For the M(t)/M(t)/2 queue the transition probabilities , of the Markov chain formed by the number N(t) of customers in the system are derived. After a suitable change of scale for the time parameter we obtain expressions for these probabilities involving the Bessel functions I n(z) and the solutions of a system of two Volterra integral equations of the second kind. The expected number of customers in the system at a given time t is also determined.
