Capacity provisioning for schedulers with tiny buffers

Abstract

Capacity and buffer sizes are critical design parameters in schedulers which multiplex many flows. Previous studies show that in an asymptotic regime, when the number of traffic flows N goes to infinity, the choice of scheduling algorithm does not have a big impact on performance. We raise the question whether or not the choice of scheduling algorithm impacts the capacity and buffer sizing for moderate values of N (e.g., few hundred). For Markov-modulated On-Off sources and for finite N, we show that the choice of scheduling is influential on (1) buffer overflow probability, (2) capacity provisioning, and (3) the viability of network decomposition in a non-asymptotic regime. This conclusion is drawn based on numerical examples and by a comparison of the scaling properties of different scheduling algorithms. In particular, we show that the per-flow capacity converges to the per-flow long-term average rate of the arrivals with convergence speeds ranging from O (√log N/N) to O(1/N) depending on the scheduling algorithm. This speed of convergences of the required capacities for different schedulers (to meet a target buffer overflow probability) is perceptible even for moderate values of N in our numerical examples.