When a Queue Looks the Same to an Arriving Customer as to an Observer.
ResearchPublished 1968
A brief proof demonstrating Poisson arrival distribution. The arrival of each customer is shown to be independent of anything occurring in the queue, i.e., numbers and types of servers available, discipline and distribution of service, as well as customer behavior after entering the queue or number of different types of customers. To ensure that the probability distribution of states of the queue at a given time is the same regardless of whether or not an arrival occurs at that time, two requirements are needed: (1) the state of the queue given in the past must not be dependent on the new arrival; (2) the arrival distribution must be Poisson. A corollary to the proof postulates stationary distribution. 3 pp. (KB)
Document Details
- Copyright: RAND Corporation
- Availability: Available
- Year: 1968
- Print Format: Paperback
- Paperback Pages: 3
- Paperback Price: $20.00
- Document Number: P-3985
Citation
RAND Style Manual
Chicago Manual of Style
Strauch, Ralph E., When a Queue Looks the Same to an Arriving Customer as to an Observer. RAND Corporation, P-3985, 1968. As of September 14, 2024: https://www.rand.org/pubs/papers/P3985.html
Strauch, Ralph E., When a Queue Looks the Same to an Arriving Customer as to an Observer. Santa Monica, CA: RAND Corporation, 1968. https://www.rand.org/pubs/papers/P3985.html. Also available in print form.
This publication is part of the RAND paper series. The paper series was a product of RAND from 1948 to 2003 that captured speeches, memorials, and derivative research, usually prepared on authors' own time and meant to be the scholarly or scientific contribution of individual authors to their professional fields. Papers were less formal than reports and did not require rigorous peer review.
This document and trademark(s) contained herein are protected by law. This representation of RAND intellectual property is provided for noncommercial use only. Unauthorized posting of this publication online is prohibited; linking directly to this product page is encouraged. Permission is required from RAND to reproduce, or reuse in another form, any of its research documents for commercial purposes. For information on reprint and reuse permissions, please visit www.rand.org/pubs/permissions.
RAND is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.