Answer:

Arrival rate

Service rate

L q = Average number of customers in the waiting line

W = Average time a customer will spend in the queue system

W q = Average waiting time in the line per customer

Given Data:

Use the following formula to calculate the average queue length:

There are on an average 0.9 cars in the queue.

Use the following formula to calculate the average time a car will spend in the total queue system:

The average waiting time in the entire system per car is 0.25 hours.

Use the following to calculate how long each car must wait:

The average waiting in line time per car is 0.15 hours.

If the arrival rate increases to 12 cars per hour, this is higher than the service rate therefore an infinite line would be formed.

Answer:

Arrival rate

Service rate

P 0 = Probability that no customers in the queue

P n = Probability that there are three customers in the queue

L = Average number of customers in the queue

L q = Average number of customers in the waiting line

W = Average time a customer will spend in the queue system

W q = Average waiting time in the line per customer

U= Probability that the server was busy

Given Data:

Customers per hour

Customers per hour

Use the following formula to solve for the probability that no customers exist in the queue :

The probability that there are no customers in the queue system is 0.33.

Use the following formula to determine the probability that there are three customers in this queue:

The probability of three customers in the queue system is 0.097

Use the following formula to calculate the average number of customers in the queue system:

The answer is 2.

Use the following formula to calculate the average number of customers in the waiting line :

The average numbers of customers waiting in the line are 1.33.

Use the following formula to calculate average time a customer will spend in the queue system:

The average waiting time in the entire system per customer is 0.125 hours.

Use the following formula to calculate the average waiting time in the line per customer:

The average waiting in line time per customer is 0.083 hours.

Use the following formula to calculate the probability that the server was busy :

There is a 0.67 probability that the server was busy and the customer waited.

Answer:

Arrival rate

Service rate

L q = Average number of products in the waiting line

U = Probability that the server was busy

I = Percentage of time the machine is idle

Given Data:

Time Interval = 7.5 min

Calculate the average number of parts waiting to be worked on, using the following formula as shown below:

The average number of parts waiting to be assembled is 3.2 parts.

The percentage of time the operator is working is calculated as shown below:

Multiplying the value of 0.8 by 100 will give us 80 percent.

The operator is working for 80 percent of the time.

In order to find the percentage of time the machine is idle use the formula below:

Multiplying the value of 0.20 by 100 will give us 20 percent.

The machine is idle for 20 percent of the time.