Exam 9: Queuing Models

The priority rule chosen for determining the next customer to be served affects both waiting time variance and average customer waiting time.

What is the Kendall notation for a queue withmaximum queue length equal to the number of servers; multiple servers working at the same, non-exponential rate;and customer interarrival time exponential.

The new community of Lemon Heights is planning to set up a paramedic station.It is estimated that calls will come into this station according to a Poisson distribution, and the station receives an average of twenty calls a day.The time an ambulance is out responding to a call follows an exponential distribution with a mean time of one hour and thirty minutes.If no ambulance is available, an ambulance from a nearby town will be dispatched, but this will significantly increase the response time.Due to the potentially tragic consequences associated with not having an ambulance readily available when a call comes in, the city council has mandated that the probability of this happening should be no more than .005.Determine how many ambulances the paramedic station should purchase.

The exponential distribution is:

Given these parameters: ? = 25 per hour, ? = 30 per hour, and W_q = .3 hours, calculate the average number of customers in the system, average number of customers in the queue, and the average time a customer spends in the system.

Which of the following is not a common steady state performance measure?

The Red Rock School District has six buses in its fleet.Maintenance of the fleet is handled by Joe Clem, a mechanic who works for the district.The time between bus failures follows an exponential distribution with a mean of twenty days.During the time a bus is out of commission, the district must lease another bus at a cost of $80 per day.Joe has put in for retirement and the district is considering hiring either Tom Meyers or Andy Johnson.Based on a skills assessment test, it is estimated that Tom can repair a bus in an average of 10 hours, while Andy will take an average of 8 hours.Tom wants a salary equivalent to $160 per working day, while Andy wants a salary equivalent to $170 per working day.A working day lasts 8 hours, and there are 200 working days per year.Which employee should the district hire? Give your reasons.

Random arrival processes must be modeled using continuous probability distributions, not discrete ones.

In order to achieve steady state performance in a queuing system, the sum of the effective service rates of all servers must:

For an M/G/1 queue, ? = 12 per hour, ? = 24 per hour, and the standard deviation of the service time ? = .05.Calculate the average number of customers in the system, average time a customer spends in the system, and the probability that there are exactly two customers in the system.

Using Little's formula, if we know the mean arrival rate, mean service rate, and the average time a customer spends in the queue (W_q), what else can we calculate?

Ray's Barber Shop has 3 barber's chairs, and 8 seats for waiting customers.The greatest number of people ever waiting for a haircut, in Ray's experience, is 6.For analytical purposes, then, Ray's queue length is:

"Balking" is:

For the post-Christmas gift returns, Paver's store added a second clerk on December 26.Paver's expects 10 customers an hour, and the mean service time is 10 minutes.Assuming an M/M/2 queue and a single waiting line, compute the average time a customer spends in the queue.What if there were two lines with jockeying allowed?

Although service times may be relatively constant at sequential work stations in an assembly line, the line still may be treated as a tandem queue.

Customers arrive at the First Fidelity Bank branch on Fridayafternoon according to a Poisson process at a mean rate of 45 per hour.The average time a teller takes to serve a customer is two and a half minutes and service time follows an exponential distribution.At present, the bank has two tellers on staff to serve customers during this time. A.Determine the average time a customer will wait in line before being served. B.Determine the probability an arriving customer will have to wait in line. C.Determine the average number of customers in the system. D.Suppose that the bank would like the average time a customer spends waiting in line to be three minutes or less.What is the fewest number of tellers they should employ to meet this goal?

In the exponential distribution of service times, the mean customer service time equals the:

If the service times are not memoryless, then the Erlangian distribution might be a better basis than the exponential distribution for modeling service.

What is the formula for the effective arrival rate of an M/M/k/F queue?

Harry and Larry have opened up an automated carwash near the edge of town.There is a single service lane, and cars line up in asingle line to enter the carwash.No special services are offered,and the time required for each vehicle to go through the facility is exactly three minutes.Throughout the day, customers arrive independently and largely at random at an average rate of twelve per hour.Because of the location, even when the queue is full,potential customers may line up in the adjacent side street. A.What percentage of time is the carwash idle? B.What is the average number of waiting vehicles? C.What will be the average elapsed time between when a vehicle enters and leaves the system? D.What percentage of time is the carwash idle? E.What is the average number of waiting vehicles? F.What will be the average elapsed time between when a vehicle enters and leaves the system?