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SDGs in Bangladesh: Implementation Challenges and Way Forward Read chapter Read first chapter

2021 | OriginalPaper | Chapter

Erlang Loss Formulas: An Elementary Derivation

Author : Jyotirmoy Sarkar

Published in: Data Science and SDGs

Publisher: Springer Singapore

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Abstract

The celebrated Erlang loss formulas, which express the probability that exactly j of c available channels/servers are busy serving customers, were discovered about 100 years ago. Today we ask: “What is the simplest proof of these formulas?” As an alternative to more advanced methods, we derive the Erlang loss formulas using (1) an intuitive limit theorem of an alternating renewal process and (2) recursive relations that are solved using mathematical induction. Thus, we make the Erlang loss formulas comprehensible to beginning college mathematics students. We illustrate decision making in some practical problems using these formulas and other quantities derived from them.

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previous chapter Statistical Analysis of Various Optimal Latin Hypercube Designs
next chapter Machine Learning, Regression and Optimization
Literature
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Metadata
Title
Erlang Loss Formulas: An Elementary Derivation
Author
Jyotirmoy Sarkar
Copyright Year
2021
Publisher
Springer Singapore
Book
Data Science and SDGs

Print ISBN: 978-981-16-1918-2

Electronic ISBN: 978-981-16-1919-9

Copyright Year: 2021

DOI
https://doi.org/10.1007/978-981-16-1919-9_14