The DOI matches its Crossref record.
The Output of a Queuing System
Abstract
For a queuing system with Poisson input, a single waiting line without defections, and identically distributed independent (negative) exponential service times, the equilibrium distribution of the number of service completions in an arbitrary time interval is shown to be the same as the input distribution, for any number of servers. This result has applications in problems of tandem queuing. The essence of the proof is the demonstration of the independence of an interdeparture interval and the state of the system at the end of the interval.
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Citations
Cited by
An introduction to queueing theory
(1993) · Computers & Operations Research · doi:10.1016/0305-0548(93)90046-l · Cited by 906
Queueing, Predictions, and Large Language Models: Challenges and Open Problems
Mitzenmacher, M., & Shahout, R. (2025) · Stochastic Systems · doi:10.1287/stsy.2025.0106 · Cited by 12
Metadata
- Authors
- Burke, P. J.
- Venue
- Operations Research
- Published
- 1956-12
- Volume
- 4
- Issue
- 6
- Pages
- 699-704
- ISSN
- 0030-364X (ISSN-L)
- 1526-5463
- OpenAlex
- W2105288904
- Cited by
- 689
- References
- 0
- FWCI
- 10.72
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: The Output of a Queuing System. https://app.cochat.ai/papers/10.1287/opre.4.6.699
- The paper
- Burke, P. J. (1956). The Output of a Queuing System. Operations Research. https://doi.org/10.1287/opre.4.6.699
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
