Observing Queues Before Joining

We consider a queueing system with two servers, each with its own queue. The interarrival times are generally distributed. The service time for each server is exponentially distributed but the rates may be different. No jockeying between the two queues is allowed. We consider situations in which a smart customer can delay joining a queue until some arrivals or service departures have been observed. All other customers join the shortest queue. We find conditions under which the smart customer can lower its expected sojourn time in the system by waiting and observing rather than immediately joining the shortest queue.