On the Maximum Queue Length in the Supermarket Model by Malwina
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چکیده
There are n queues, each with a single server. Customers arrive in a Poisson process at rate λn, where 0 < λ < 1. Upon arrival each customer selects d ≥ 2 servers uniformly at random, and joins the queue at a leastloaded server among those chosen. Service times are independent exponentially distributed random variables with mean 1. We show that the system is rapidly mixing, and then investigate the maximum length of a queue in the equilibrium distribution. We prove that with probability tending to 1 as n → ∞ the maximum queue length takes at most two values, which are ln lnn/ lnd +O(1).
منابع مشابه
On the Maximum Queue Length in the Supermarket Model
There are n queues, each with a single server. Customers arrive in a Poisson process at rate λn, where 0< λ < 1. Upon arrival each customer selects d ≥ 2 servers uniformly at random, and joins the queue at a least-loaded server among those chosen. Service times are independent exponentially distributed random variables with mean 1. We show that the system is rapidly mixing, and then investigate...
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تاریخ انتشار 2004