Clockwise Hysteresis Loops in the Macroscopic Fundamental Diagram

A recent study reported that the Macroscopic Fundamental Diagram of a medium size city exhibited a clockwise hysteresis loop on a day in which a major disturbance caused many drivers to switch to unfamiliar routes. This paper shows that clockwise loops are to be expected when there are disturbances, especially if the disturbances cause a significant fraction of the drivers to not change routes adaptively. It is shown that when drivers are not adaptive networks are inherently more unstable as they recover from congestion than as they are loaded. In other words, during recovery congestion tends more strongly toward unevenness because very congested areas clear more slowly than less congested areas. Since it is known that uneven congestion distributions reduce network flows, it follows that lower network flows should arise during recovery, resulting in clockwise loops. Fortunately, in sufficient numbers, drivers that choose routes adaptively to avoid congested areas help to even out congestion during recovery, increasing flow. Thus, clockwise loops are less likely to occur when driver adaptivity is high.