CIVL2700 · Transport Systems
Public Transport Operation & Planning
The Week-12 closing topic of CIVL2700 Transport Systems at the University of Sydney turns bus and rail operations into a handful of exact calculations. You model dwell time as a deterministic queue, use a load-factor boarding rate to explain why fuller vehicles stop longer, and apply transit economics — generalised cost versus benefit — to decide how far a line is worth building. It reuses the deterministic queue and value-of-time machinery from earlier in the semester, so it is an efficient place to bank marks in the comprehensive final exam.
What this chapter covers
- 01Dwell time as a D/D/1 queue: passengers accumulate at rate λ over a headway H, board at rate μ
- 02Minimum dwell τ = λH / μ, with λ = P/3600 pax/s (convert demand and headway to seconds first)
- 03Platform queue at arrival Q_max = λH; validity condition μ > λ so the stop can clear
- 04Load-factor boarding-rate law r = 15 − 10·(onboard / seats): fuller vehicle → slower boarding → longer dwell
- 05Dwell from the rate law: τ = (passengers boarding/alighting at the stop) / r
- 06How dwell compounds down a line as load factor climbs — the seed of schedule slippage and bus bunching
- 07Generalised cost of a trip g = fare F + VoT × travel time (x/v), all in dollars
- 08Willingness-to-travel: ride only if daily two-way cost 2g ≤ benefit B
- 09Line length L from 2[F + VoT·(L/v)] = B — the distance beyond which nobody is willing to travel
- 10Off-peak vs peak dwell: lower demand and faster boarding, offset by longer headways
How far is a transit corridor worth building?
- +1One-way generalised cost = fare + value-of-time × travel time = F + VoT·(L/v) = 3 + 16·(L/25) = 3 + 0.64L [$].
- +1The trip is made both ways every day, so the willingness-to-travel condition sets the DOUBLED daily cost equal to the daily benefit: 2·(3 + 0.64L) = 38.
- +1Solve: 6 + 1.28L = 38 ⇒ 1.28L = 32 ⇒ L = 32 / 1.28.
- +1L = 25 km. Check: one-way time 25/25 = 1 h → time cost $16; + $3 fare = $19 one-way; × 2 = $38 = benefit. ✓
Key terms
- Dwell time (τ)
- The time a bus or train stands at a stop to let passengers board and alight; modelled as the time to clear a passenger queue [s].
- Headway (H)
- The time between successive services on a route [s or min]; a shorter headway means more frequent service and a smaller accumulated queue.
- Arrival rate (λ)
- The rate at which passengers arrive at a stop [pax/s]; from a peak demand of P passengers per hour, λ = P/3600.
- Boarding / service rate (μ)
- How many passengers board per second [pax/s]; reduced by alighting and on-board crowding. The stop can only clear if μ > λ.
- Load factor (LF)
- The ratio of on-board passengers to seats (capacity). A higher load factor lowers the boarding rate, so a fuller vehicle dwells longer.
- Generalised cost (g)
- The full money cost of a trip = fare + value-of-time × travel time [$]. It lets time and money be compared in one currency.
- Value of time (VoT)
- The money a traveller effectively charges for time spent travelling [$/h]; multiplies the travel time x/v in the generalised cost.
- Willingness-to-travel
- The rule that a person makes a trip only if the benefit is at least the (two-way daily) generalised cost; it sets the length a line is worth building.
Public Transport Operation & Planning FAQ
Is the Week-12 public-transport material examinable in CIVL2700?
Yes. Public transport operation and planning is part of the University of Sydney CIVL2700 syllabus and is fair game in the comprehensive final exam (worth 40% of the unit, a supervised 2.5-hour paper covering the whole semester). The dwell-time and transit-economics calculations are short and formula-light, making them an efficient place to earn marks. Confirm the exam scope, date and the open/closed-book rule on Canvas.
Why does a fuller train dwell longer at a stop?
Because the boarding rate falls as the vehicle fills. The course's load-factor rate law r = 15 − 10·(onboard/seats) drops from 15 pax/s when empty to 5 pax/s when full, so the same number of boarders takes longer to load. Dwell = boarders / r, so higher load factor → lower r → longer dwell — the mechanism behind schedule slippage and bus bunching.
Can AI help me with public transport operation and planning in CIVL2700?
Yes — Sia works through it step by step. It can define dwell time, headway and load factor, explain why τ = λH/μ follows from the deterministic queue, and walk you through a generalised-cost or line-length calculation using your own numbers so you see each step. Sia is a study aid that explains the method and checks your reasoning; it does not sit your exam, do your assignment for you, or promise any grade or mark.
Exam move
Anchor Week 12 to machinery you already know rather than memorising it fresh: dwell time is just the deterministic (D/D/1) queue from Weeks 5–6 with passengers as the queue and the arriving service as the server, and transit economics is the value-of-time / generalised-cost idea from Weeks 2–4. Drill the unit conversions until they are automatic — turn a per-hour demand into pax/s (÷3600) and a headway from minutes into seconds before you divide, since a 60× unit slip is the most common lost mark. For each calculation, write the formula, substitute with units, then state the answer with its unit (s, pax/s, km or $). Practise the direction checks aloud: a fuller train boards more slowly and dwells longer, and a daily return commute doubles the one-way cost. Rehearse both worked patterns — τ = λH/μ for dwell and 2[F + VoT·L/v] = B for line length — with fresh numbers until you can reproduce them under time pressure, and confirm the exam date, room and open/closed-book status on Canvas.
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