An occupancy model that has arisen in the investigation of randomized distributed schedules in all-optical networks is considered. The model consists of B initially empty urns, and at stage j of the process dj ≤ B balls are placed in distinct urns with uniform probability. Let Mi(j) denote the number of urns containing i balls at the end of stage j. An explicit expression for the joint factorial moments of M0(j) and M1(j) is obtained. A multivariate generating function for the joint factorial moments of Mi(j), 0 ≤ i ≤ I, is derived (where I is a positive integer). Finally, the case in which the dj, j ≥ 1, are independent, identically distributed random variables is investigated.
