Holding strategies in a bus-route model

Scott Hill, Physics, Southern Methodist U,

While traffic dynamics has been a hot topic recently, the dynamics of bus routes has seen less study in physics circles; bus behavior differs from automobile behavior due to interaction with passengers at designated stops. Bus routes have an inherent instability, which can cause exponentially increasing delays, leading in turn to the formation of bus clusters (two or more buses moving in tandem) which are often seen in large cities. Bus dispatchers fight this instability by building slack into their schedules and by holding buses that are running too early. In this talk, we will introduce a deterministic headway-based model incorporating holding and slack. We will determine the minimum amount of slack needed to counter delays, and discuss the merits of schedule-based holding versus headway-based holding.