Page 2 Lecture Notes in Computer Science 2865 Edited by G. Goos ...

Steiner Systems for Topology-TransparentAccess Control in MANETsCharles J. Colbourn 1,⋆ , Violet R. Syrotiuk 1,⋆⋆ , and Alan C.H. Ling 21 Computer Science & Engineering, Arizona State University, Tempe, AZ 85287-54062 Computer Science, University of Vermont, Burlington, VT 05405Abstract. In this paper we examine the combinatorial requirements oftopology-transparent transmission schedules for channel access in mobilead hoc networks. We formulate the problem as a combinatorial questionand observe that its solution is a cover-free family. The mathematicalproperties of certain cover-free families have been studied extensively. Indeed,we show that both existing constructions for topology-transparentschedules (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 thenexplore the minimum and expected throughput for Steiner systems ofsmall strength, first using the acknowledgement scheme proposed earlierand then using a more realistic model of acknowledgements. We contrastthese results with the results for comparable orthogonal arrays, indicatingsome important trade-offs for topology-transparent access controlprotocols.1 IntroductionIn any network based on a shared broadcast channel, the means by which accessto the channel is controlled has a fundamental impact on the overall networkperformance. While these networks include satellites and local area networks,our interest is in mobile ad hoc networks (MANETs). A MANET is a collectionof mobile wireless nodes. What distinguishes a MANET from other wirelessnetworks is that it self-organizes without the aid of any centralized control or anyfixed infrastructure. Since the radio transmission range of each node is limited,it may be necessary to forward over multiple hops in order for a packet to reachits destination (as such, MANETs have also been called multi-hop and packetradionetworks). This also offers the opportunity for concurrent transmissionswhen nodes are sufficiently separated. The challenge in medium access control(MAC) protocols for MANETs is to find a satisfactory trade-off between the twoobjectives of minimizing delay and maximizing throughput.Of the myriad of access control techniques, our focus is on topology- transparentapproaches. Unlike topology-dependent protocols, which recompute accesswhenever the network topology changes, a topology-transparent protocol acts independentlyof topology change. One class of protocols which may be viewed as⋆ This work was supported in part by ARO grant DAAD 19-01-1-0406.⋆⋆ This work was supported in part by NSF grant ANI-0105985.S. Pierre, M. Barbeau, and E. Kranakis (Eds.): ADHOC-NOW 2003, LNCS 2865, pp. 247–258, 2003.c○ Springer-Verlag Berlin Heidelberg 2003