Size- and state-aware dispatching problem with queue-specific job sizes

We consider the dispatching problem in a size- and state-aware multi-queue system with Poisson arrivals and queue-specific job sizes. By size- and state-awareness, we mean that the dispatcher knows the size of an arriving job and the remaining service times of the jobs in each queue. By queue-specific job sizes, we mean that the time to process a job may depend on the chosen server. We focus on minimizing the mean sojourn time (i.e., response time) by an MDP approach. First we derive the so-called size-aware relative values of states with respect to the sojourn time in an M/G/1 queue operating under FIFO, LIFO, SPT or SRPT disciplines. For FIFO and LIFO, the size-aware relative values turn out to be insensitive to the form of the job size distribution. The relative values are then exploited in developing efficient dispatching rules in the spirit of the first policy iteration.

► First we derive relative values of state with respect to sojourn time in M/G/1 queues.
► For FIFO and LIFO, the results are insensitive to the job size distribution.
► For SPT and SRPT, the results are integral expressions.
► The results are applied to size-aware dispatching problems with heterogeneous servers.
► New dispatching rules are obtained by the first policy iteration of the MDP framework.