Delay Optimal Scheduling for ARQ-Aided Power-Constrained Packet Transmission Over Multi-State Fading Channels

Abstract

In this paper, we study the delay optimal scheduling policy for a multi-state wireless fading channel, by taking bursty packet arrivals and automatic repeat request-based packet transmission into account. In our system, the average delay each packet experiences includes the time it waits in the queue and the time it may take to retransmit due to packet delivery failure. To reduce the average delay, we propose a joint channel-aware and queue-aware stochastic scheduling policy to determine whether and with which probability the source should transmit based on channel and buffer states, subject to an average power constraint at the transmitter. To find the optimal scheduling probabilities, we formulate a non-linear power-constrained delay minimization problem with the aid of controlled Markov decision processes. The optimization problem is then converted into an equivalent linear programming problem by introducing new variables from the steady-state probabilities of the underlying Markov chain and transmission probabilities. By analyzing its property, we derive the structure of the optimal solution, and exploit it to obtain the optimal probabilities analytically. It is found that the optimal scheduling policy has a double threshold structure, and can significantly reduce the average delay.