Transmission scheduling for wireless and satellite systems

Abstract

We study queuing systems with time-varying service rates, as a natural model of satellite and wireless communication systems. Packets arrive at a satellite to be transmitted to one of the sub-regions (channels) in a service area. The packets are stored in an on-board buffer and in a separate queue for each channel. The satellite has a limited power available for scheduling transmissions, and a fixed number of transmitters. The power allocated to a particular channel, in conjunction with the channel state, determines the transmission rate of the channel, i.e., the service rate for the queue corresponding to that channel. The assignment of transmitters to the queues as well as the power allocated to each transmitter are modeled as control variables. The goal is to design a power allocation policy so that the expected queue size, in steady-state, is minimized. We model the system as a slotted system with N queues, and i.i.d. Bernoulli arrivals at each queue during each slot. Each queue is associated with a channel that changes between "on" and "off" states according to i.i.d. Bernoulli processes. We assume that the system has K identical transmitters ("servers").

(cont.) Each server, during each slot, can transmit up to Co packets from a queue associated with an "on" channel. We show that when K and Co are arbitrary and a total of up to KCo packets can be served from all the N queues in a time slot, a policy that assigns the K servers to the "on" channels associated with the K longest queues is optimal. We also consider a "fluid" service model under which fractional packets can be served, for the case K = N, and subject to a constraint that at most C packets can be served in total over all of the N queues. We show that there is an optimal policy which serves the queues so that the resulting vector of queue lengths is "Most Balanced." We also describe techniques to upper bound the expected queue size in steady-state under an optimal policy.