Queuing ProblemsQueuing Problems

Simulation vs. Simulation vs.

Queuing TheoryQueuing Theory

Problem 1Problem 1

A tool crib has exponential inter-arrival A tool crib has exponential inter-arrival and service times, and it serves a very and service times, and it serves a very large group of mechanics. large group of mechanics. • The mean time between arrivals is 4 minutes. The mean time between arrivals is 4 minutes. • It takes 3 minutes on average for a tool-crib It takes 3 minutes on average for a tool-crib

attendant to service a mechanic. attendant to service a mechanic. • The attendant is paid $10 per hour and the The attendant is paid $10 per hour and the

mechanic is paid $15 per hour. mechanic is paid $15 per hour. Would it be advisable to have a second Would it be advisable to have a second

tool-crib attendant?tool-crib attendant?

Problem 2Problem 2

A two-runway (one for landing and one for A two-runway (one for landing and one for taking off) airport is being designed for taking off) airport is being designed for propeller driven aircraft. propeller driven aircraft.

The time to land an airplane is known to The time to land an airplane is known to be exponentially distributed with a mean be exponentially distributed with a mean of 1½ minutes. of 1½ minutes.

If airplane arrivals are assumed to occur at If airplane arrivals are assumed to occur at random, what arrival rate can be tolerated random, what arrival rate can be tolerated if the average wait in the sky is not to if the average wait in the sky is not to exceed 3 minutes?exceed 3 minutes?

Problem 3Problem 3 The Port of Trop can service only one ship at a time. The Port of Trop can service only one ship at a time. However, there is mooring space for three more ships. However, there is mooring space for three more ships. Trop is a favorite port of call, but if no mooring space if Trop is a favorite port of call, but if no mooring space if

available, the ships have to go to the Port of Prot. available, the ships have to go to the Port of Prot. • An average of seven ships arrive each week, according to a An average of seven ships arrive each week, according to a

Poisson process. Poisson process. • The Port of Trop has the capacity to handle an average of eight The Port of Trop has the capacity to handle an average of eight

ships per week, with service times exponentially distributed. ships per week, with service times exponentially distributed. What is the expected number of ships waiting or in service What is the expected number of ships waiting or in service

at the Port of Trop?at the Port of Trop? How much business is lost to the Port of Prot?How much business is lost to the Port of Prot?

Problem 4Problem 4 A machine shop repairs small electric motors that A machine shop repairs small electric motors that

arrive according to a Poisson process at a rate of arrive according to a Poisson process at a rate of 12 per week (5-day, 40-hour workweek). 12 per week (5-day, 40-hour workweek).

An analysis of past data indicates that engines An analysis of past data indicates that engines can be repaired, on average, in 12.5 hours, with a can be repaired, on average, in 12.5 hours, with a variance of 1 hourvariance of 1 hour22. .

How many working hours should a customer How many working hours should a customer expect to leave a motor at the repair shop (not expect to leave a motor at the repair shop (not knowing the status of the system)? knowing the status of the system)?

If the variance of the repair time could be If the variance of the repair time could be controlled, what variance would reduce the controlled, what variance would reduce the expected waiting time to 6.5 hours?expected waiting time to 6.5 hours?