A service facility consists of one server who can serve an average of two customers per hour (service times are exponential). An average of three customersper hour arrive at the facility (interarrival times are assumed to be exponential). The system capacity isthree customers: two waiting and one being served.a. On average, how many potential customers enter the system each hour?b. What is the probability that the server is busy at atypical point in time?

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter12: Queueing Models
Section12.4: Important Queueing Relationships
Problem 6P
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A service facility consists of one server who can serve an average of two customers per hour (service times are exponential). An average of three customers
per hour arrive at the facility (interarrival times are assumed to be exponential). The system capacity isthree customers: two waiting and one being served.
a. On average, how many potential customers enter the system each hour?
b. What is the probability that the server is busy at atypical point in time?

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