An average of 100 customers arrive each hour at theGotham City Bank. The average service time for eachcustomer is 1 minute. Service times and interarrival timesare exponential. The manager wants to ensure that no morethan 1% of all customers will have to wait in line for morethan 5 minutes. If the bank follows the policy of having allcustomers join a single line, how many tellers must the bankhire?

An average of 100 customers arrive each hour at theGotham City Bank. The average service time for eachcustomer is 1 minute. Service times and interarrival timesare exponential. The manager wants to ensure that no morethan 1% of all customers will have to wait in line for morethan 5 minutes. If the bank follows the policy of having allcustomers join a single line, how many tellers must the bankhire?

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Description: An average of 100 customers arrive each hour at theGotham City Bank. The average service time for eachcustomer is 1 minute. Service times and interarrival timesare exponential. The manager wants to ensure that no morethan 1% of all customers will hav

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section12.5: Analytic Steady-state Queueing Models

Problem 9P

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On average, 100 customers arrive per hour at theGotham City Bank. The average service time for eachcustomer is one minute. Service times and interarrivaltimes are exponentially distributed. The manager wantsto ensure that no more than 1% of all customers willhave to wait in line for more than five minutes. If thebank follows the policy of having all customers join asingle line, how many tellers must the bank hire?
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A supermarket is trying to decide how many cash registers to keep open. Suppose an average of 18 customers arrive each hour, and the average checkout time for a customer is four minutes. Interarrival times and servicetimes are exponentially distributed, and the system can be modeled as an M/M/s system. (In contrast to the situation at most supermarkets, we assume that all customers wait in a single line.) It costs $20 per hour tooperate a cash register, and a cost of $0.25 is assessed for each minute the customer spends in the cash register area (in line or being served). How many registers should the store open to minimize the expected hourly cost?