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On Niu's Conjecture for Two-Station Tandem Queues

  • Hao Cao
  • Jian-Qiang Hu
  • Qixin Wang
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Abstract

In this paper, we prove a long standing conjecture in queueing theory made by Niu (1980): in a two-station tandem queueing system with constant service time (c) at station 1, the stationary average waiting time at station 2 is nonincreasing in c. Two very different proofs are provided: one for the general case and one for a special case in which the arrival process is Poisson and the service time at station 2 is exponential.

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Cite

BibTeXRIS
BibTeX
@misc{cao2026nius,
  title = {{On Niu's Conjecture for Two-Station Tandem Queues}},
  author = {Hao Cao and Jian-Qiang Hu and Qixin Wang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.22837},
  eprint = {2610.22837},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.22837},
}
RIS
TY  - UNPB
TI  - On Niu's Conjecture for Two-Station Tandem Queues
AU  - Hao Cao
AU  - Jian-Qiang Hu
AU  - Qixin Wang
PY  - 2026
DA  - 2026/10/16
PB  - arXiv
DO  - 10.48550/arxiv.2610.22837
UR  - https://arxiv.org/abs/2610.22837
AB  - In this paper, we prove a long standing conjecture in queueing theory made by Niu (1980): in a two-station tandem queueing system with constant service time (c) at station 1, the stationary average waiting time at station 2 is nonincreasing in c. Two very different proofs are provided: one for the general case and one for a special case in which the arrival process is Poisson and the service time at station 2 is exponential.
ER  -