An Extension of Palm's Theorem for (M|G|s) Queues to the Case Where Arrival and Service Rates Depend on the Number of Busy Channels
Expert InsightsPublished 1966
An s channel queueing facility is considered where arrivals are Poisson. When all s channels are busy, subsequent arrivals are lost. There is one arbitrary service distribution applicable to all channels, but the service rate depends on the number of busy channels. It is shown that the steady state probabilities are those that would be obtained under the assumption of exponential service. The model is related to an inventory problem with expediting. By previously established methods, the derivation can be extended to compound Poisson arrivals. (See also RM-4176-1-PR.)
Document Details
- Copyright: RAND Corporation
- Availability: Web Only
- Year: 1966
- Pages: 11
- DOI: https://doi.org/10.7249/pubs
- Document Number: P-3406-1
Citation
RAND Style Manual
Sherbrooke, Craig C., An Extension of Palm's Theorem for (M|G|s) Queues to the Case Where Arrival and Service Rates Depend on the Number of Busy Channels, RAND Corporation, P-3406-1, 1966. As of July 11, 2026: https://www.rand.org/pubs/papers/P3406-1.html
Chicago Manual of Style
Sherbrooke, Craig C., An Extension of Palm's Theorem for (M|G|s) Queues to the Case Where Arrival and Service Rates Depend on the Number of Busy Channels. Santa Monica, CA: RAND Corporation, 1966. https://www.rand.org/pubs/papers/P3406-1.html.
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.