Dispatching in nonobservable parallel queues with finite capacities

Consideration is given to the problem of optimal centralized routing in one simple model of volunteer computer systems. The model consists of the finite number of parallel finite-capacity FIFO (first in, first out) queues, each with a single server, and a single dispatcher. Homogeneous jobs arrive one-by-one in a stochastic manner to the dispatcher which must instantly make a routing decision based solely on its previous routing decisions and, possibly, the time instants at which those decisions were made. Although no feedback from the queues is available, the dispatcher knows the maximum queues' capacities, all service rates, the distribution of job sizes, and the inter-arrival time distribution. The new algorithm for generating routing decisions “on the fly” which optimizes the given cost function of the stationary mean sojourn time and the loss probability is proposed.