Bad luck when joining the shortest queue
A frequent observation in service systems with queues in parallel is that customers in other queues tend to be served faster than those in ones own queue. This paper quantifies the probability that ones service would have started earlier if one had joined another queue than the queue that was actually chosen, for exponential multiserver systems with queues in parallel in which customers join one of the shortest queues upon arrival and in which jockeying is not possible.
queueing join-the-shortest-queue probability of bad luck power-series algorithm overtaking customers dedicated customers