On General Multi-Server Queues with Non-Poisson Arrivals and Medium Traffic: A New Approximation and a COVID-19 Ventilator Case Study

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.

Department(s)

Engineering Management and Systems Engineering

Keywords and Phrases

G/G/k Queue; Medium Traffic; Multi-Server Queue; Non-Poisson Arrivals

International Standard Serial Number (ISSN)

1866-1505; 1109-2858

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2022 Springer, All rights reserved.

Publication Date

01 Jan 2022

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