Stable routing scheduling algorithms in multi-hop wireless networks

Stability is an important issue in order to characterize the performance of a network, and it has become a major topic of study in the last decade. Roughly speaking, a communication network system is said to be stable if the number of packets waiting to be delivered (backlog) is finitely bounded at any one time. In this paper we introduce a number of routing scheduling algorithms which, making use of certain knowledge about the network's structure, guarantee stability for certain injection rates. First, we introduce two new families of combinatorial structures, which we call universally strong selectors and generalized universally strong selectors, that are used to provide a set of transmission schedules. Making use of these structures, we propose two local-knowledge packet-oblivious routing scheduling algorithms. The first proposed routing scheduling algorithm only needs to know some upper bounds on the number of links and on the network's degree, and is asymptotically optimal regarding the injection rate for which stability is guaranteed. The second proposed routing scheduling algorithm is close to be asymptotically optimal, but it only needs to know an upper bound on the number of links. For such algorithms, we also provide some results regarding both the maximum latencies and queue lengths. Furthermore, we also evaluate how the lack of global knowledge about the system topology affects the performance of the routing scheduling algorithms.