MALS: multiple access scheduling based on Latin squares

A Latin square of order n is an n × n square matrix that consists of n distinct symbols, where the symbols of each row and column are distinct. The number of different Latin squares beyond a very small order, such as 10 grows almost to infinity for practical applications. The distinctiveness and orderliness of each symbol in the Latin square present very attractive features in applying Latin squares to the scheduling problems. We propose a medium access scheme based on Latin squares, called MALS (medium access based on Latin squares), from which deterministic time-division channel access schedules are generated for nodes in ad hoc networks. In MALS, each node is assigned with an index of a row in a dynamic Latin square, and the columns of the Latin square corresponds to the time-slotted channel. The value of the symbol in the Latin square for each time slot determines the priority of the node to access the channel. Because of the distinctiveness of the symbol value in each column, a unique priority is assigned to each node in each time slot, and the channel access at any moment is guaranteed collision-free. We apply MALS in both macro-time division channel access scheduling, where each time slot is long enough to contain a packet, and micro-time division channel access scheduling, where the time slot is comparable to the duration of the round trip time in point-to-point wireless communication. Simulations for both scenarios show the near-optimum performance of MALS for channel access scheduling in comparison with UxDMA and IEEE 802.11 DCF, respectively.