Please see attached for fully formatted questions.
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1.
a. The expected number of customer that will arrive in a five minutes period is
b. The probability that exactly 0,1,2 and 3 customer will arrive during a five minutes period is
c. The probability of delays will occur is
The probability of more than three customers arriving during 3 minutes

2.
a. the probability the service time is one minute or less
b. the probability the service time is two minute or less
c. the probability the service time is more than two minute

3.
a. The probability that no customers are in the system
b. The average number of customers waiting
c. The average time a customer in the system
d. the average time a customer spends waiting
e. the average time a customer spends in the system
f. the probability that arriving customers will have to wait for service.

4. Use the single - channel drive -up bank teller operation referred to in problem 1-3 to determine the probabilities of 0, 1, 2 and 3 customers in the system. What is the probability than more than three customers will be in the drive -up teller system at the same time?

1.
λ = 24 customers per hour = 0.4 customer per minute
a. The expected number of customer that will arrive in a five minutes period is
λ = 0.4*5 = 2
b. The probability that exactly 0,1,2 and 3 customer will arrive during a five minutes period is
customers probability
0 0.000045
1 0.00045
2 0.00022
3 0.00453

c. The probability of delays will occur is
The probability of more than three customers arriving during 3 minutes
= 1- {P( x=0) + p( x= 1) + p(x=2) + p(x=3)}
= 1 - ...

Solution Summary

Waiting line models are analyzed. The expected number of customers waiting longer than a five minute period is determined.

These problems are WaitingLineModels. (1,2,3)
The problems I need work out are: Problem 14, 19, and 20.
See attached file for full problem description.

Waitingline theories are valuable tools in operations. One model is based on the Poisson arrival distribution, FIFO line discipline, and customers arrive at the rate of two per minute. This is a single phase operation and each server operates at the average rate of 160 customers served per hour. Management is concerned by th

You usually have to wait at the airport to check in. Waitinglines are part of our culture. If more than three people stand behind each other in an airport line, everyone else will get in line.
Which of the following waitingline formats would you prefer? Why?
See *ATTACHED* file for complete details!

In a waitingline situation, arrivals occur at a rate of 2 per minute, and the service times average 18 seconds per customer. Assume the Poisson and exponential distributions. Carry all answers to at least 3 decimals.
a. What is lambda?
b. What is mu?
c. What is the probability of no units in the system?
d. What is t

Suppose that the service rate to a waitingline system is 10 customers per hour (exponentially distributed). Analyze how the average waiting time is expected to change as the arrival rate varies from two to ten customers per hour (exponentially distributed).

Customers enter the waitingline at a cafeteria on a first come, first served basis in two serving lines.
The arrival rate follows a Poisson distribution, while service times follow an exponential distribution.
If the average number of arrivals is two per minute and the average service rate of three customers per minute,

The Sea View Resort uses a multiple-channel queue registration system. If the average service time is 9 minutes, there are three registration clerks, and guests arrive at the rate of one every 6 minutes, find
a. Arrival and service rate.
b. the probability all three clerks are idle.
c. the probability a g

You are the manager of a local bank where three tellers provide services to customers. On average, each teller takes three minutes to serve a customer. Customers arrive, on average, at a rate of 50 per hour. Having recently received complaints from some customers that they waited a long time before being served, your boss asks

In a waitingline model situation, arrivals occur around the clock at a rate of six per day, and the service occurs at one very three hours. Assume the Poisson and exponential distributions.
a. What is Mean Arrival Rate?
b. What is Mean Service Rate?
c. Find probability of no units in the system.
d. Find average number of

Please help with the given problem:
It seems that simulation could handle any situation or study. But is that always true? Discuss instances in which a simulation would be important and useful, and then a situation in which a simulation would not be appropriate. Finally, include a set of rules you would use to determine if