762 PART 4 Quantitative Modules D.9 Zimmerman\'s Bank is the only bank in the sm

Question

762 PART 4 Quantitative Modules D.9 Zimmerman's Bank is the only bank in the small town to of St. Thomas. On a typical Friday, an average of 10 customers per h hour arrive at the bank to transact business. There is one teller at the o bank, and the average time required to transact business is 4 min- P utes. It is assumed that service times may be described by the expo- nential 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. f) Zimmerman is considering adding a second teller (who would work at the same rate as the first) to reduce the waiting time for cus- tomers. She assumes that this will cut the waiting time in half. If a second teller is added, find the new answers to parts (a) to (e). Px

Explanation / Answer

Arrival rate ? = 10

Service Rate ? = 60/4 = 15

? = ?/? =2/3

a) Average Time in Line = ?/(?-?) = 8 minutes

b) Average No. in Line = ?^2/(1-?) = 4/3 = 1.33 persons

c) Average time in System = 1/(?-?) = 12 min

d) Average No. in System = 1+ Average no. in Line = 2.33 persons

e) The Probabilty that bank is empty = p0 = 1-? =  1/3 = 0.33

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