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Job placement with unknown duration and no preemption

We consider the age-old problem of job placement in a distributed server system. Jobs (tasks) arrive according to a Poisson Process and must each be dispatched to exactly one of several host machines for processing. We assume for simplicity that these host machines are identical and that there is no cost for dispatching jobs to hosts. The rule for assigning jobs to host machines is known as the task assignment policy. In this paper we consider the particular model of a distributed server system in which jobs are not preemptible i.e. each job is run-to-completion (no timesharing between jobs). Our model is motivated by batch job schedulers like Load-Leveler, LSF, PBS, and NQS which typically only support run-to-completion [11]. The processing requirements of the jobs are assumed to be i.i.d, according to some distribution G, which we typically assume to be heavy-tailed (to be defined shortly). We assume that the processing requirement of the job is not known at the time the job arrives (although the distribution G could be deduced after many observations). We will use the terms processing requirement, service demand, and size interchangably.