaching positions in the following French universities: ENSIMAG, INSA-Toulouse and IUT-Blagnac.

His research interests are the modelling, optimization and performance evaluation of stochastic systems such as telecommunication or electric networks.

This event will be conducted in English