In a queuing system with an ordered sequence of stations, the arrivals process is arbitrary and service times are regular at all stations. The case where each station consists of the same number of servers in parallel and the service times at all servers belonging to one station are the same is investigated and shown to possess the following properties: (a) The time spent in the system by any customer is independent of the order of the stations and of the allowable sizes of the intermediate queues; (b) The waiting time (not including service) of any customer equals the time the same customer would have been waiting in the queue of a single station system with regular service time, equaling the longest service time of the sequence (assuming the same arrivals process in both systems). These properties enable one to obtain waiting time distributions and other characteristics of such queuing processes.