Performance Analysis of Joining the Shortest Queue Model Among a Large Number of Queues

Consider a queueing network with a large number N nodes, in which each queue has a dedicated input stream, and, in addition, there is an extra input stream, balancing the network load by directing its arrivals to the shortest queue(s). A mean field interaction model is set up to study the performance of this network in terms of limiting results. One of our results shows that the stationary behavior of any of the queues is approximated by that of the M/M/1 queue with a modified arrival rate when the queue length is around zero.

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