Transient analysis of an affine Queue-Hawkes process

Benjamin Legros ()
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Benjamin Legros: Métis Lab EM Normandie - EM Normandie - École de Management de Normandie = EM Normandie Business School

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Abstract: We investigate the transient behavior of a multi-server queue with a linearly increasing arrival rate, also called affine Queue-Hawkes process. We obtain expressions of the Laplace Transform of the transient probabilities involving confluent hypergeometric functions. When the arrival rate without congestion-attraction is higher than the service rate or with an initial condition with all servers busy, these Laplace Transforms can be numerically inverted. Our numerical investigations show that convergence to the stationary regime is slower than for an M/M/s queue.

Keywords: Queueing; Transient analysis; Queue-Hawkes; Laplace Transform (search for similar items in EconPapers)
Date: 2021-05-01
Note: View the original document on HAL open archive server: https://hal.science/hal-03605436v1
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Citations: View citations in EconPapers (1)

Published in Operations Research Letters, 2021, 49 (3), pp.393-399. ⟨10.1016/j.orl.2021.04.001⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03605436

DOI: 10.1016/j.orl.2021.04.001

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