Product Form Solution for the Steady-State Distribution of a Markov Chain Associated with a General Matching Model with Self-loops

Abstract

We extend the general matching graph model to deal with matching graph where every node has a self loop. Thus the states on the Markov chain are associated with the independent sets of the matching graph. We prove that under i.i.d. arrivals assumptions the steady-state distribution of the Markov chain has a product form solution.