Have you ever driven out of a traffic jam only to find that nothing was apparently causing it?


When the cause of a freeway traffic jam, e.g., an accident, a brief stall, a temporarily overcrowded freeway entrance or exit, etc., is removed or is no longer in effect, the jam does not disappear instantaneously. It takes time to do so. This is no different from a queue of cars at a red traffic signal, which does not dissipate immediately when the light turns green. In both cases, freeways and streets, jams need time to dissipate, and the heavier traffic is the longer the process. During the rush hour a freeway jam can take much longer to dissipate than to grow in the first place. The evolving jam moves over the freeway in the direction opposite to traffic, affecting it far from the location of the original cause. Drivers exiting the jam see nothing unusual, much to their surprise.

A computer animation showing the effects of a jam created by an incident downstream of a freeway off-ramp (a "diverge") can be seen by clicking on the icon below. The "movie" is a "cell-transmission" simulation of a symmetric freeway diverge with constant input flow where 50% of the vehicles go in each direction. Numbers in each cell are proportional to the number of cars in the cell at the given time. Decimals have been truncated (e.g., 3.5 appears as 3). Low numbers (green) correspond to freely flowing conditions. Numbers greater than 8 (in red: 9, A, B, C...) correspond to queues. The higher the letter the higher the congestion.

The simulation depicts what happens to this system when a brief incident ( from time "70" to time "115") partially blocks the upper branch of the diverge. Note how the queue grows, and that when it reaches the diverge shortly after time "100" it affects traffic on the bottom branch. After the incident is removed (at time "115") the front of the queue begins to move backwards, chasing the back of the queue. Eventually, the entire queue moves entirely upstream of the diverge. If a driver were to pass through the queue during this phase, e.g. at time "135", (s)he would see nothing; except that traffic would be clearing for no apparent reason. But there was a reason; it just happened earlier, somewhere else. Note finally, how the queue eventually dissipates at time "196". The incident lasted 45 time units but was felt for 126 units.

In reality, the fronts and backs of queues move about 4 times more slowly than shown in this animation but the effects you have seen are qualitatively correct: real queues move less in space but the duration of the effect is similar. If the incident happens when traffic is saturated (numbers in the cells equal to 8 in our example), or if it happens inside a queue (numbers greater than 8), the fronts and backs of queue generated by the incident move at the same speed and the queue does not die down. This is why during a rush hour, the effects of a 5 minute incident can often be felt for the duration of the rush.

This cell-transmission (CT) example was prepared in 1994 with the assitance of then PhD student Wei H. Lin.


  1. "The NETCELL Simulation Package: Technical Description", California PATH Research Report, UCB-ITS-PRR-97-23, May 1997 (with R. Cayford and W. Lin).
  2. Daganzo, C.F. "The cell transmission model: A dynamic representation of highway traffic consistent with the hydrodynamic theory", Trans. Res. 28B (4), 269-287 (1994).
  3. Daganzo, C.F. "The cell transmission model. Part II: Network traffic", Trans. Res. 29B(2), 79-93 (1995).