Achieving delay differentiation by scheduling based on optimal balancing of weighted instantaneous and cumulative queue lengths

Scheduling policies for statistical multiplexing should provide delay differentiation between different traffic classes, where each class represents an aggregate traffic of individual applications having the same target queueing delay requirements. We propose scheduling to optimally balance weighted queue lengths as an approach to delay differentiation, class weights being set inversely proportional to the respective products of target delays and packet arrival rates. We formulate the problem in the framework of Markov decision theory, assuming a discrete-time, two-class, single-server queueing model with unit service time per packet. We first find a scheduling policy based on weighted instantaneous queue lengths, for the case of Bernoulli packet arrivals, that minimizes the stationary mean of the absolute value of the difference of the weighted instantaneous queue lengths. We then find a scheduling policy based on weighted cumulative queue lengths, for the case of i.i.d. packet batch arrivals, that achieves target mean queueing delays in simulation.