Queues with Time-Dependent Arrival Rates I : The Transition through Saturation

@inproceedings{Newell2016QueuesWT,
  title={Queues with Time-Dependent Arrival Rates I : The Transition through Saturation},
  author={G. F. Newell},
  year={2016}
}
Suppose that the arrival rate A(t) of customers to a service facility increases with time at a nearly constant rate, dA(t)/dt = a, so as to pass through the saturation condition, ,A(t)= =t = service capacity, at some time which we label as t = 0. The stochastic properties of the queue are investigated here through use of the diffusion approximation (Fokker-Planck equation). It is shown that there is a characteristic time T proportional to a-2/3 such that if t < 0, jt T, then the queue… CONTINUE READING

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