Formulas and representations for cyclic Markovian networks via Palm calculus

We present an extension of the arrival theorem for the output process from a node in closed Markovian networks which we use to obtain simple representations and explicit expressions for the throughput, the distribution of the cycle time, and the joint distribution of interoutput times from a node in single class closed networks with exponential servers. Our approach uses tools from Palm calculus to obtain a recursion on the number of customers in the system. The analysis relies on a non-overtake condition and thus many of the results obtained here apply only to cyclic, single server networks. One of the surprising conclusions of our analysis is that the interoutput times that comprise the cycle time of a customer are (finitely) exchangeable, i.e., that their joint distribution is invariant under permutations.