Bivariate Markov Processes of Intervals

Bivariate Markov interval processes were introduced by Cox and Lewis as natural bivariate analogs of renewal processes. The two-state semi-Markov process and the superposition of two independent renewal processes are each recovered as special cases. The present paper investigates the dependency structure of the B.M.I.P. and gives some of its simpler properties. An application is given to a simple non-Markovian pure loss queueing system.