Stochastic Matching Model with Returning Items.

We consider a stochastic matching model with general compatibility graph and returning items. The return time is modeled by the sojourn time in a Jackson network. After being matched at their arrival, the items move to a Jackson network where they spend some time before eventually returning to the matching system. This general setting includes phase-type return times as a special case. We prove that under some assumptions about the routing and service in the Jackson network, the steady-state distribution of the Markov chain has a product form solution.