Students arrive at the Administrative Services Office at an average of one every 20 minutes, and their requests take, on average, 12 minutes to be processed. The service counter is staffed by only one clerk, Judy Gumshoes, who works eight hours per day. Assume Poisson arrivals and exponential service times. What percentage of time is Judy idle? Note: Round your answer to 1 decimal place.   How much time, on average, does a student spend waiting in line? Note: Do not round intermediate calculations. Round your answer to 1 decimal place.   How long is the (waiting) line on average? Note: Round your answer to 2 decimal places.   What is the probability that an arriving student (just before entering the Administrative Services Office) will find at least one other student waiting in line? Note: Do not round intermediate calculations. Round your answer to 2 decimal places.

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
icon
Related questions
Question

Students arrive at the Administrative Services Office at an average of one every 20 minutes, and their requests take, on average, 12 minutes to be processed. The service counter is staffed by only one clerk, Judy Gumshoes, who works eight hours per day. Assume Poisson arrivals and exponential service times.

  1. What percentage of time is Judy idle?

    Note: Round your answer to 1 decimal place.

     
  2. How much time, on average, does a student spend waiting in line?

    Note: Do not round intermediate calculations. Round your answer to 1 decimal place.

     
  3. How long is the (waiting) line on average?

    Note: Round your answer to 2 decimal places.

     
  4. What is the probability that an arriving student (just before entering the Administrative Services Office) will find at least one other student waiting in line?

    Note: Do not round intermediate calculations. Round your answer to 2 decimal places.

     
 
 
 
 
 
 
Expert Solution
steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Inventory management
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, operations-management and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
Practical Management Science
Practical Management Science
Operations Management
ISBN:
9781337406659
Author:
WINSTON, Wayne L.
Publisher:
Cengage,
Marketing
Marketing
Marketing
ISBN:
9780357033791
Author:
Pride, William M
Publisher:
South Western Educational Publishing