OPTIMAL FLOW-CONTROL ALLOCATION POLICIES IN COMMUNICATION-NETWORKS WITH MULTIPLE MESSAGE CLASSES

We consider M (greater-than-or-equal-to 2) transmitting stations sending packets to a single receiver over a slotted time-multiplexed link. For each phase consisting of T consecutive slots, the receiver dynamically allocates these slots among the M transmitters. The cost per slot for holding a packet may vary among the transmitters, and may be interpreted in terms of multiple classes of messages. Our objective is to characterize policies that minimize the discounted and long-term average costs due to holding packets at the M stations, based on delayed information on the numbers of packets being held at the respective transmitters. We derive properties of optimal (discounted) policies that reduce the computational complexity of the optimal How control algorithm. For M = 2, we show that the minimal total cost is convex and submodular in the state, and we prove the following properties of optimal policies: 1) when the state at transmitter i increases by unity while the state at the other transmitter j is fixed, the optimal allocation is either unchanged, or increases by one at transmitter i and decreases hy one at transmitter j; and 2) the optimal policy is of the threshold type. We use these properties to show that the optimization reduces to the calculation of optimal allocations for a finite number of states. In addition, for each such state (excluding the origin), property 1) implies a significant reduction in the computation of optimal allocations. As an application, we further characterize optimal policies when the message generation at the transmitter of higher priority is stochastically larger than the message generation at the other. Under additional restrictions on the average arrival rate and the second moment of the number of arrivals per slot, similar results are derived for optimal policies with time-average costs.