We present some, partly tentative, results of our joint work with Jim Wolfe, that was in progress at the time of his death. The work concerns the interpretation of the routing matrix in an infinite-server queueing network as a 'linear' operator on valued random vectors. This enables us to define the concepts of operator-selfdecomposability and stability for such vectors. It turns out that there is an intimate correspondence between operator-selfdecomposable distributions and limit distributions in queueing networks. Various other analogues to results for real random vectors by Sharpe  and Sato and Yamazato  are discussed and related to the queueing model.
|Journal||Communications in Statistics. Part C, Stochastic Models|
|Publication status||Published - 1986|