Insensitive Job Assignment With Throughput and Energy Criteria for Processor-Sharing Server Farms

We study the problem of stochastic job assignment in a server farm comprising multiple processor-sharing servers with various speeds and finite buffer sizes. We consider two types of assignment policies: without jockeying, where an arriving job is assigned only once to an available server, and with jockeying, where a job may be reassigned at any time. We also require that the underlying Markov process under each policy is insensitive. Namely, the stationary distribution of the number of jobs in the system is independent of the job size distribution except for its mean. For the case without jockeying, we derive two insensitive heuristic policies: One aims at maximizing job throughput, and the other trades off job throughput for energy efficiency. For the case with jockeying, we formulate the optimal assignment problem as a semi-Markov decision process and derive optimal policies with respect to various optimization criteria. We further derive two simple insensitive heuristic policies with jockeying: One maximizes job throughput, and the other aims at maximizing energy efficiency. Numerical examples demonstrate that, under a wide range of system parameters, the latter policy performs very close to the optimal policy. Numerical examples also demonstrate energy/throughput tradeoffs for the various policies and, in the case with jockeying, they show a potential of substantial energy savings relative to a policy that optimizes throughput.