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Erlang Loss Formulas: An Elementary Derivation

In: Data Science and SDGs

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  • Jyotirmoy Sarkar

    (Indiana University–Purdue University Indianapolis)

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.

Suggested Citation

  • Jyotirmoy Sarkar, 2021. "Erlang Loss Formulas: An Elementary Derivation," Springer Books, in: Bikas Kumar Sinha & Md. Nurul Haque Mollah (ed.), Data Science and SDGs, pages 165-176, Springer.
    • Handle: RePEc:spr:sprchp:978-981-16-1919-9_14
    DOI: 10.1007/978-981-16-1919-9_14
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