Estimate the Expected Stop Time for Someone Passing Through a Road Junction

An interviewer asks you how long the average person waits at an intersection. Decide exactly what you are estimating, build the estimate from clearly labeled assumptions, work through the arithmetic, and check whether the result is plausible. ```hint Not every arrival stops Someone who reaches the light while it is green waits nothing, and a main road and a side street get very different shares of green time. Make sure your model reflects both. ``` ### Clarifying Questions - Should the estimate cover people in cars, people on foot, or everyone passing through? - Does "wait" mean only time stopped at a red light, or also time lost queuing behind other vehicles and yielding at stop signs? - Is the answer per intersection crossed, or a total per day or over a lifetime? - Are we picturing a busy city traffic signal, or every kind of intersection, including those with stop signs or no controls at all? ### What a Strong Answer Covers - A precise definition of who waits, at what kind of intersection, and per what unit, agreed before any arithmetic. - An explicit equation that links signal timing and arrival patterns to expected wait, including travelers who meet a green light. - Labeled round-number assumptions for cycle length, green splits, traffic shares and turning movements, with arithmetic that checks out. - A sanity check against intuition or a known reference point, and how the answer shifts for pedestrians, congestion or other intersection types. ### Follow-up Questions - At rush hour some drivers must sit through more than one red. How would you adjust the estimate? - A city installs signals that adapt to live traffic. How would you measure whether average waits fell? - How would you estimate the total hours a city's residents spend waiting at intersections in a year?