Scheduling flows with unknown sizes

Abstract

Previous job scheduling studies indicate that providing rapid response to interactive jobs which place frequent but small demands, can reduce the overall system average response time [1], especially when the job size distribution is skewed (see [2] and references therein). Since the distribution of Internet flows is skewed, it is natural to design a network system that favors short file transfers through service differentiation. However, to maintain system scalability, detailed per-flow state such as flow length is generally not available inside the network. As a result, we usually resort to a threshold-based heuristic to identify and give preference to short flows. Specifically, packets from a new flow are always given the highest priority. However, the priority is reduced once the flow has transferred a certain amount of packets.In this paper, we use the MultiLevel (ML) feedback queue [3] to characterize this discriminatory system. However, the solution given in [3] is in the form of an integral equation, and to date the equation has been solved only for job size distribution that has the form of mixed exponential functions. We adopt an alternative approach, namely using a conservation law by Kleinrock [1], to solve for the average response time in such system. To that end, we approximate the average response time of jobs by a linear function in the job size and solve for the stretch (service slowdown) factors. We show by simulation that such approximation works well for job (flow) size distributions that possess the heavy-tailed property [2], although it does not work so well for exponential distributions.Due to the limited space available, in Section 2 we briefly describe the queueing model and summarize our approximation approach to solving for the average response time of the M/G/1/ML queueing system. We conclude our paper in Section 3.