Exam 15: Waiting Line Models

If some maximum number of customers is allowed in a queuing system at one time,the system has a finite calling population.

For an M/M/1 queuing system,if the service rate,µ,is doubled,the average wait in the system,W,is cut in half.

Use of the Poisson probability distribution assumes that arrivals are not random.

In a multiple channel system

The 8 students in a seminar class must come to the professor's office to turn in a paper and give a 5-minute oral summary.Assume there is a service rate of 10 per hour and adequate time is available for all.The arrival rate for each unit is 5 per hour.What is the probability there is no one in the office or waiting when you come?

The Quick Snap photo machine at the Lemon County bus station takes four snapshots in exactly 75 seconds.Customers arrive at the machine according to a Poisson distribution at the mean rate of 20 per hour.On the basis of this information,determine the following: a.the average number of customers waiting to use the photo machine b.the average time a customer spends in the system c.the probability an arriving customer must wait for service.

For an M/M/k system,the average number of customers in the system equals the customer arrival rate times the average time a customer spends waiting in the system.

Quick Clean Rooter cleans out clogged drains.Due to the competitive nature of the drain cleaning business,if a customer calls Quick Clean and finds the line busy,they immediately try another company and Quick Clean loses the business. Quick Clean management estimates that on the average,a customer tries to call Quick Clean every three minutes and the average time to take a service order is 200 seconds.The company wishes to hire enough operators so that at most 4% of its potential customers get the busy signal. a.How many operators should be hired to meet this objective? b.Given your answer to a),what is the probability that all the operators are idle?

The postmaster at the Oak Hill Post Office expects the mean arrival rate of people to her customer counter will soon increase by fifty percent due to a large apartment complex being built.Currently,the mean arrival rate is 15 people per hour.The postmaster can serve an average of 25 people per hour.By what percentage must the postmaster's mean service rate increase when the apartment complex is completed in order that the average time spent at the post office remains at its current value?

Adding more channels always improves the operating characteristics of the waiting line and reduces the waiting cost.

In waiting line systems where the length of the waiting line is limited,the mean number of units entering the system might be less than the arrival rate.

Waiting line models describe the transient-period operating characteristics of a waiting line.