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1. E. Hyytiä, A. Penttinen, S. Aalto and J. Virtamo, Dispatching problem with fixed size jobs and processor sharing discipline, in 23rd International Teletraffic Congress (ITC'23), 2011 (bib)

   Abstract: We consider a distributed server system with m servers operating under the processor sharing (PS) discipline. A stream of fixed size tasks arrives to a dispatcher, which assigns each task to one of the servers. We are interested in minimizing the mean sojourn time, i.e., the mean response time. To this end, we first analyze an M/D/1-PS queue in the MDP framework. In particular, we derive a closed form expression for the so-called relative value of state, that sums up the deviation from the average rate at which sojourn times are accumulated in the infinite time horizon. This result can be applied in numerous situations. Here we give few examples in the context of dispatching problems by deriving efficient and robust state-dependent dispatching policies for homogeneous and heterogeneous server systems. The obtained policies are further demonstrated by numerical examples.