12 passengers per minute arrive at the concourse of a busy
airport according to a Poisson process. After arrival, passengers
travel down various routes according to the probabilities on the
diagram below. (Notice that the diagram was drawn in Simio for
convenience, but this is not a SImio problem. It is a Jackson queue
problem.) Assume processing times at each stage are from the
exponential distribution. Assume all travel times between nodes are
zero.The tasks, and the order in which they are performed, are as
follows.
As you analyze this system, make sure that 100% of your entities
make it through the system. The number of servers at each node and
the service times per server are given this table:
- Queueing Theory 12 Passengers Per Minute Arrive At The Concourse Of A Busy Airport According To A Poisson Process Afte 1 (46.68 KiB) Viewed 42 times
- Queueing Theory 12 Passengers Per Minute Arrive At The Concourse Of A Busy Airport According To A Poisson Process Afte 2 (99.59 KiB) Viewed 42 times
- Queueing Theory 12 Passengers Per Minute Arrive At The Concourse Of A Busy Airport According To A Poisson Process Afte 3 (143.23 KiB) Viewed 42 times
- Queueing Theory 12 Passengers Per Minute Arrive At The Concourse Of A Busy Airport According To A Poisson Process Afte 4 (129.55 KiB) Viewed 42 times
3/4 2/3 KioskCheckin 1 DetailedTSAScreen 1/12 1/4 1 1 DEL ArriveAtAirport 11/12 1/4 EaggageWeighin BagageSecurity IDCheck InitialTSAScreen Gate 1/3 AgentCheckin 3/4
Pitfall: Be clear on your distinction between times and rates. You need to use the stability condition 2<su for the part B. In this context 2 and u are both rates, and the units should be in passengers per time unit. If the facts that you are given are not what you need, you need to convert them. A. Which of the following is needed for this system to be a Jackson queue (circle your answer for each)? If an assumption is inconsistent with being a Jackson queue, classify it as not needed. Service times at all nodes are from the exponential distribution: NEEDED Finite space for queue at each node: NEEDED Infinite population available for arrivals: NEEDED Deterministic interarrivals from outside of the system: NEEDED NOT NEEDED NOT NEEDED NOT NEEDED NOT NEEDED B. Which nodes are stable (circle answer for each)? NOT STABLE NOT STABLE NOT STABLE Kiosk Check In STABLE Agent Check In STABLE Baggage Weigh In STABLE Baggage Security STABLE ID Check STABLE Initial TSA Screen STABLE Detailed TSA Screen STABLE NOT STABLE NOT STABLE NOT STABLE NOT STABLE
C. From the moment a passenger steps away from the Initial TSA Screen to the moment they arrive at the gate, what is the expected time (Hint: use a weighted average based on which path they take. So your answer should be 1/12 times something plus 11/12 times something else. Your job is to figure out what the “somethings” are.) min D. What is the mean time between departures from the Baggage Weigh In station? (Hint: should rate in = rate out in this situation? Have you been asked for a rate or a time? Do you need to convert?) min E. The Baggage Security station has a limited amount of space for people to put their carryon luggage into bins. Would this be a good reason to model it with a finite queue queueing model? Circle one: Yes No