Decision Science
1. The Reggae Rhythm Electronics Corporation retains a service crew to repair machine breakdowns that occur on an average of 3 per day (approximately Poisson in nature). The crew can service an average of 8 machines per day, with a repair time distribution that resembles the exponential distribution.
a. What is the utilization rate for this service?
b. What is the average downtime for a machine that is broken?
c. How many machines are waiting to be serviced at any given time?
d. What is the probability that more than one machine is broken and waiting to be repaired or being serviced? ( that is the probability of more than one machine being in the system)
2. ‘Fridaz Car Wash at the UTech Barn’ estimates that dirty cars arrive at the rate of 10 per hour all day Friday. With the Hotters’ Girl crew working the single wash line, it is estimated that cars can be cleaned at the rate of one every 5 minutes. One car at a time is cleaned. Assuming Poisson arrivals and exponential service times, find the
a. average number of cars in line.
b. average time a car waits before being washed.
c. average time a ca spends in the service system.
d. utilization rate of the car wash.
e. probability that no cars are in the system.
3. Jucier Foods has just opened a new cafeteria in Papine square just for university students. This is a self-serve facility in which the students select the food items they want and then form a single line to pay the cashier. Students arrive at a rate of about 4 per minute according to a Poisson distribution. The single cashier ringing up sales takes about 12 seconds per customer, following an exponential distribution.
a. What is the probability that the system is empty?
b. How long will the average student have to wait before reaching the cashier?
c. What is the expected number of students in the queue?
d. What is the average number in the system?
4 Black Beard’s Barber Shop has one barber. Customers arrive at
a. What is the utilization rate for this service?
b. What is the average downtime for a machine that is broken?
c. How many machines are waiting to be serviced at any given time?
d. What is the probability that more than one machine is broken and waiting to be repaired or being serviced? ( that is the probability of more than one machine being in the system)
2. ‘Fridaz Car Wash at the UTech Barn’ estimates that dirty cars arrive at the rate of 10 per hour all day Friday. With the Hotters’ Girl crew working the single wash line, it is estimated that cars can be cleaned at the rate of one every 5 minutes. One car at a time is cleaned. Assuming Poisson arrivals and exponential service times, find the
a. average number of cars in line.
b. average time a car waits before being washed.
c. average time a ca spends in the service system.
d. utilization rate of the car wash.
e. probability that no cars are in the system.
3. Jucier Foods has just opened a new cafeteria in Papine square just for university students. This is a self-serve facility in which the students select the food items they want and then form a single line to pay the cashier. Students arrive at a rate of about 4 per minute according to a Poisson distribution. The single cashier ringing up sales takes about 12 seconds per customer, following an exponential distribution.
a. What is the probability that the system is empty?
b. How long will the average student have to wait before reaching the cashier?
c. What is the expected number of students in the queue?
d. What is the average number in the system?
4 Black Beard’s Barber Shop has one barber. Customers arrive at