AP4: Queuing OPS 3880 Jeremy Bernard Time to refresh. You mosey over to your favorite place but with a history of a line. Usually, you can expect there to be 20 people in line any time you come here (there is only one order taker). Service time averages 20 seconds. SHOW ALL WORK! 1 1 Remembering π = ππ , πΏ = ππ, π = π−π , πΏπ = ππΏ = πΏ − π, ππ = ππ = π − , ππ = (1 − π)ππ π a. What is the utilization of the server? ___71.43__% The utilization of the server is the percentage of time that the server is busy.. ππ‘ππππ§ππ‘πππ = π΄π£πππππ π΄ππππ£ππ π ππ‘π / π΄π£πππππ ππππ£πππ π ππ‘π = 7 / 20 = 0.357143 = 71.43% b. What is the expected time between people arriving to this system? __8.57143 __ seconds π΄π£πππππ π΄ππππ£ππ π ππ‘π = 7 ππππππ / ππππ’π‘π = 7 / 60 π ππππππ = 0.116667 ππππππ / π πππππ πΈπ₯ππππ‘ππ ππππ π΅ππ‘π€πππ π΄ππππ£πππ = 1 / π΄π£πππππ π΄ππππ£ππ π ππ‘π = 1 / 0.116667 π ππππππ = 8.57143 π ππππππ c. What is the expected wait until service starts? __14.2857 ___ seconds The expected wait time is the average amount of time that a customer has to wait before being served. πΈπ₯ππππ‘ππ ππππ‘ ππππ = ππ‘ππππ§ππ‘πππ ∗ π΄π£πππππ ππππ£πππ ππππ = 0.714286 ∗ 20 π ππππππ = 14.2857 π ππππππ d. What is the probability of 3 or fewer people in line upon your arrival? _92.86___% ππππππππππ‘π¦ ππ 3 ππ πΉππ€ππ ππππππ ππ πΏπππ = (1 − ππ‘ππππ§ππ‘πππ)^3 = (1 − 0.714286)^3 AP4: Queuing OPS 3880 = 0.9286 = 92.86% Jeremy Bernard
