Exam 9: Queuing Models

The computer help desk at Averill University receives an average of 40 calls per hour and calls come in according to a Poisson distribution. The average time a technician takes to diagnose a problem is three minutes and twenty seconds, and the service time follows an exponential distribution. For 60% of the callers the diagnosis is satisfactory, but for 40% of the callers, the technician must transfer the call to a specialist. The time a caller speaks to a specialist follows an exponential distribution with a mean of five minutes. For ninety five percent of callers transferred to a specialist, the problem is solved, but five percent of callers will need an on-site visit from a service technician. The average time a technician takes to fix a computer on-site is forty minutes with a standard deviation of ten minutes. The help desk operation has three technicians answering the incoming calls, two specialists handling calls, and one on-site technician. If a caller needs to have on-site service, determine the average time it will take to have the service completed form the time the initial call is made.

Suppose a penny arcade worker is in charge of keeping ten machines in operation.The failure rate of each machine follows an exponential distribution with a mean time of ten hours and the time required to repair each machine follows an exponential distribution with a mean time of thirty minutes.Over the long run, approximately what percentage of machines, on average, will be operating?

"Jockeying" occurs when a customer in the waiting line gets upset with the time the process is taking and leaves the system.

Airline passenger arrivals at U.S.Customs counters, at a port-of-entry airport, would not likely be modeled as Poisson due to arriving in groups.

You go to your local hospital for your complete annual physical exam.From a queuing standpoint, you are facing:

In a situation where the distribution of service times is assumed exponential, suppose the probability that service time is under five minutes is 0.40.If a given customer has already had five minutes of service, the probability that he/she will have service totally completed in less than ten minutes, is:

If the standard deviation of service time in an M/G/1 queue is zero, what type of system does it become? What if ? = 1/??

If a service facility changes from a first-come, first-served basis to a random basis in selecting the next customer to be served, one should expect average customer waiting time to:

One method for reducing the randomness of customer arrivals at a retail business is to allow for customer appointments.

Where would one most likely face a tandem queue?

The steady state service measure formulas for the M/G/k/k queue are the same as those for the M/M/k/k queue.

The probability distribution for the arrival process can be estimated if we know either the time between customer arrivals or the number of customers in a given time interval.

A Markovian queuing process has a(n) __________ arrival pattern, and a(n)__________ service pattern.

Ajax, Inc.specializes in the maintenance and repair of all types of electronic products.Tools and test equipment needed by its many skilled technicians on various diverse jobs must be drawn from and returned to a centrally-located tool room.Technicians arrive at the tool room at the rate of 20 per hour according to a Poisson process and earn $16 per hour per person.The company can hire tool room clerks at $10 per hour.It is estimated that it takes an average of 4 minutes for a clerk to serve a technician and service time follows an exponential distribution.Determine the optimal number of tool room clerks that Ajax should hire.

For an M/M/k queue to reach steady state, the service rate for each server μ must be greater than the arrival rate λ.

The size of the population of potential customers may have an impact on the validity of the Poisson arrival pattern assumption.

What does the Excel formula EXPONDIST(A10,B3,FALSE) return?

The average waiting time in the system is less than the sum of the average waiting time in the queue plus the average service time because some customers do not have to wait in the queue.

Which of the following is a basic component of a queuing system?

If ? is the non-constant average arrival rate, and ? (or k? with multiple servers) is the average service rate, why does a queuing system not approach maximum efficiency when these two values are approximately the same?