An ice cream truck is parked at a local beach and customers queue up to buy ice creams at a rate of one per minute. The arrival pattern of people buying ice cream is essentially random. It takes 40 seconds on average to serve a customer ice cream, with a standard deviation of 20 seconds. Find the following expected measures of performance for this system: the expected time in the queue for ice cream, the expected total time to get an ice cream, and the expected number of customers waiting for ice cream.

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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An ice cream truck is parked at a local beach and customers queue up to buy ice creams at a rate
of one per minute. The arrival pattern of people buying ice cream is essentially random. It takes
40 seconds on average to serve a customer ice cream, with a standard deviation of 20 seconds.
Find the following expected measures of performance for this system: the expected time in the
queue for ice cream, the expected total time to get an ice cream, and the expected number of
customers waiting for ice cream.
Transcribed Image Text:An ice cream truck is parked at a local beach and customers queue up to buy ice creams at a rate of one per minute. The arrival pattern of people buying ice cream is essentially random. It takes 40 seconds on average to serve a customer ice cream, with a standard deviation of 20 seconds. Find the following expected measures of performance for this system: the expected time in the queue for ice cream, the expected total time to get an ice cream, and the expected number of customers waiting for ice cream.
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