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# Load Balancing in Processor Sharing Systems

1 MAESTRO - Models for the performance analysis and the control of networks
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : In this paper, we investigate optimal load balancing strategies for a multi-class multi-server processor-sharing system with a Poisson input stream, heterogeneous service rates, and a server-dependent holding cost per unit time. Specifically, we study $(i)$ the centralized setting in which a dispatcher routes incoming jobs based on their service time requirements so as to minimize the weighted mean sojourn time in the system; and $(ii)$ the decentralized, distributed non-cooperative setting in which each job, aware of its service time, selects a server with the objective of minimizing its weighted mean sojourn time in the system. For the decentralized setting we show the existence of a potential function, which allows us to transform the non-cooperative game into a standard convex optimization problem. For the two aforementioned settings, we characterize the set of optimal routing policies and obtain a closed form expression for the load on each server under any such policy. Furthermore, we show the existence of an optimal policy that routes a job independently of its service time requirement. We also show that the set of servers used in the decentralized setting is a subset of set of servers used in the centralized setting. Finally, we compare the performance perceived by jobs in the two settings by studying the so-called Price of Anarchy (PoA), that is, the ratio between the decentralized and the optimal centralized solutions. When the holding cost per unit time is the same for all servers, it is known that the PoA is upper bounded by the number of servers in the system. Interestingly, we show that the PoA for our system can be unbounded. In particular this indicates that in our system, the performance of selfish routing can be extremely inefficient.
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https://hal.archives-ouvertes.fr/hal-00286455
Contributeur : Balakrishna Prabhu Connectez-vous pour contacter le contributeur
Soumis le : mardi 10 juin 2008 - 09:15:56
Dernière modification le : mardi 19 octobre 2021 - 23:16:22
Archivage à long terme le : : vendredi 25 novembre 2016 - 21:42:57

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lbpss.pdf
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• HAL Id : hal-00286455, version 2

### Citation

Eitan Altman, Urtzi Ayesta, Balakrishna Prabhu. Load Balancing in Processor Sharing Systems. Telecommunication Systems, Springer Verlag (Germany), 2011, 47 (1-2), pp.35-48. ⟨hal-00286455v2⟩

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