Customers arrive to a local bakery with an average time between arrivals of5 minutes. However, there is quite a lot of variability in the customers’ arrivals, asone would expect in an unscheduled system. The single bakery server requires anamount of time having the exponential distribution with mean 4.5 minutes to servecustomers (in the order in which they arrive). No customers leave without service.c. How many customers are in the bakery on average?

Customers arrive to a local bakery with an average time between arrivals of5 minutes. However, there is quite a lot of variability in the customers’ arrivals, asone would expect in an unscheduled system. The single bakery server requires anamount of time having the exponential distribution with mean 4.5 minutes to servecustomers (in the order in which they arrive). No customers leave without service.c. How many customers are in the bakery on average?

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section: Chapter Questions

Problem 52P

See similar textbooks

Similar questions

Customers arrive to a local bakery with an average time between arrivals of5 minutes. However, there is quite a lot of variability in the customers’ arrivals, asone would expect in an unscheduled system. The single bakery server requires anamount of time having the exponential distribution with mean 4.5 minutes to servecustomers (in the order in which they arrive). No customers leave without service.d. Calculate the probability a customer will spend more than an hour at the bakery(time in queue plus service time).
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? 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? g) Find the probability that total time spent by a woman in the coiffeur is more than 120 minutes?
Customers arrive to a local bakery with an average time between arrivals of5 minutes. However, there is quite a lot of variability in the customers’ arrivals, asone would expect in an unscheduled system. The single bakery server requires anamount of time having the exponential distribution with mean 4.5 minutes to servecustomers (in the order in which they arrive). No customers leave without service.b. Calculate how long customers spend on average to complete their transactionsat the bakery (time in queue plus service time). What percentage of that time isspent queueing?
. 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?
12-17 Automobiles arrive at the drive-through window at a post office at the rate of four every 10 minutes. The average service time is 2 minutes. The Poisson distribution is appropriate for the arrival rate and service times are exponentially distributed. a. What is the average time a car is in the system? b. What is the average number of cars in the system? c. What is the average time cars spend waiting to receive service? d. What is the average number of cars in line behind the customer receiving service? e. What is the probability that there are no cars at the window? f. What percentage of the time is the postal clerk busy? g. What is the probability that there are exactly two cars in the system?