23-Ind-A6 Systems Simulation · December 2017

Question 8 of 8: Airport Check-In Simulation: Model Description & Process Flow Diagram

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Question 8 — Airport Check-In Simulation: Model Description & Process Flow Diagram (10 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. A single 4-hour (240-minute) check-in window for one flight, opening at $t=0$ with the flight departing at $t=240$ min. Passenger mix and routing probabilities:

Service: kiosk check-in $\mathrm{Unif}(3,7)$ min (both classes); luggage — Agents 1–3 (economy-only) $\mathrm{Expo}(9)$ min, Agent 4 (business-only) $\mathrm{Expo}(5)$ min, Agent 5 (either, priority to business) $\mathrm{Unif}(2,5)$ min business / $\mathrm{Unif}(3,9)$ min economy. Economy balks (skips straight to security) if it finds $>15$ already waiting in the economy luggage line. Business passengers who find $>3$ waiting get upset; 20% of those demand a supervisor (1 available), adding a 3-minute joint discussion plus $\mathrm{Unif}(2,4)$ min extra processing before proceeding to security.

Find. A model description precise enough to code directly, the three requested output statistics defined formally, and a process flow diagram.

Expected passenger-flow breakdown (deterministic, for capacity sizing — not a full stochastic run). Applying the given percentages to $N{=}50$/$200$:

So roughly 40 (25+15% of 100) business and 160 economy passengers are expected to need the luggage-drop stage — the luggage queues, not the 50 kiosks, are the likely system bottleneck given Economy's much higher arrival rate (75/hr vs. 18/hr) into just 3 dedicated economy agents.

Correlation to model code. Each block is a resource/queue the code would instantiate and each arrow an entity transition on an event: an Arrival event (two independent Poisson processes, rates 18/hr and 75/hr, capped at $N{=}50$/$200$ respectively) creates a passenger entity with attributes {class, checked-in-online?, luggage-pieces}, drawn as Bernoulli/categorical variates from the given percentages; a Kiosk-Check-in event (only for the not-checked-in-online fraction) seizes one of 50 kiosk resources (business entities may seize any of the 50; economy entities may seize only the 35 non-reserved) for $\mathrm{Unif}(3,7)$ min; a Luggage-Drop event routes no-luggage entities directly to Security and luggage-carrying entities into the class-specific FIFO queue for Agents 1–3 (economy) or Agent 4 / shared priority Agent 5 (business), the latter checking queue length $>3$ on arrival to flag "upset" and, for 20% of those, inserting a Supervisor-seize sub-event (1 unit, 3 min joint discussion $+\ \mathrm{Unif}(2,4)$ min) before completing luggage processing; a Balk check on the economy queue (if queue length $>15$ at arrival) sends the entity directly to Security instead of joining the queue; and a final Security/Exit event logs each entity's exit timestamp, which is exactly what the three requested output statistics are computed from.

The three requested output statistics, defined precisely.

1. 1. Average total time to exit. Over all 250 passengers, $\overline{T} = \frac{1}{250}\sum_{i=1}^{250}\big(t_{\text{exit},i}-t_{\text{arrival},i}\big)$ — the mean sojourn time from arrival to security-exit, averaged (per the standard replication/deletion method of Question 3) over multiple independent replications to get a confidence interval, not read off a single run.
2. 2. Passengers reaching security with $<$1 hour remaining. With the flight departing at $t=240$ min, this counts entities whose exit time satisfies $240 - t_{\text{exit},i} < 60$, i.e. $t_{\text{exit},i} > 180$ min; report the mean count of such passengers across replications.
3. 3. $P(\text{at least 1 missed flight})$. A passenger misses the flight if $t_{\text{exit},i} > 240-15 = 225$ min. Define the replication-level indicator $Y = \mathbb{1}\{\exists\, i:\ t_{\text{exit},i}>225\}$; the requested probability is $\hat p = \frac{1}{R}\sum_{r=1}^{R} Y_r$ across $R$ replications — a proportion, not a single-run yes/no answer, since it is a rare-event probability that only stabilizes with many replications.