Assignment – Queuing
Theory
1. Two technicians, working as a team, monitor
a group of 5 computers that run an automated manufacturing facility. It
takes an average of 15 minutes (exponentially distributed) to adjust a computer
that develops a problem (4 computers an hour). Computers run for an average
of 85 minutes (Poisson distributed) without requiring adjustments. For this
problem, M = 2 (two technicians). Determine the following:
* The average number of computers waiting for adjustment.
* The average number being adjusted.
* The average number of computers not in working order.
2. At the start of the football season, the ticket office gets
very busy the day before the first game. Customers arrive at the rate
of 4 every 10 minutes, and the average time to transact business is 2
minutes. What is the average number of people in line? What is the average
time that a person will spend at the ticket office? What proportion of
time is the server busy?
3. A car wash is open 6 days a week, bit its busiest day is always
Saturday. From historical data, it is estimated that dirty cars arrive
at the rate of 20 per hour all day Saturday. With a full crew working
the hand-wash line, it is figured that cars can be cleaned at the rate
of one every 2 minutes. One car at a time is cleaned. Assuming Poisson
arrivals and exponential service times, what is the average number of
cars in line? What is the average time that a car waits before it is washed?
What is the average time that a car spends in the service system. What
is the utilization rate of the car wash? What is the probability that
no cars are in the system?
