A system where Poisson arrivals are allocated to K parallel single-server queues by a Bernoulli process is considered. After having been served, the jobs are required to leave the system in the order of arrival. This type of problem has become important in such areas as parallel processing, database management, and telecommunications.

The paper derives some new stochastic results concerning the behavior of the sojourn time of an individual job in its queue, and the resequencing time needed to fulfill the ordering requirement.

The results form an interesting addition to the theory of resequencing. On the other hand, these results are not too exciting: they are more or less a verification and refinement of what could have been expected. The derivations of the formulas are easy to follow, if the reader has an adequate background in stochastics.

The validity and applicability of the results have not been considered.