Broadcast stability in random access

We introduce and study the problem of broadcast stability in a network where nodes utilize the ALOHA protocol to gain random access to the channel. We make use of the dominating systems argument used in previous works and also develop a novel method for finding the region of stable arrival rates of packets. The stability region is obtained by analyzing the broadcast service process for a channel with multipacket reception. Our results exhibit the effect of probabilistic reception and multipacket reception on the broadcast stability region. We also show that the broadcast stability region is contained within the stability region for unicast transmission. Our work is applicable to the broadcast transmission that underlies communication in many wireless networks, including multihop networks. In addition, our new method for finding the stability region may be applicable to previously unsolved problems, including the stability region for arbitrarily many sources and destinations