Tracy, working as a single hairstylist at coiffeur, dresses hair of women at a rate of 5 women per hour. The hairdressing time is exponentially distributed. Women arrive to the coiffeur according to a Poisson distribution with a rate of 4 per hour. a) What is the probability that Tracy is busy? b) What is the probability that there are 3 or more women in the coiffeur? c) On average, how many women are waiting for hairdressing?

Tracy, working as a single hairstylist at coiffeur, dresses hair of women at a rate of 5 women per hour. The hairdressing time is exponentially distributed. Women arrive to the coiffeur according to a Poisson distribution with a rate of 4 per hour. a) What is the probability that Tracy is busy? b) What is the probability that there are 3 or more women in the coiffeur? c) On average, how many women are waiting for hairdressing?

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section12.5: Analytic Steady-state Queueing Models

Problem 9P

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. Tracy and Diane, working as twohairstylists at coiffeur, dress hair of women at a rate of 3 women per hour. The hairdressing time for Tracy and Dianeis exponentially distributed. Women arrive to the coiffeur according to a Poisson distribution with a rate of 5 per hour. a) What is the probability that Tracy is busy? b) What is the probability that Diane is idle? c)On average, how many women are waiting for hairdressing? d)On average, how long must a woman wait before hairdressing begins? e) What is the average time a woman spends in the coiffeur? f) Find the probability that a woman’s waiting time in the coiffeur is more than 90 minutes?
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