Minimum delay scheduling with multi-packet transmission in wireless networks

This paper studies the problem of minimum delay scheduling in wireless networks with multi-packet transmission capability. Specifically, we assume that the network employs superposition coding at the physical layer in order to implement multi-packet transmission. While most studies on superposition coding assume that unbounded number of packets can be coded together, physical and MAC layer limitations restrict the number of concurrent packets in a transmission set. Taking this constraint into consideration, we formulate the minimum delay scheduling as a combinatorial optimization problem and study its computational complexity under different transmission set sizes. We show that, when the transmission set size is limited to 2 packets, the problem can be solved optimally in polynomial time. Moreover, while the complexity of the problem for larger transmission set sizes is unknown, we present close-to-optimal heuristic algorithms that compute efficient solutions for the problem in polynomial time. Numerical results are also presented to study the efficiency and utility of the presented scheduling algorithms. Our results show that the heuristic algorithms are highly efficient, achieving delays that are less than 2% away from the optimal values.