Scaling limits for infinite-server systems in a random environment

@inproceedings{Heemskerk2017ScalingLF,
  title={Scaling limits for infinite-server systems in a random environment},
  author={Mariska Heemskerk and Johan van Leeuwaarden and Michel Mandjes},
  year={2017}
}
This paper studies the effect of an overdispersed arrival process on the performance of an infinite-server system. In our setup, a random environment is modeled by drawing an arrival rate Λ from a given distribution every ∆ time units, yielding an i.i.d. sequence of arrival rates Λ1,Λ2, . . .. Applying a martingale central limit theorem, we obtain a functional central limit theorem for the scaled queue length process. We proceed to large deviations and derive the logarithmic asymptotics of the… CONTINUE READING

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