Delay-minimal transmission for average power constrained multi-access communications

We investigate the problem of minimizing the overall transmission delay of packets in a multi-access wireless communication system, where the transmitters have average power constraints. We use a multi-dimensional Markov chain to model the medium access control layer behavior. The state of the Markov chain represents current queue lengths. Our goal is to minimize the average packet delay through controlling the probability of departure at each state, while satisfying the average power constraint for each queue. We consider a general asymmetric system, where the arrival rates to the queues, channel gains and average power constraints of the two users are arbitrary. We formulate the problem as a constrained optimization problem, and then transform it to a linear programming problem. We analyze the linear programming problem, and develop a procedure by which we determine the optimal solution analytically. We show that the optimal policy has a threshold structure: when the sum of the queue lengths is larger than a threshold, both users should transmit a packet during the current slot; when the sum of the queue lengths is smaller than a threshold, only one of the users, the one with the longer queue, should transmit a packet during the current slot. We provide numerical examples for both symmetric and asymmetric settings.