Abstract
In this paper we propose a highly accurate approximate performance analysis of a heterogeneous server system with a processor sharing service discipline and a general job-size distribution under a generalized join the shortest queue (GJSQ) routing protocol. The GJSQ routing protocol is a natural extension of the well-known join the shortest queue routing policy that takes into account the non-identical service rates in addition to the number of jobs at each server. The performance metrics that are of interest here are the equilibrium distribution and the mean and standard deviation of the number of jobs at each server. We show that the latter metrics are near-insensitive to the job-size distribution using simulation experiments. By applying a single queue approximation we model each server as a single server queue with a state-dependent arrival process, independent of other servers in the system, and derive the distribution of the number of jobs at the server. These state-dependent arrival rates are intended to capture the inherent correlation between servers in the original system and behave in a rather atypical way.
Highlights
1.1 MotivationThis work is motivated by web server farms
We provide an approximate performance analysis of a queueing system consisting of two heterogeneous processor sharing (PS) servers with service rates 1 and s ∈ N, respectively, a general job-size distribution and generalized join the shortest queue (GJSQ) routing
In order to apply single queue approximation (SQA), we established that the GJSQ system is near-insensitive to the job-size distribution and we approximated the system at hand with exponentially distributed job-sizes
Summary
This work is motivated by web server farms. Server farms have gained popularity for providing scalable and reliable computing and web services. In [5] the authors consider a server farm consisting of homogeneous servers, where upon arrival jobs are routed according to the JSQ routing protocol. This protocol in case of homogeneous servers, due to the PS service discipline, is performing near-optimal in terms of the mean response time. In case of general job-size distributions and heterogeneous servers we assume that the only available information are the service rates and the number of jobs at each server, i.e. we do not keep track of residual processing times. Due to the complexity and the various challenges that the model at hand presents, we restrict our analysis to the case
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