Mountain Road Traffic Jams: A Mathematical Puzzle of Queue Lengths

While stuck in slow-moving traffic on a winding mountain road, the author pondered the length of the queues. He initially attempted to calculate the average queue length using probability theory, but the result (an average of 2 cars) drastically contradicted his experience. Subsequently, a simulation revealed a much larger average queue length, leading to a correction of the initial derivation. The correct formula for the queue length distribution was obtained, but its expected value diverges to infinity, implying that mountain road queues can be infinitely long.