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On general multi-server queues with non-poisson arrivals and medium traffic: a new approximation and a COVID-19 ventilator case study

Author

Listed:
  • Carlos Chaves

    (Boeing, Inc.)

  • Abhijit Gosavi

    (Missouri University of Science and Technology)

Abstract

We consider the multi-server, single-channel queue, i.e., a G/G/k queue with k identical servers in parallel, under the first-come-first-served discipline in which the inter-arrival process is non-Poisson, the service time has any given distribution, and traffic is of medium intensity. Such queues are common in factories, airports, and hospitals, where the inter-arrival times and service times are typically not exponentially distributed, but rather have double-tapering distributions whose probability density functions taper on both sides, e.g., gamma, triangular etc. For these conditions, a new closed-form approximation based on only the mean and variance of the two inputs, the inter-arrival and service times, is presented. Determining distributions of inputs typically requires additional human effort in terms of histogram-fitting and running a goodness-of-fit test, which is avoided here. The new approximation is tested on a variety of scenarios and its performance is benchmarked against simulation. Further, the new approximation is also implemented on a ventilator case study from the recent COVID-19 pandemic to demonstrate its utility in optimizing server capacity. The approximation provides errors typically in the range 1–15% and 31% in the worst case. In systems where data change rapidly and decisions must be made quickly, this approximation will be particularly useful.

Suggested Citation

  • Carlos Chaves & Abhijit Gosavi, 2022. "On general multi-server queues with non-poisson arrivals and medium traffic: a new approximation and a COVID-19 ventilator case study," Operational Research, Springer, vol. 22(5), pages 5205-5229, November.
    • Handle: RePEc:spr:operea:v:22:y:2022:i:5:d:10.1007_s12351-022-00712-2
    DOI: 10.1007/s12351-022-00712-2
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    References listed on IDEAS

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