Question

Zimmerman Bank

Zimmerman’s Bank is the only bank in the small town of St. Thomas. On a typical Friday, an average of 10 customers per hour arrive at the bank to transact business. There is one teller at the bank, and the average time required to transact business is 4 minutes. It is assumed that service times may be described by the exponential distribution. A single line would be used, and the customer at the front of the line would go to the first available bank teller. If a single teller is used, find:

a) The average time in the line

b) The average number in the line.

c) The average time in the system

d) The average number in the system

e) The probability that the bank is empty

Answer 1

Given that ,    = 10 arrival rate

Service rate , = 60/ 4 = 15

Now , 1) The average time in the line / queue will be

Wq= / ( - )

= 10/ 15 ( 15-10)

= 2/15

=0.13 minutes

2) The average number in the line will be

= /   (   -   )

= 10×10/ 15( 15-10)

=20/15

= 1.33

3) The average time in the system/ bank will be

= 1/ -

= 1/ 15-10

= 0.2 minutes

4) The average no in the system ,

= / -

= 10/ 15-10

=10/ 5

= 2

5) The probability that the bank is empty,

1 - /

= 1- 10/15

= 5/15

= 0.33

Or 33.33%

Answer