Zimmerman Bank Solution

f) Zimmerman is considering adding a second teller (who would work at the same rate as the first) to reduce the waiting time for customers. She assumes that this will cut the waiting time in half. If a second teller is added, find the new answers to parts a) through d) above.

Arrival Rate (l) 10 customers/hr

Service time 4 minutes P(0)=

Service Rate (m) 15 customers/hr

Arrival Rate /Service Rate 0.67

Number of servers K 2

r

0.333

Average time a customer will spend in waiting a line (Wq)

First calculating P(0) i (Arrival Rate /Service Rate)^i (Arrival Rate /Service Rate)^i /i! (Arrival Rate /Service Rate)^K P(0)

- 1.0000 1.0000 0.4444

1.0000 0.6667 0.6667 L = Lq + / 

1.6667 0.3333 0.5000

P(0) 0.5000 W = Wq + 1 / 

a) The average time in the line

Average time in line Wq 0.0083 Hrs

0.500 Minutes

b) The average number in the line.

Average number in the line Lq 0.0833

c) The average time in the system

Average time in the system (W) 0.075

4.5 Minutes

d) The average number in the system

Average no of customers in the System(L) 0.75

Answer : Adding 1 advisor to the current system will bring the waiting time in the acceptable range.