On the variance of the least attained service policy and its use in multiple bottleneck networks

Size-based scheduling has proved to be effective in a lot of scenarios involving Internet traffic. In this work, we focus on the Least Attained Service Policy, a popular size-based scheduling policy. We tackle two issues that have not received much attention so far. First, the variance of the conditional response time. We prove that the classification proposed by Wierman et al. [11], which classifies LAS has an always unpredictable policy, is overly pessimistic. We illustrate the latter by focusing on the M/M/1/LAS queue. Then we consider LAS queues in tandem. We provide preliminary results concerning the characterization of the output process of an M/M/1/LAS queue and the conditional average response time and its variance for LAS queues in tandem.