Question: (a) Customers arrive at a mobile post office with an average rate of 40 customers per hour. There is one clerk on duty, who serves

(a) Customers arrive at a mobile post office with an average rate of 40 customers per

hour. There is one clerk on duty, who serves an average of 1 customer per minute.

The customer arrival rate follows the Poisson distribution, while the service time

follows the exponential distribution.

(i) What are the arrival rate and service rate in hours? (4 marks)

(ii) Find the average number of customers in waiting line. Explain the meaning of

this number.

(5 marks)

(iii) The average time a customer waits before he/she is served. (4 marks)

(b) The post office uses a multiple channel queue, where customers wait in a single

line for the first available window. The average service time is one customer every

minute. The arrival rate is six customers every five minutes. Three service

windows are open.

(i) What is the probability both windows are idle? (6 marks)

(ii) What is the probability a customer will have to wait? (6 marks)

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Q:

During the early morning hours, customers arrive at a branch post office at an average rate of 40 per hour (Poisson), while a clerk can provide service at a rate of 10 per hour. If the cost of a...

Q:

During the early morning hours, customers arrive at a branch post office at an average rate of 20 per hour (Poisson), while clerks can handle transactions in an average time (exponential) of 2...

Q:

During the early morning hours, customers arrive at a branch post office at an average rate of 27 per hour (Poisson), while clerks can provide services at a rate of 9 per hour. If clerk cost is...

Q:

A bank has a single ATM in a small town. On average, one customer arrives at the ATM every three minutes and spends two minutes using the ATM. What is the probability that a customer has to wait less...

Q:

Can anyone help me with these 12 questions? QUESTION 1 A single-server queueing system has an average service time of 16 minutes per customer, which is exponentially distributed. The manager is...

Q:

1 A single-server queueing system has an average service time of 16 minutes per customer, which is exponentially distributed. The manager is thinking of converting to a system with a constant service...

Q:

During the early morning hours, customers arrive at a branch post office at an average rate of 4 5 per hour ( Poisson ) , while clerks can handle transactions in an average time ( exponential ) of 4...

Q:

Question 10 options: During the early morning hours, customers arrive at a branch post office at an average rate of 45 per hour (Poisson), while clerks can handle transactions in an average time...

Q:

1 The Anderson Palmer Hospital would like to reduce the cost of its inventory by calculating the optimal order size for hypodermic needles. On average, the hospital uses 80 needles per month. The...

Q:

A Quality Analyst wants to construct a control chart for determining whether five machines, all producing the same product, are under control with regard to a particular quality variable....

Q:

Jordan Carr is preparing a worksheet. Explain to Jordan how he should extend the following adjusted trial balance accounts to the financial statement columns of the worksheet. Service Revenue ..........

Q:

A company declares a dividend of 22 cents per share, with an ex dividend date of 14 September. Immediately prior to the declaration of the dividend, the share price was $4.79. At the close of trading...

Q:

Consider a portfolio value with two currencies: euro and pound. Suppose the proportion of portfolio value in euro is 3 0 percent and the standard deviation of percentage changes in euro is 2 0...

Q:

A company is preparing completing their Cash Budget. The following data has been prepared for cash receipts and payments. January February March Cash receipts $1,061,200 $1,182,400 $1,091,700 Cash...