Rate-based randomized routing in large heterogeneous processor sharing systems

Randomized load balancing techniques are effective solutions to reduce mean waiting time of jobs in large web server farms, where obtaining state information of all the servers becomes costly. The classical power-of-two routing scheme, which has already been analyzed for systems of identical servers, requires the instantaneous state information of two randomly selected servers at each job-arrival instant. In this paper, we consider variants of the classical power-of-two scheme for multiserver systems where the servers may have different service rates. We modify the classical power-of-two scheme for the heterogeneous system so that it now incorporates server speeds into the criterion for server selection. We analytically characterize the stability region, stationary load distribution, and the mean sojourn time of jobs of this modified scheme. It is shown that, in the heterogeneous case, the stability region of the modified scheme may be a subset of the maximum achievable stability region. To improve the stability region, we propose and analyze another scheme which combines the power-of-two routing scheme with randomized state independent routing scheme. We show that this new scheme achieves the maximum stability region and results in the least mean sojourn time of jobs among all the schemes considered in the paper.