Minimizing Mean Response Time in Nonobservable Distributed Processing Systems with Nodes Operating under Egalitarian Processor-Sharing Policy

Consideration is given to the dispatching problem in an almost nonobservable distributed processing system with M, M >= 2, single-server queues operating in parallel, each under the processor-sharing discipline. Jobs having the same job size distribution arrive one-by-one to the dispatcher, which immediately routes it to one of the queues. When making a routing decision, the dispatcher has no online information about the system (like current queues sizes, size of arriving job, etc.). The only information available to the dispatcher is job-size distribution, job-interarrival-time distribution, server speeds, time instants of previously arrived jobs, and previous routing decisions. Under these conditions, one is interested in the routing policies that minimize the job long-run mean response time. A new class of dispatching policies is proposed that, according to the numerical experiments, may significantly outperform all classical dispatching policies available for such system: (optimal) probabilistic policy and the round-robin policy.