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
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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.

  1. a) What is the probability that Tracy is busy?
  2. b) What is the probability that there are 3 or more women in the coiffeur?
  3. c) On average, how many women are waiting for hairdressing?
  4. d) On average, how long must a woman wait before hairdressing begins?
  5. e) What is the average time a woman spends in the coiffeur?
  6. f) Find the probability that a woman’s waiting time in the coiffeur is more than 90 minutes?
  7. g) Find the probability that total time spent by a woman in the coiffeur is more than 120 minutes?
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