Energy Optimal Packet Scheduling with Individual Packet Delay Constraints

We consider a problem of scheduling packets in a fading link where each packet is required to reach the destination before a delay deadline. Time is slotted, and at the beginning of each slot, a packet arrives according to an arrival process. A packet on arrival is stored in a buffer, and it is required to reach the destination before a total delay of $d+ 1$ slots (i.e., the maximum waiting time in the buffer can be d time-slots and one time-slot delay for transmission). At the beginning, the transmitter is provided with a finite energy $E_{0}$, and the problem that we consider is to obtain an optimum scheduler that decides which time-slots to be used for transmission such that it maximizes the number of packet transmissions with a total energy $E_{0}$, and within a delay deadline of $d+1$ time-slots for each packet. We model this problem as a Markov Decision process, and provide a dynamic programming (DP) based solution which is prohibitively complex, but can be numerically solved. The computational complexity of the DP solution motivates us to provide two sub-optimal heuristic solutions to the scheduling problem. We provide the throughput and average energy performance of the heuristic solutions.