The attractiveness of the fixed points of a ·/GI/1 queue
نویسنده
چکیده
We consider an infinite tandem of first-come-first-served queues. The service times have unit mean, and are independent and identically distributed across queues and customers. Let I be a stationary and ergodic interarrival sequence with marginals of mean τ > 1, and suppose it is independent of all service times. The process I is said to be a fixed point for the first, and hence for each, queue if the corresponding interdeparture sequence is distributed as I. Assuming that such a fixed point exists, we show that it is the distributional limit of passing an arbitrary stationary and ergodic interarrival process of mean τ through the infinite queueing tandem.
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