Exam 26: Waiting Line Models

Customers at an amusement park arrive at the rate of 10 customers per hour.The entry booth is staffed by one employee.The mean service time at the booth to provide service to each customer is 5 minutes.The arrival rate follows a Poisson distribution,and the service time at the booth follows a negative exponential distribution.Determine the probability of exactly five customers in the system.

ABS specializes in repair and maintenance of industrial machines.One repair technician has been assigned to five identical grinding machines for repair and maintenance.The machine breaks down after about 20 hours of use,and breakdowns have a Poisson probability distribution.It takes 6 hours to repair a machine,and repair times follow an exponential distribution.Machine downtime costs the company $250 an hour,and the technician is paid $50 an hour.Determine the average number of machines that will break down.

The owner of an amusement park has decided to open a second entry booth and hire another employee to service customers entering the park.Customers arrive at the rate of 20 per hour and will wait in a single line until one of the two employees is available to provide service.The average service time of both employees is 2 minutes to provide service.The arrival rate follows Poisson distribution,and the service time follows a negative exponential distribution.Determine the average number of customers waiting in the system.

______ is the number of customer arrivals per unit of time.

The owner of an amusement park has decided to open a second entry booth and hire another employee to service customers entering the park.Customers arrive at the rate of 20 per hour and will wait in a single line until one of the two employees is available to provide service.The average service time of both employees is 2 minutes to provide service.T The arrival rate follows Poisson distribution,and the service time follows a negative exponential distribution.It is estimated that the cost of customer waiting time associated with dissatisfied customers and loss of goodwill is $20 per hour.The employee at the service booth is paid $10 an hour.Determine the customer waiting time cost per day for the waiting line system.Assume total hours of operation as 10 hours per day.

The mathematical expression for the Poisson distribution is shown as P(x)= e⁻λλˣ/x! The term λ stands for ______.

ABS specializes in repair and maintenance of industrial machines.One repair technician has been assigned to five identical grinding machines for repair and maintenance.The machine breaks down after about 20 hours of use,and breakdowns have a Poisson probability distribution.It takes 6 hours to repair a machine,and repair times follow an exponential distribution.Machine downtime costs the company $250 an hour,and the technician is paid $50 an hour.Determine the average number of machines working.

Consider a scenario in which customers decide not to wait and receive service from a competitor.The lost sales are an example of ______.

A waiting line grows infinitely long when ______.

The owner of an amusement park has decided to open a second entry booth and hire another employee to service customers entering the park.Customers arrive at the rate of 20 per hour and will wait in a single line until one of the two employees is available to provide service.The average service time of both employees is 2 minutes to provide service.The arrival rate follows Poisson distribution,and the service time follows a negative exponential distribution.It is estimated that the cost of customer waiting time associated with dissatisfied customers and loss of goodwill is $20 per hour.The employee at the service booth is paid $10 an hour.Determine the total expected cost per day for the waiting line system.Assume total hours of operation as 10 hours per day.

In the notation used to identify the single-channel queuing model (M/M/1),the second M refers to ______.

In waiting line models,the variable interarrival time is assumed to follow a probability distribution known as the ______,which is a probability distribution that describes the time between events in a process in which events occur continuously and independently at a constant average rate.

An automatic car wash with a single bay takes a constant 3 minutes to wash.The arrival rate is 10 cars per hour.Determine the average time a car spends in the system.The arrival rate of cars tends to follow a Poisson distribution.

If the average number of customers served per hour is five,then the probability that the service exceeds 21 minutes for any customer is ______.

A discrete random variable is a variable whose outcomes take on numerical values ______.

Which of the following statements is FALSE about random arrivals?

The primary objective of managing waiting lines is to ______ throughout any service or manufacturing facility.

ABS specializes in repair and maintenance of industrial machines.One repair technician has been assigned to five identical grinding machines for repair and maintenance.The machine breaks down after about 20 hours of use,and breakdowns have a Poisson probability distribution.It takes 6 hours to repair a machine,and repair times follow an exponential distribution.Machine downtime costs the company $250 an hour,and the technician is paid $50 an hour.Determine the average cost per hour of downtime.

Customers at an amusement park arrive at the rate of 10 customers per hour.The entry booth is staffed by one employee.The mean service time at the booth to provide service to each customer is 5 minutes.The arrival rate follows a Poisson distribution,and the service time at the booth follows a negative exponential distribution.Determine the capacity utilization for the system.

If the average number of customers served per hour is two,then the probability that the service exceeds 45 minutes for any customer is ______.