Customers arrive at the company's service office at an average of one every 20 minutes. Their requests take, on average, 15 minutes to be processed. The service counter is staffed by only one employee, who works six hours per day. Assume Poisson arrivals and exponential service times.  How much time, on average, does a customer spend waiting in line? What is the probability that an arriving customer, just before entering the office, will find at least one other customer waiting in line?

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
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Customers arrive at the company's service office at an average of one every 20 minutes. Their requests take, on average, 15 minutes to be processed. The service counter is staffed by only one employee, who works six hours per day. Assume Poisson arrivals and exponential service times. 

  1. How much time, on average, does a customer spend waiting in line?
  2. What is the probability that an arriving customer, just before entering the office, will find at least one other customer waiting in line?
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