8.1.5 Buses Come in Bunches

Other student projects did not meet with such immediate success, and some were simply ignored by decision makers. One topic that received the attention of two project groups (in two succeeding years) and resulted in two Master's theses is the "bunching" or "clumping" problem of buses. (See Chapter 1, including the letter to the editor from an irritated bus passenger.) To restate the problem, briefly, the clumping of buses tends to occur naturally even when buses are dispatched at prescribed intervals from one end of a transportation route. Any system perturbation (e.g., more passengers than average, traffic delays) will cause one bus to slow down (operating behind schedule). This slowdown becomes more pronounced at each successive stop, as more and more passengers have accumulated since the time of the most recent bus. Meanwhile, the bus immediately behind the slowed bus 11 speeds up," since it finds fewer and fewer passengers waiting (because of the shortened bus interarrival time). Eventually, the buses "clump"; that is, they come together due to this accelerating process.

Our students developed both analytical and simulation models to discover ways to reduce the occurrences of clumping. Several guidelines were established that involved only local controls, such as delaying the departure of a bus at a stop if the most recent bus left the stop "too recently." However, no one could be found in the local public transportation services who viewed this as a problem deserving of their attention. So, considerably more (and quite original) analytical work was done on bus clumping than on the school busing problem, but no implementation can be reported.