Students arrive at Panda Express in the student center in accordance with a Poisson process with rate λ. However, if the the student arriving finds n students already in line (including all who are waiting and who are currently being served), then the student will enter the line with probability αn. Assume that there is only one person working at Panda Express and the time spent with each student follows an exponential distribution with rate μ. Set up this process as a birth and death process and determine the birth and death rates. Draw the rate diagram (state transition diagram).

Students arrive at Panda Express in the student center in accordance with a Poisson process with rate λ. However, if the the student arriving finds n students already in line (including all who are waiting and who are currently being served), then the student will enter the line with probability αn. Assume that there is only one person working at Panda Express and the time spent with each student follows an exponential distribution with rate μ. Set up this process as a birth and death process and determine the birth and death rates. Draw the rate diagram (state transition diagram).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 32E

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