%0 Conference Paper %1 Vasantam18ITC30 %A Vasantam, Thirupathaiah %A Mazumdar, Ravi R. %B 30th International Teletraffic Congress (ITC 30) %C Vienna, Austria %D 2018 %K Session_1:_Performance_Evaluation itc itc30 %T On Occupancy Based Randomized Routing Schemes in Large Systems of Shared Servers %U https://gitlab2.informatik.uni-wuerzburg.de/itc-conference/itc-conference-public/-/raw/master/itc30/Vasantam18ITC30.pdf?inline=true %X Recently there has been a great interest in randomized load balancing schemes for large systems of parallel servers. Various policies such as SQ(d) (shortest queue amongst d randomly sampled), threshold policies, JIQ (join the idle queue) etc have been studied via a mean-field approach. All these policies are special cases of occupancy based routing decisions. In this paper we present a unified mean-field approach that holds for any routing scheme that only depends on the server occupancy in a system with a large numbers of of processor sharing servers as an archetype of shared resource systems. The mean-field equations we obtain hold for general job length distributions unlike most recent works that assume exponentially distributed job lengths. We then show that the probability measure of occupancy defined on the set of non-negative integers \$\mathcalZ_+\$ obtained from a fixed-point of the mean-field also satisfies the stationary mean-field equations under the assumption that the job lengths are exponential with the same average length. If the mean-field under exponential case has unique fixed-point, then the fixed point is insensitive to the job length distribution. The approach is via a measure-valued Markov process approach.

@inproceedings{Vasantam18ITC30, abstract = {Recently there has been a great interest in randomized load balancing schemes for large systems of parallel servers. Various policies such as SQ(d) (shortest queue amongst d randomly sampled), threshold policies, JIQ (join the idle queue) etc have been studied via a mean-field approach. All these policies are special cases of occupancy based routing decisions. In this paper we present a unified mean-field approach that holds for any routing scheme that only depends on the server occupancy in a system with a large numbers of of processor sharing servers as an archetype of shared resource systems. The mean-field equations we obtain hold for general job length distributions unlike most recent works that assume exponentially distributed job lengths. We then show that the probability measure of occupancy defined on the set of non-negative integers \$\mathcalZ_+\$ obtained from a fixed-point of the mean-field also satisfies the stationary mean-field equations under the assumption that the job lengths are exponential with the same average length. If the mean-field under exponential case has unique fixed-point, then the fixed point is \em insensitive to the job length distribution. The approach is via a measure-valued Markov process approach.}, added-at = {2018-09-12T17:41:00.000+0200}, address = {Vienna, Austria}, author = {Vasantam, Thirupathaiah and Mazumdar, Ravi R.}, biburl = {https://www.bibsonomy.org/bibtex/2c82979059c0c128f63b3df2cf8a25e8b/itc}, booktitle = {30th International Teletraffic Congress (ITC 30)}, interhash = {65bbaca0e3b75d5db573aa5cfad1d274}, intrahash = {c82979059c0c128f63b3df2cf8a25e8b}, keywords = {Session_1:_Performance_Evaluation itc itc30}, timestamp = {2020-05-24T20:14:34.000+0200}, title = {On Occupancy Based Randomized Routing Schemes in Large Systems of Shared Servers}, url = {https://gitlab2.informatik.uni-wuerzburg.de/itc-conference/itc-conference-public/-/raw/master/itc30/Vasantam18ITC30.pdf?inline=true}, year = 2018 }