SUMMARYThe method of differential-difference equations is used to investigate the case in which each arrival to a system of two queues joins the shorter queue, or, if they are of equal length, one particular queue. In case each person must remain in the queue which he originally joins, relations are obtained between the asymptotic state probabilities. If queuers are permitted to change queues whenever it seems advantageous to do so, the formulation is simplified, and explicit expressions are obtained.