A joint routing and scheduling scheme for wireless networks with multi-packet reception and directional antennas

In this paper, we present a linear programming formulation for the throughput optimization problem in wireless networks that support multi-packet reception (MPR) capability. The formulation takes into account the use of both directional and omni-directional antennas as well as the use of multiple transmitter interfaces per node. The joint routing and scheduling problem is decoupled into routing and scheduling subproblems. We show that the scheduling subproblem is intractable, and propose a polynomial time scheduling algorithm to solve it. We further demonstrate that, for certain type of networks, the completion time of the scheduling algorithm is at most two times the completion time of the the optimal scheduler, which is unknown. We use the proposed scheme for a preliminary study of several design parameters on the performance of MPR-capable networks, including the number of interfaces, the MPR capability and the beamwidth of the antennas.