  In this paper, the problem of assigning channel slots to a number of
contending stations is modeled as a Constraint Satisfaction Problem (CSP). A
learning MAC protocol that uses deterministic backoffs after successful
transmissions is used as a decentralized solver for the CSP. The convergence
process of the solver is modeled by an absorbing Markov chain (MC), and
analytical, closed-form expressions for its transition probabilities are
derived. Using these, the expected number of steps required to reach a solution
is found. The analysis is validated by means of simulations and the model is
extended to account for the presence of channel errors. The results are
applicable in various resource allocation scenarios in wireless networks.
