Exam 15: Waiting Line Models

For all waiting lines,P₀ + P_w = 1.

​List six steady-state operating characteristics for a single-channel waiting line with Poisson arrivals and exponential service times.

A multiple-channel system has more than one waiting line.

For an M/G/1 system with λ = 6 and μ = 9,with σ = .03,find a.the probability the system is idle. b.the average length of the queue. c.the average number in the system.

​How can a system be changed to improve the service rate?

The insurance department at Shear's has two agents,each working at a mean speed of 8 customers per hour.Customers arrive at the insurance desk at a mean rate of one every six minutes and form a single queue.Management feels that some customers are going to find the wait at the desk too long and take their business to Word's,Shear's competitor. In order to reduce the time required by an agent to serve a customer Shear's is contemplating installing one of two minicomputer systems: System A which leases for $18 per day and will increase an agent's efficiency by 25%;or,System B which leases for $23 per day and will increase an agent's efficiency by 50%.Agents work 8-hour days. If Shear's estimates its cost of having a customer in the system at $3 per hour,determine if Shear's should install a new minicomputer system,and if so,which one.

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

Little's flow equations

Operating characteristics formulas for the single-channel queue do NOT require

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.

Before waiting lines can be analyzed economically,the arrivals' cost of waiting must be estimated.

​Discuss the importance of the utilization factor in a queuing system and the assumptions made about its value.

The Sea View Resort uses a multiple-channel queue registration system.If the average service time is 8 minutes,there are three registration clerks,and guests arrive at the rate of one every 5 minutes,find a.λ and μ. b.the probability all three clerks are idle. c.the probability a guest will have to wait. d.the average time a customer is in line. e.the average number of customers in line.

For a single-channel waiting line,the utilization factor is the probability that an arriving unit must wait for service.

Decision makers in queuing situations attempt to balance

​Single-booth ticket sales at a theater would be an example of which queuing model?

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

Performance measures dealing with the number of units in line and the time spent waiting are called

Andy Archer,Ph.D. ,is a training consultant for six mid-sized manufacturing firms.On the average,each of his six clients calls him for consulting assistance once every 25 days.Andy typically spends an average of five days at the client's firm during each consultation. Assuming that the time between client calls follows an exponential distribution,determine the following: a.the average number of clients Andy has on backlog b.the average time a client must wait before Andy arrives to it c.the proportion of the time Andy is busy

For many waiting line situations,the arrivals occur randomly and independently of other arrivals and it has been found that a good description of the arrival pattern is provided by