Performance Analysis of a Recursive Cyclic Scheduler for Class-based Scheduling

In this paper, we consider the problem of determining a cyclic (or loop) scheduler that allocates slots to flows as periodically as possible. We use the second moment of the inter-allocation distance for each flow as its periodicity metric. We establish the optimality of a Weighted-Round Robin with spreading (WRR-sp2) scheduler for a two-flow scenario. We consider a class-based scheduling scenario where flows are grouped according to their relative bandwidth demands. We propose a C-class scheduler that recursively performs inter-class scheduling using the corresponding C-1 class scheduler, prior to intra-class scheduling. Optimality is achieved for C = 2 with the WRR-sp2 as the inter-class scheduler. Through numerical results, we show that the recursive scheduler achieves the best periodicity performance at the expense of intra-class fairness, which is desirable for class-based scheduling. Thereby, we expose a trade-off between periodicity and fairness performance in the design of loop schedulers.