Erlang Loss Formulas: An Elementary Derivation

Jyotirmoy Sarkar ()
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Jyotirmoy Sarkar: Indiana University–Purdue University Indianapolis

A chapter in Data Science and SDGs, 2021, pp 165-176 from Springer

Abstract: 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.

Keywords: Alternating renewal process; Cycle time; Ergodicity; Queuing system; Renewal time; Semi-Markov process; Primary 60J28; 60K20; Secondary 62-01 (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-16-1919-9_14

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DOI: 10.1007/978-981-16-1919-9_14

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