Chaoticity results for ``join the shortest queue'' (Q2752208)

Consider a large number of \(N\) parallel M/M/1 queues each with infinite waiting room. The queues are coupled by arriving customers being allowed to select their queue according to the shortest queue rule among a randomly selected subset of fixed size \(L\) of the queues. It is shown that this coupling improves the performance of the system and the performance increases in \(L\). The number \(N\) of queues is considered to grow unboundedly. With suitable assumptions on the initial states it is shown that asymptotically the queues behave as if they are independent with adjusted parameters, i.e., the network exhibits asymptotic chaoticity. The case of stationary systems is studied explicitly in more detail, again chaoticity results are proved.NEWLINENEWLINEFor the entire collection see [Zbl 0964.00028].