Throughput optimization in single commodity slotted ALOHA multi-hop packet radio networks

The authors investigate the maximum throughput that can be supported between a pair of nodes in a multihop packet radio network using slotted ALOHA. The optimization problem can be formulated as a nonlinear programming problem. The authors study different topologies where source and destination are connected with a number of independent paths and consider the cases in which the flow from source to destination is equally split among all of the independent paths connecting them or optimally split in order to maximize the throughput. For the equal split case and networks with three or more independent s-d paths, it is possible to find a closed-form expression for the maximum throughput and the optimum transmitting probabilities for each node. For optimally splitting the flow among the alternate paths, the authors solve the optimization problem for some small configurations and find a singular behavior for the network with two independent paths two hops each in length