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 dist
ribution of the cycle time, and the joint distribution of interoutput
times from a node in single class closed networks with exponential ser
vers. Our approach uses tools from Palm calculus to obtain a recursion
on the number of customers in the system. The analysis relies on a no
n-overtake condition and thus many of the results obtained here apply
only to cyclic, single server networks. One of the surprising conclusi
ons of our analysis is that the interoutput times that comprise the cy
cle time of a customer are (finitely) exchangeable, i.e., that their j
oint distribution is invariant under permutations.