## Strong approximation for the supermarket model.(English)Zbl 1080.60086

The supermarket model is a system of $$N$$ single-server queues. Customers arrive as a Poisson process of rate $$N\lambda$$, where $$\lambda \in (0,1)$$. Each customer examines $$d$$ queues, chosen randomly from all queues, and joins the shortest of these $$d$$ queues, choosing randomly if the shortest queue is not unique. The paper establishes a law of large numbers, a jump process approximation and a central limit theorem for this supermarket model.

### MSC:

 60K25 Queueing theory (aspects of probability theory) 60F15 Strong limit theorems

### Keywords:

join the shortest queue; law of large numbers
Full Text:

### References:

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