# Understanding waiting line models

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?

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#### Solution Preview

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.