Lex-Optimal Multiclass Scheduling with Deadlines

A new optimality criterion and associated scheduling and dropping algorithm are presented for multiclass packets with deadlines. Equal length packets with deadlines and priority labels are either scheduled by their deadlines or dropped on or possibly before their deadlines. An L-bit priority label is used to handle up to 2 priority classes. A scheduling policy is called lex-optimal within the class of causal scheduling policies if it has the following L properties: (1) For any arrival sequence, it maximizes the cumulative throughput of packets with first priority bit equal to zero, and (2) Subject to (1), for any arrival sequence, it maximizes the cumulative throughput of packets with second priority bit equal to zero. The other properties are similar–the kth property is that subject to the preceding k-1 properties, for any arrival sequence, the policy maximizes the cumulative throughput of packets with kth priority bit equal to zero. A lex-optimal scheduling algorithm is presented with complexity per packet O(LB), where L is the log of the number of priority classes, and B is the maximum buffer size. The algorithm requires no more packets to be buffered than any throughput optimal algorithm, which need not account for priority classes. Keywords—multiclass scheduling, priorities, deadlines