Relations among the Queue-Length Probabilities in the Pre-Arrival, Random, and Post-Departure Epochs in the GI/Ma,b/c Queue
Abstract
:1. Introduction
2. Model Description
3. Relations among Queue-Length Probabilities at the p.a.e., r.e., and p.d.e.
3.1. The Idle-Server System
- Special cases:
- GI/M/c:Setting , Equations (5) and (8) can be simplified into
3.2. The Busy-Server System
- Special cases:
4. Discussion
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Gai, J.; Chaudhry, M. Relations among the Queue-Length Probabilities in the Pre-Arrival, Random, and Post-Departure Epochs in the GI/Ma,b/c Queue. Mathematics 2024, 12, 2609. https://doi.org/10.3390/math12172609
Gai J, Chaudhry M. Relations among the Queue-Length Probabilities in the Pre-Arrival, Random, and Post-Departure Epochs in the GI/Ma,b/c Queue. Mathematics. 2024; 12(17):2609. https://doi.org/10.3390/math12172609
Chicago/Turabian StyleGai, Jing, and Mohan Chaudhry. 2024. "Relations among the Queue-Length Probabilities in the Pre-Arrival, Random, and Post-Departure Epochs in the GI/Ma,b/c Queue" Mathematics 12, no. 17: 2609. https://doi.org/10.3390/math12172609