A teller works at a rural bank. Customers arrive to complete their banking transactions on average one every 10 minutes; their arrivals follow a Poisson arrivalprocess. Because of the range of possible transactions, the time taken to serve eachcustomer may be assumed to follow an exponential distribution with a mean timeof 7 minutes. Customers wait in a single queue to get their banking done and nocustomer leaves without service.a. Calculate the average utilization of the teller.b. Calculate how long customers spend on average to complete their transactionsat the bank (time in queue plus service time). What percentage of that time isspent queueing?

A teller works at a rural bank. Customers arrive to complete their banking transactions on average one every 10 minutes; their arrivals follow a Poisson arrivalprocess. Because of the range of possible transactions, the time taken to serve eachcustomer may be assumed to follow an exponential distribution with a mean timeof 7 minutes. Customers wait in a single queue to get their banking done and nocustomer leaves without service.a. Calculate the average utilization of the teller.b. Calculate how long customers spend on average to complete their transactionsat the bank (time in queue plus service time). What percentage of that time isspent queueing?

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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