Steiner systems for topology-transparent access control in MANETs

In this paper we examine the combinatorial requirements of topology-transparent transmission schedules for channel access in mobile ad hoc networks. We formulate the problem as a combinatorial question and observe that its solution is a cover-free family. The mathematical properties of certain cover-free families have been studied extensively. Indeed, we show that both existing constructions for topology-transparent schedules (which correspond to orthogonal arrays) give a cover-free family. However, a specific type of cover-free family - called a Steiner system - supports the largest number of nodes for a given frame length. We then explore the minimum and expected throughput for Steiner systems of small strength, first using the acknowledgement scheme proposed earlier and then using a more realistic model of acknowledgements. We contrast these results with the results for comparable orthogonal arrays, indicating some important trade-offs for topology-transparent access control protocols.