QUESTION 6 It is common in banks for bank tellers to have to access a single cen

Question

QUESTION 6

It is common in banks for bank tellers to have to access a single central cash window in order to get cash for customers. Consider such a bank, which has seven tellers, each requiring service from the cash window approximately 19 times per hour (assume Poisson arrivals) and an average time being served at the window (assume negative exponential distribution) of 40 seconds. How busy will the server at the central cash window be, on average (i.e., what percentage of the time should they expect to be serving someone)?

50%

60%

70%

80%

90%

50%

60%

70%

80%

90%

Explanation / Answer

Service required for each teller per hour =19 times

Inter arrival time=1/19*7 hour =0.007518797 hr

Arrival rate=1/ inter arrival time=1/0.007518797

Service time=40sec/(60*60)= 0.011111111 hour

Service rate=1/service time=1/0.011111111

Server Utilization (probability that the server is busy )=Q= service rate/Arrival rate

Q=service rate/Arrival rate= 1/0.011111111/(1/0.007518797)=70%

Hence Option C

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.