Expected discrimination frequency for multi-server queues

Bara Kim; Jeongsim Kim

doi:10.1016/j.spl.2026.110711

Expected discrimination frequency for multi-server queues

Bara Kim
, Jeongsim Kim^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

This paper investigates the discrimination frequency (DF), a measure of fairness, in two queueing systems: an M/M/c queue and a system of c parallel M/M/1 queues. We derive exact closed-form expressions for the expected DF in both systems. Using these expressions, we show that the M/M/c queue has a smaller expected DF than the parallel system, thereby resolving the conjecture of Neumann and Baumann (2018).

Original language	English
Article number	110711
Journal	Statistics and Probability Letters
Volume	234
DOIs	https://doi.org/10.1016/j.spl.2026.110711
Publication status	Published - 2026 Jul

Bibliographical note

Publisher Copyright:
© 2026 Elsevier B.V.

Keywords

Discrimination frequency
M/M/c queue
Parallel queue

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1016/j.spl.2026.110711

Cite this

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title = "Expected discrimination frequency for multi-server queues",

abstract = "This paper investigates the discrimination frequency (DF), a measure of fairness, in two queueing systems: an M/M/c queue and a system of c parallel M/M/1 queues. We derive exact closed-form expressions for the expected DF in both systems. Using these expressions, we show that the M/M/c queue has a smaller expected DF than the parallel system, thereby resolving the conjecture of Neumann and Baumann (2018).",

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AB - This paper investigates the discrimination frequency (DF), a measure of fairness, in two queueing systems: an M/M/c queue and a system of c parallel M/M/1 queues. We derive exact closed-form expressions for the expected DF in both systems. Using these expressions, we show that the M/M/c queue has a smaller expected DF than the parallel system, thereby resolving the conjecture of Neumann and Baumann (2018).

KW - Discrimination frequency

KW - M/M/c queue

KW - Parallel queue

UR - https://www.scopus.com/pages/publications/105031844797

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DO - 10.1016/j.spl.2026.110711

M3 - Article

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VL - 234

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

M1 - 110711

ER -

Expected discrimination frequency for multi-server queues

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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