A collision resolution algorithm for a finite user model

The authors consider that initial collision multiplicity or the number of active users at the beginning of the collision resolution epoch is known, and obtain an optimal collision resolution algorithm. They then assume that the probability distribution over the initial states is given, suggest a sub-optimal algorithm and compare its performance with that of the optimal algorithm. The dynamic programming solution for the collision resolution problem formulated as an optimal first passage problem of a Markovian decision process derives an algorithm which is optimal in the sense of minimising the expected time of termination or collision resolution epoch when the number of active users is known