Optimal prioritized conflict resolution on a multiple access channel

A multiple access broadcast network (MABN) is a computer network in which there is a single shared communication channel and every network node can receive all messages transmitted over the channel. A major difficulty in using broadcast communication is the issue of access to the channel. The authors deal with the following prioritized conflict resolution problem: a collection of c messages is initially distributed among nodes on an MABN; each message is associated with a value representing its priority or deadline; and it is required that the messages be broadcast in ascending order of this value. This problem is solved by a distributed prioritized conflict resolution algorithm. It is proved that the expected waiting time of the ith network node to transmit is Θ(i+log c), which is optimal. It is also shown that the algorithm runs in the expected linear time, which is optimal in both the number of slots used and the total elapsed time including local processing