Travel decisions often fail when one mean replaces a distribution. People who must arrive on time need evidence about the delayed tail as well as the typical journey.
The original case gives Route A ten trips with a22-minute mean and nearest-rank95th percentile of42 minutes. Route B is24 minutes every time. A is faster on average; B is more reliable in the supplied sample.
FHWA guidance grounds percentile time, buffer index and planning time index. The trips are fictional and do not describe a real route.
The method preserves route, mode, direction, time window, trip completion, incident status, percentile convention and free-flow reference.
This specialist guide belongs to the Urban Systems root. It also connects to The Gold Standard of Education | Learning That Transfers into Life and the How X Works hub. The worked cases are original teaching examples; their numbers are stipulated so that the reasoning can be checked.
eduKateSG · Urban Systems
Find your next learning step
Average travel time describes a centre; reliability describes variation or the time needed for a stated on-time probability. A route can be faster on average and still demand a much larger planning buffer.
ROUTE 6 · CHAPTERS 25–28
Extend and continue
Check deeper boundaries and follow verified reading routes.
Chapter contents
Define the quantities · Chapters 1–5
3. Define a reliability question
Work the mechanism · Chapters 6–10
6. Complete the central two-route example
Control the comparison · Chapters 11–15
11. Preserve day and time stratification
13. Choose percentile conventions explicitly
Audit the evidence · Chapters 16–20
16. Carry sampling uncertainty
17. Compare travellers and modes fairly
18. Relate reliability to accessibility carefully
Test transfer · Chapters 21–24
21. Repair the lower average means more reliable shortcut
22. Repair the 95th percentile is worst case shortcut
Extend and continue · Chapters 25–28
25. Separate day-to-day variability from within-trip delay
26. Match temporal aggregation to the decision
Begin with the reported quantity. Average time and reliability must describe the same origin, destination, mode, direction and time window before they can be compared.
Work the original teaching case step by step. Route A has ten fictional weekday trips in one peak window.
Make the result independently checkable. Preserve every trip time rather than only a summary.
Test transfer by changing one consequential condition. Change the analysis to weekends.
Keep the claim boundary visible. A mixed population can manufacture apparent variability.
Use this chapter as a prediction check. Before reading the recalculation, write down the expected direction and the one observation that would reverse it. Then Preserve every trip time rather than only a summary. In the changed case, Change the analysis to weekends. Compare the result with the prediction and explain any mismatch without changing the definitions after the fact.
The evidence receipt for “Define the trip population” records the source observation, transformation, changed-context prediction and limit on separate lines. For Urban Systems, the receipt retains every trip and the percentile convention so averages, tails, incidents and user consequences remain auditable.
Separate the objects before comparing them. The arithmetic mean describes the centre of recorded times but does not show the upper tail.
Work the original teaching case step by step. Route A times sum to220 minutes across ten trips, so the mean is22 minutes.
Make the result independently checkable. Recompute the sum and count.
Test transfer by changing one consequential condition. Replace the 42-minute trip with22 minutes.
Keep the claim boundary visible. The mean is sensitive to extreme trips and missing observations.
Turn this distinction into a two-column mini audit. In the first column record the observation; in the second record the inference it can support. Apply this check: Recompute the sum and count. Next change the setting deliberately: Replace the 42-minute trip with22 minutes. If the conclusion changes, name the changed assumption rather than calling the earlier result wrong.
The evidence receipt for “Define average travel time” records the source observation, transformation, changed-context prediction and limit on separate lines. For Urban Systems, the receipt retains every trip and the percentile convention so averages, tails, incidents and user consequences remain auditable.
Name the mechanism before interpreting the number. Travel-time reliability asks how much travel time varies or how much time a traveller must plan for a stated on-time level.
Work the original teaching case step by step. The lesson uses the nearest-rank 95th percentile and a planning buffer.
Make the result independently checkable. Name the percentile convention.
Test transfer by changing one consequential condition. Use the 90th percentile instead.
Keep the claim boundary visible. Reliability is not one universal statistic.
Practise transfer before memorising a label. Rebuild the result using this independent check: Name the percentile convention. Then make one controlled change: Use the 90th percentile instead. State which quantity should move, which should stay fixed and what evidence would count against the prediction. This makes the mechanism testable instead of merely plausible.
The evidence receipt for “Define a reliability question” records the source observation, transformation, changed-context prediction and limit on separate lines. For Urban Systems, the receipt retains every trip and the percentile convention so averages, tails, incidents and user consequences remain auditable.
Keep observation, calculation and decision in separate columns. Two routes can have different means and upper-tail times, producing different rankings.
Work the original teaching case step by step. Route B takes24 minutes on every one of ten trips.
Make the result independently checkable. Compare mean, median and chosen percentile.
Test transfer by changing one consequential condition. Add one disruption to Route B.
Keep the claim boundary visible. A constant fictional route is a teaching contrast, not a real network claim.
Close the chapter with a decision receipt. Record the input, unit, scope, transformation and claim in separate fields, then apply: Compare mean, median and chosen percentile. For the transfer trial, Add one disruption to Route B. Keep the original result beside the new one so the reader can see exactly which condition changed and why the interpretation follows.
The evidence receipt for “Separate typical and near-worst travel” records the source observation, transformation, changed-context prediction and limit on separate lines. For Urban Systems, the receipt retains every trip and the percentile convention so averages, tails, incidents and user consequences remain auditable.
Use the short answer only after fixing scope and units. Planning-time indices may compare a percentile with an ideal or free-flow time, while buffer indices compare percentile with average time.
Work the original teaching case step by step. The fictional free-flow reference is15 minutes.
Make the result independently checkable. State how free-flow was estimated.
Test transfer by changing one consequential condition. Use18 minutes as a different justified reference.
Keep the claim boundary visible. An unstable reference changes the index even if trips do not change.
Use this chapter as a prediction check. Before reading the recalculation, write down the expected direction and the one observation that would reverse it. Then State how free-flow was estimated. In the changed case, Use18 minutes as a different justified reference. Compare the result with the prediction and explain any mismatch without changing the definitions after the fact.
The evidence receipt for “Keep free-flow time separate” records the source observation, transformation, changed-context prediction and limit on separate lines. For Urban Systems, the receipt retains every trip and the percentile convention so averages, tails, incidents and user consequences remain auditable.
Begin with the reported quantity. Route A has mean22 and nearest-rank P95=42; Route B has mean24 and P95=24.
Work the original teaching case step by step. A is faster on average by2 minutes, but B has a much smaller high-percentile time.
Make the result independently checkable. Sort every observation and show the percentile rule.
Test transfer by changing one consequential condition. Remove A’s disrupted trip and recompute.
Keep the claim boundary visible. Ten trips are deliberately small and do not support a population claim.
Turn this distinction into a two-column mini audit. In the first column record the observation; in the second record the inference it can support. Apply this check: Sort every observation and show the percentile rule. Next change the setting deliberately: Remove A’s disrupted trip and recompute. If the conclusion changes, name the changed assumption rather than calling the earlier result wrong.
The evidence receipt for “Complete the central two-route example” records the source observation, transformation, changed-context prediction and limit on separate lines. For Urban Systems, the receipt retains every trip and the percentile convention so averages, tails, incidents and user consequences remain auditable.
Separate the objects before comparing them. Buffer time is the selected percentile time minus average time under the stated FHWA-style example.
Work the original teaching case step by step. Route A buffer=42-22=20 minutes; Route B buffer=24-24=0.
Make the result independently checkable. Check that times use the same period.
Test transfer by changing one consequential condition. Add a 30-minute trip to B.
Keep the claim boundary visible. Zero observed buffer in a tiny sample does not prove zero future variation.
Practise transfer before memorising a label. Rebuild the result using this independent check: Check that times use the same period. Then make one controlled change: Add a 30-minute trip to B. State which quantity should move, which should stay fixed and what evidence would count against the prediction. This makes the mechanism testable instead of merely plausible.
The evidence receipt for “Calculate buffer time” records the source observation, transformation, changed-context prediction and limit on separate lines. For Urban Systems, the receipt retains every trip and the percentile convention so averages, tails, incidents and user consequences remain auditable.
Name the mechanism before interpreting the number. Buffer index divides buffer time by average travel time and expresses the result as a percentage.
Work the original teaching case step by step. A gives20/22≈90.9%; B gives0%.
Make the result independently checkable. Retain numerator and denominator beside the percentage.
Test transfer by changing one consequential condition. Increase A’s mean while holding P95 fixed.
Keep the claim boundary visible. The index can move because either centre or tail changes.
Close the chapter with a decision receipt. Record the input, unit, scope, transformation and claim in separate fields, then apply: Retain numerator and denominator beside the percentage. For the transfer trial, Increase A’s mean while holding P95 fixed. Keep the original result beside the new one so the reader can see exactly which condition changed and why the interpretation follows.
The evidence receipt for “Calculate buffer index” records the source observation, transformation, changed-context prediction and limit on separate lines. For Urban Systems, the receipt retains every trip and the percentile convention so averages, tails, incidents and user consequences remain auditable.
Keep observation, calculation and decision in separate columns. Planning time index divides the selected percentile travel time by free-flow travel time.
Work the original teaching case step by step. A gives42/15=2.8; B gives24/15=1.6.
Make the result independently checkable. Use the same free-flow definition for both routes.
Test transfer by changing one consequential condition. Give B a different legitimate route-specific free-flow time.
Keep the claim boundary visible. Cross-route comparison needs consistent and meaningful references.
Use this chapter as a prediction check. Before reading the recalculation, write down the expected direction and the one observation that would reverse it. Then Use the same free-flow definition for both routes. In the changed case, Give B a different legitimate route-specific free-flow time. Compare the result with the prediction and explain any mismatch without changing the definitions after the fact.
The evidence receipt for “Calculate planning time index” records the source observation, transformation, changed-context prediction and limit on separate lines. For Urban Systems, the receipt retains every trip and the percentile convention so averages, tails, incidents and user consequences remain auditable.
Use the short answer only after fixing scope and units. A traveller choosing the lowest expected time may prefer A, while a time-critical trip may prefer B.
Work the original teaching case step by step. The decision record names the cost of lateness.
Make the result independently checkable. Separate descriptive metrics from the value judgement.
Test transfer by changing one consequential condition. Make the appointment flexible.
Keep the claim boundary visible. No metric chooses priorities on behalf of the user.
Turn this distinction into a two-column mini audit. In the first column record the observation; in the second record the inference it can support. Apply this check: Separate descriptive metrics from the value judgement. Next change the setting deliberately: Make the appointment flexible. If the conclusion changes, name the changed assumption rather than calling the earlier result wrong.
The evidence receipt for “State the decision purpose” records the source observation, transformation, changed-context prediction and limit on separate lines. For Urban Systems, the receipt retains every trip and the percentile convention so averages, tails, incidents and user consequences remain auditable.
Begin with the reported quantity. Combining peak, off-peak and weekend trips can inflate variability or hide a recurring problem.
Work the original teaching case step by step. A’s 42-minute trip occurs during a specific peak incident.
Make the result independently checkable. Tag time period and incident.
Test transfer by changing one consequential condition. Analyse only incident-free days.
Keep the claim boundary visible. Removing disruptions answers a narrower reliability question.
Practise transfer before memorising a label. Rebuild the result using this independent check: Tag time period and incident. Then make one controlled change: Analyse only incident-free days. State which quantity should move, which should stay fixed and what evidence would count against the prediction. This makes the mechanism testable instead of merely plausible.
The evidence receipt for “Preserve day and time stratification” records the source observation, transformation, changed-context prediction and limit on separate lines. For Urban Systems, the receipt retains every trip and the percentile convention so averages, tails, incidents and user consequences remain auditable.
Separate the objects before comparing them. Cancelled, abandoned or unobserved trips can be informative and should not vanish silently.
Work the original teaching case step by step. One trip is missing after a service suspension.
Make the result independently checkable. State censoring and coverage.
Test transfer by changing one consequential condition. Assign a defined failure outcome in a sensitivity analysis.
Keep the claim boundary visible. A numeric imputation is a modelling choice, not an observation.
Close the chapter with a decision receipt. Record the input, unit, scope, transformation and claim in separate fields, then apply: State censoring and coverage. For the transfer trial, Assign a defined failure outcome in a sensitivity analysis. Keep the original result beside the new one so the reader can see exactly which condition changed and why the interpretation follows.
The evidence receipt for “Handle incomplete trips” records the source observation, transformation, changed-context prediction and limit on separate lines. For Urban Systems, the receipt retains every trip and the percentile convention so averages, tails, incidents and user consequences remain auditable.
CHAPTER 13 OF 28 · Control the comparison
13. Choose percentile conventions explicitly
Name the mechanism before interpreting the number. Small samples produce different interpolated and nearest-rank percentile values.
Work the original teaching case step by step. With ten observations, the nearest-rank 95th percentile selects the tenth value.
Make the result independently checkable. Document the software method.
Test transfer by changing one consequential condition. Use a larger sample and compare conventions.
Keep the claim boundary visible. A percentile without its algorithm can be irreproducible.
Use this chapter as a prediction check. Before reading the recalculation, write down the expected direction and the one observation that would reverse it. Then Document the software method. In the changed case, Use a larger sample and compare conventions. Compare the result with the prediction and explain any mismatch without changing the definitions after the fact.
The evidence receipt for “Choose percentile conventions explicitly” records the source observation, transformation, changed-context prediction and limit on separate lines. For Urban Systems, the receipt retains every trip and the percentile convention so averages, tails, incidents and user consequences remain auditable.
Keep observation, calculation and decision in separate columns. The median resists a single extreme time but still does not describe reliability.
Work the original teaching case step by step. A’s median is20 minutes even though one trip takes42.
Make the result independently checkable. Report the distribution or tail measure too.
Test transfer by changing one consequential condition. Add several moderately delayed trips.
Keep the claim boundary visible. Robust centre and reliability answer different questions.
Turn this distinction into a two-column mini audit. In the first column record the observation; in the second record the inference it can support. Apply this check: Report the distribution or tail measure too. Next change the setting deliberately: Add several moderately delayed trips. If the conclusion changes, name the changed assumption rather than calling the earlier result wrong.
The evidence receipt for “Use medians without losing tails” records the source observation, transformation, changed-context prediction and limit on separate lines. For Urban Systems, the receipt retains every trip and the percentile convention so averages, tails, incidents and user consequences remain auditable.
CHAPTER 15 OF 28 · Control the comparison
15. Separate recurring from nonrecurring delay
Use the short answer only after fixing scope and units. Daily demand and rare incidents can create different patterns with different remedies.
Work the original teaching case step by step. The fictional extreme is marked as incident-related.
Make the result independently checkable. Use incident logs and calendar data.
Test transfer by changing one consequential condition. Raise every trip by5 minutes without adding variation.
Keep the claim boundary visible. A slower but equally variable route has a different problem.
Practise transfer before memorising a label. Rebuild the result using this independent check: Use incident logs and calendar data. Then make one controlled change: Raise every trip by5 minutes without adding variation. State which quantity should move, which should stay fixed and what evidence would count against the prediction. This makes the mechanism testable instead of merely plausible.
The evidence receipt for “Separate recurring from nonrecurring delay” records the source observation, transformation, changed-context prediction and limit on separate lines. For Urban Systems, the receipt retains every trip and the percentile convention so averages, tails, incidents and user consequences remain auditable.
Begin with the reported quantity. A high percentile from few trips is unstable, so the sample size belongs beside the estimate.
Work the original teaching case step by step. The central P95 comes from only ten trips.
Make the result independently checkable. Bootstrap or collect more days when inference is required.
Test transfer by changing one consequential condition. Expand to one hundred observations.
Keep the claim boundary visible. A precise displayed percentile can remain uncertain.
Close the chapter with a decision receipt. Record the input, unit, scope, transformation and claim in separate fields, then apply: Bootstrap or collect more days when inference is required. For the transfer trial, Expand to one hundred observations. Keep the original result beside the new one so the reader can see exactly which condition changed and why the interpretation follows.
The evidence receipt for “Carry sampling uncertainty” records the source observation, transformation, changed-context prediction and limit on separate lines. For Urban Systems, the receipt retains every trip and the percentile convention so averages, tails, incidents and user consequences remain auditable.
Separate the objects before comparing them. Different users face walking, transfer, accessibility and schedule conditions that change both mean and reliability.
Work the original teaching case step by step. The same route is analysed for a wheelchair user with an elevator transfer.
Make the result independently checkable. Preserve door-to-door boundaries.
Test transfer by changing one consequential condition. Remove one accessible transfer option.
Keep the claim boundary visible. A network-wide average can conceal unequal reliability.
Use this chapter as a prediction check. Before reading the recalculation, write down the expected direction and the one observation that would reverse it. Then Preserve door-to-door boundaries. In the changed case, Remove one accessible transfer option. Compare the result with the prediction and explain any mismatch without changing the definitions after the fact.
The evidence receipt for “Compare travellers and modes fairly” records the source observation, transformation, changed-context prediction and limit on separate lines. For Urban Systems, the receipt retains every trip and the percentile convention so averages, tails, incidents and user consequences remain auditable.
CHAPTER 18 OF 28 · Audit the evidence
18. Relate reliability to accessibility carefully
Name the mechanism before interpreting the number. Unreliable time can reduce dependable access to destinations even when a map is connected.
Work the original teaching case step by step. A job is reachable within30 minutes on most trips but not on the delayed tail.
Make the result independently checkable. Report threshold exceedance.
Test transfer by changing one consequential condition. Change the arrival deadline.
Keep the claim boundary visible. Connectivity and accessibility remain separate from reliability.
Turn this distinction into a two-column mini audit. In the first column record the observation; in the second record the inference it can support. Apply this check: Report threshold exceedance. Next change the setting deliberately: Change the arrival deadline. If the conclusion changes, name the changed assumption rather than calling the earlier result wrong.
The evidence receipt for “Relate reliability to accessibility carefully” records the source observation, transformation, changed-context prediction and limit on separate lines. For Urban Systems, the receipt retains every trip and the percentile convention so averages, tails, incidents and user consequences remain auditable.
Keep observation, calculation and decision in separate columns. Index averages need justified weights such as trips or vehicle-distance and compatible definitions.
Work the original teaching case step by step. Two corridors have different numbers of observations.
Make the result independently checkable. Show the weighting rule.
Test transfer by changing one consequential condition. Swap equal weighting for trip weighting.
Keep the claim boundary visible. An aggregate can hide the corridor with severe tail delay.
Practise transfer before memorising a label. Rebuild the result using this independent check: Show the weighting rule. Then make one controlled change: Swap equal weighting for trip weighting. State which quantity should move, which should stay fixed and what evidence would count against the prediction. This makes the mechanism testable instead of merely plausible.
The evidence receipt for “Avoid averaging route indices blindly” records the source observation, transformation, changed-context prediction and limit on separate lines. For Urban Systems, the receipt retains every trip and the percentile convention so averages, tails, incidents and user consequences remain auditable.
Use the short answer only after fixing scope and units. Each row records start, end, mode, date, departure, elapsed time, incident flag and completion status.
Work the original teaching case step by step. The ten Route A rows reproduce mean and percentile.
Make the result independently checkable. Keep raw rows with the summary.
Test transfer by changing one consequential condition. Correct one timestamp and version the result.
Keep the claim boundary visible. A complete ledger still needs representative sampling.
Close the chapter with a decision receipt. Record the input, unit, scope, transformation and claim in separate fields, then apply: Keep raw rows with the summary. For the transfer trial, Correct one timestamp and version the result. Keep the original result beside the new one so the reader can see exactly which condition changed and why the interpretation follows.
The evidence receipt for “Build a reproducible trip ledger” records the source observation, transformation, changed-context prediction and limit on separate lines. For Urban Systems, the receipt retains every trip and the percentile convention so averages, tails, incidents and user consequences remain auditable.
CHAPTER 21 OF 28 · Test transfer
21. Repair the lower average means more reliable shortcut
Begin with the reported quantity. A route can be faster on average while having a much worse upper tail.
Work the original teaching case step by step. Route A beats B by2 minutes on mean but loses by18 minutes on P95.
Make the result independently checkable. Compare at least one centre and one tail measure.
Test transfer by changing one consequential condition. Remove the rare disruption.
Keep the claim boundary visible. The ranking depends on the question and sample.
Use this chapter as a prediction check. Before reading the recalculation, write down the expected direction and the one observation that would reverse it. Then Compare at least one centre and one tail measure. In the changed case, Remove the rare disruption. Compare the result with the prediction and explain any mismatch without changing the definitions after the fact.
The evidence receipt for “Repair the lower average means more reliable shortcut” records the source observation, transformation, changed-context prediction and limit on separate lines. For Urban Systems, the receipt retains every trip and the percentile convention so averages, tails, incidents and user consequences remain auditable.
CHAPTER 22 OF 28 · Test transfer
22. Repair the 95th percentile is worst case shortcut
Separate the objects before comparing them. A 95th percentile leaves about five percent of the target distribution beyond it under the definition.
Work the original teaching case step by step. The teaching value is a planning benchmark, not a maximum.
Make the result independently checkable. Report maxima separately when useful.
Test transfer by changing one consequential condition. Use the 99th percentile.
Keep the claim boundary visible. No finite percentile guarantees an on-time arrival.
Turn this distinction into a two-column mini audit. In the first column record the observation; in the second record the inference it can support. Apply this check: Report maxima separately when useful. Next change the setting deliberately: Use the 99th percentile. If the conclusion changes, name the changed assumption rather than calling the earlier result wrong.
The evidence receipt for “Repair the 95th percentile is worst case shortcut” records the source observation, transformation, changed-context prediction and limit on separate lines. For Urban Systems, the receipt retains every trip and the percentile convention so averages, tails, incidents and user consequences remain auditable.
Name the mechanism before interpreting the number. A redesign can lower the tail without moving the mean much, or lower the mean while leaving severe disruptions.
Work the original teaching case step by step. New Route A times give mean21 and P95=30.
Make the result independently checkable. Compare component changes.
Test transfer by changing one consequential condition. Add a scheduled recovery buffer.
Keep the claim boundary visible. Before-and-after claims need matched seasons and conditions.
Practise transfer before memorising a label. Rebuild the result using this independent check: Compare component changes. Then make one controlled change: Add a scheduled recovery buffer. State which quantity should move, which should stay fixed and what evidence would count against the prediction. This makes the mechanism testable instead of merely plausible.
The evidence receipt for “Transfer to an improved service” records the source observation, transformation, changed-context prediction and limit on separate lines. For Urban Systems, the receipt retains every trip and the percentile convention so averages, tails, incidents and user consequences remain auditable.
CHAPTER 24 OF 28 · Test transfer
24. Add an on-time probability when a deadline matters
Keep observation, calculation and decision in separate columns. A percentile is one view of reliability; the share arriving within a meaningful threshold can answer a direct service promise.
Work the original teaching case step by step. Seven of ten Route A trips arrive within25 minutes, while all ten Route B trips do.
Make the result independently checkable. State the threshold and count every eligible trip.
Test transfer by changing one consequential condition. Move the threshold to20 minutes and recompute.
Keep the claim boundary visible. An on-time percentage is conditional on the chosen deadline and sample.
Close the chapter with a decision receipt. Record the input, unit, scope, transformation and claim in separate fields, then apply: State the threshold and count every eligible trip. For the transfer trial, Move the threshold to20 minutes and recompute. Keep the original result beside the new one so the reader can see exactly which condition changed and why the interpretation follows.
The evidence receipt for “Add an on-time probability when a deadline matters” records the source observation, transformation, changed-context prediction and limit on separate lines. For Urban Systems, the receipt retains every trip and the percentile convention so averages, tails, incidents and user consequences remain auditable.
CHAPTER 25 OF 28 · Extend and continue
25. Separate day-to-day variability from within-trip delay
Use the short answer only after fixing scope and units. Repeated door-to-door times measure variation across trips, while a single trip can also contain waiting, transfer and in-vehicle components.
Work the original teaching case step by step. The 42-minute trip contains a long transfer wait rather than slower movement on every segment.
Make the result independently checkable. Keep component timestamps as well as total time.
Test transfer by changing one consequential condition. Reduce the transfer wait while holding in-vehicle time fixed.
Keep the claim boundary visible. A total-time tail does not identify the operational component without the decomposition.
Use this chapter as a prediction check. Before reading the recalculation, write down the expected direction and the one observation that would reverse it. Then Keep component timestamps as well as total time. In the changed case, Reduce the transfer wait while holding in-vehicle time fixed. Compare the result with the prediction and explain any mismatch without changing the definitions after the fact.
The evidence receipt for “Separate day-to-day variability from within-trip delay” records the source observation, transformation, changed-context prediction and limit on separate lines. For Urban Systems, the receipt retains every trip and the percentile convention so averages, tails, incidents and user consequences remain auditable.
CHAPTER 26 OF 28 · Extend and continue
26. Match temporal aggregation to the decision
Begin with the reported quantity. An hourly summary may hide a fifteen-minute reliability failure, while a very narrow bin may have too few observations.
Work the original teaching case step by step. The peak-hour mean is22 minutes, but the final quarter-hour contains the delayed trip.
Make the result independently checkable. Publish counts and distribution summaries for every bin.
Test transfer by changing one consequential condition. Combine four weeks before estimating the quarter-hour tail.
Keep the claim boundary visible. Finer resolution improves localisation only when sampling remains adequate.
Turn this distinction into a two-column mini audit. In the first column record the observation; in the second record the inference it can support. Apply this check: Publish counts and distribution summaries for every bin. Next change the setting deliberately: Combine four weeks before estimating the quarter-hour tail. If the conclusion changes, name the changed assumption rather than calling the earlier result wrong.
The evidence receipt for “Match temporal aggregation to the decision” records the source observation, transformation, changed-context prediction and limit on separate lines. For Urban Systems, the receipt retains every trip and the percentile convention so averages, tails, incidents and user consequences remain auditable.
CHAPTER 27 OF 28 · Extend and continue
27. Use redundancy without double-counting reliability
Separate the objects before comparing them. Alternative routes can improve a traveller’s options, but correlated disruptions may affect all routes at once.
Work the original teaching case step by step. Routes A and B share one bridge, so a bridge closure delays both despite their normal-time differences.
Make the result independently checkable. Map shared links and common failure modes.
Test transfer by changing one consequential condition. Add a truly independent crossing and recompute the choice set.
Keep the claim boundary visible. Two named routes do not guarantee two independent reliability options.
Practise transfer before memorising a label. Rebuild the result using this independent check: Map shared links and common failure modes. Then make one controlled change: Add a truly independent crossing and recompute the choice set. State which quantity should move, which should stay fixed and what evidence would count against the prediction. This makes the mechanism testable instead of merely plausible.
The evidence receipt for “Use redundancy without double-counting reliability” records the source observation, transformation, changed-context prediction and limit on separate lines. For Urban Systems, the receipt retains every trip and the percentile convention so averages, tails, incidents and user consequences remain auditable.
Name the mechanism before interpreting the number. Travel reliability complements connectivity, accessibility and equilibrium-route questions.
Work the original teaching case step by step. Use the linked accessibility article when the question becomes reachable destinations.
Make the result independently checkable. Keep metric ownership explicit.
Test transfer by changing one consequential condition. Move from trip times to service catchments.
Keep the claim boundary visible. This article owns average travel time versus reliability.
Close the chapter with a decision receipt. Record the input, unit, scope, transformation and claim in separate fields, then apply: Keep metric ownership explicit. For the transfer trial, Move from trip times to service catchments. Keep the original result beside the new one so the reader can see exactly which condition changed and why the interpretation follows.
The evidence receipt for “Continue through verified urban routes” records the source observation, transformation, changed-context prediction and limit on separate lines. For Urban Systems, the receipt retains every trip and the percentile convention so averages, tails, incidents and user consequences remain auditable.
Continue through the verified reading route
Network connectivity and destination accessibility
Network connectivity and destination accessibility. Use this when the question changes from time variability to reachable opportunities.
Service catchment area and served population
Service catchment area and served population. Use this when a mapped area must be translated into people actually served.
Added links and equilibrium journey time
Added links and equilibrium journey time. Use this when route choice changes after a connection is added.
Frequently asked questions
Can the faster average route be less reliable?
Yes. Route A averages22 minutes but has a42-minute upper-tail trip in the teaching set.
Is the95th percentile the worst trip?
No. It is a chosen percentile benchmark and is not a maximum guarantee.
Why state the percentile algorithm?
Small samples can produce different values under different interpolation conventions.
Does reliability equal accessibility?
No. Reliability affects dependable access, while accessibility concerns reachable opportunities under stated conditions.
Authoritative sources and further reading
FHWA Travel Time Reliability Primer. Official definitions and examples for travel-time index, buffer index, planning time index and failure measures.
FHWA Making It There on Time. Official technical explanation of percentile times and reliability indices.
FHWA Reliability Analysis Guidance. Official guidance for reliability analysis and reporting.
US DOT Bureau of Transportation Statistics. Official transport-statistics context for travel-time reliability.
Return to the Urban Systems subject guide, The Gold Standard of Education, or the How X Works hub.