In this paper the authors study the queues that build up in a minor stream of traffic waiting to cross or merge with a major stream. The criterion for joining or crossing is that a gap between vehicles in the major stream be greater than or equal to some constant value. Several authors have studied the case where bulk service is provided for the minor stream queue with the appearance of each gap, in this paper the authors emphasize the higher flow rate situations where one car in the minor stream queue is released in a first-come first-serve fashion with the appearance of a gap. It is assumed that the minor stream is Poisson-fed while the intervehicle headways in the major stream are arbitrary but identically and independently distributed random variables.