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On the asymptotic insensitivity of the supermarket model in processor sharing systems

Boekbijdrage - Boekabstract Conferentiebijdrage

The supermarket model is a popular load balancing model where each incoming job is assigned to a server with the least number of jobs among d randomly selected servers. Several authors have shown that the large scale limit in case of processor sharing servers has a unique insensitive fixed point, which naturally leads to the belief that the queue length distribution in such a system is insensitive to the job size distribution as the number of servers tends to infinity. Simulation results that support this belief have also been reported. However, global attraction of the unique fixed point of the large scale limit was not proven except for exponential job sizes, which is needed to formally prove asymptotic insensitivity. The difficulty lies in the fact that with processor sharing servers, the limiting system is in general not monotone.
Boek: ACM SIGMETRICS 2021, June 14-18, 2021, Beijing, China
Pagina's: 1 - 28
Jaar van publicatie:2021
Trefwoorden:P1 Proceeding
Toegankelijkheid:Closed