Analysis of SITA policies

We analyze the performance of Size Interval Task Assignment (SITA) policies, for multi-host assignment in a non-preemptive environment. Assuming Poisson arrivals, we provide general bounds on the average waiting time independent of the job size distribution. We establish a general duality theory for the performance of SITA policies. We provide a detailed analysis of the performance of SITA systems when the job size distribution is Bounded Pareto and the range of job sizes tends to infinity. In particular, we determine asymptotically optimal cutoff values and provide asymptotic formulas for average waiting time and slowdown. We compare the results with the Least Work Remaining policy and compute which policy is asymptotically better for any given set of parameters. In the case of inhomogeneous hosts, we determine their optimal ordering.