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For the M/M/N/∞ system, the probability that an arrival will find all servers busy and will be forced to wait in queue is an important measure of performance of the M/M/N/∞ system. This probability is given by PopN N!(1 – p/N) Po = and is known as the Erlang C formula. Please derive the equation. What is the expected number of customers waiting in the queue (not in service)?

For the M/M/N/∞ system, the probability that an arrival will find all servers busy and will be forced to wait in queue is an important measure of performance of the M/M/N/∞ system. This probability is given by PopN N!(1 – p/N) Po = and is known as the Erlang C formula. Please derive the equation. What is the expected number of customers waiting in the queue (not in service)?

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.7: Probability
Problem 41E
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For the M/M/N/o system, the probability that an arrival will find all servers busy and will be forced to wait in queue is an important measure of performance of the M/M/N/∞ system. This probability is given by PQ N!(1 – p/N) | and is known as the Erlang C formula. Please derive the equation. What is the expected number of customers waiting in the queue (not in service)?
Transcribed Image Text:For the M/M/N/o system, the probability that an arrival will find all servers busy and will be forced to wait in queue is an important measure of performance of the M/M/N/∞ system. This probability is given by PQ N!(1 – p/N) | and is known as the Erlang C formula. Please derive the equation. What is the expected number of customers waiting in the queue (not in service)?
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