Possible explanations of phase transitions in highway traffic

It is shown that all the phase transitions in and out of freely flowing traffic reported earlier for a German site could be caused by bottlenecks, as are all the transitions observed at two other sites examined here. The evidence suggests that bottlenecks cause these transitions in a predictable way, and does not suggest that stoppages (jams) appear spontaneously in free flow traffic for no apparent reason. It is also shown that many of the complicated instability phenomena observed at all locations can be explained qualitatively in terms of a simple Markovian theory specific to traffic that does not necssarily include spontaneous transi­ tions into the queued state as a feature. This paper provides additional empirical observations and an alternative explanation of some traffic data from a German highway described previously in Kerner and Rehborn (1997). This work will be referred to as ‘PRL,’ and figures from this work will be denoted ‘Fig. PRL#.’ 1 Other observations are contained in Kerner and Rehborn (1996a,b). Section 1 describes the explanation and Section 2 presents a possible modeling framework. 1. Interpretation of some empirical evidence A few studies of North American freeways have also identified related traffic flow properties and the origin of traffic disturbances (Cassidy and Windover, 1995; Cassidy and Bertini, 1997). Reassuringly, the observations on both continents are consistent with each other. However, it will also be shown that neither the German nor the North American data support the PRL conclusion: Daganzo, C.F.; Cassidy, M.J.; Bertini, R.L. Transportation Research Part A 33(5) 365-379. 1999. that free flowing traffic will spontaneously break down randomly, without obvious reasons, and then remain in that state due to traffic’s tendency to self-maintain congestion. Rather, the evi­ dence indicates that traffic breaks down (queues form) at locations of freeway inhomogeneities (bottlenecks) due to reproducible exogenous reasons, and that, following breakdown, the bottle­ neck flow behaves in a predictable way. We see no evidence that queues self-maintain away from a bottleneck. Highways appear to behave like crowds of people going through a series of queues at well defined locations; e.g. fans who wait in line to buy football tickets and then queue through one or more gates to enter the stadium. Some definitions derived from this analogy are intro­ duced below; see e.g. Daganzo (1997a) for additional explanations. Free flow (or unqueued) conditions refer to that state of traffic where small disturbances can only flow forward in space (e.g. as in supersonic gas flow). People walking away from the ticket window, for example, are in free flow because if one of them momentarily slows down just a little, this does not affect the queue upstream of the server. The free flow status of highway traffic can be determined by correlating the curves of cumulative flow at successive detectors with a time lag, as described in Cassidy and Windover (1995) and shown below. Conditions that are not free flow will be called queued. In queued traffic, disturbances can and do flow upstream. Bottlenecks are those inhomogeneous locations such as a ticket window where queues can form and persist with free flow downstream. A bottleneck in this state will be said to be active. Note that a bottleneck may be deactivated by a queue from a downstream bottleneck that blocks it and also when its own queue dissipates. If the flow through an active bottleneck is nearly constant and reproducible this flow will be called the bottleneck capacity. The evidence available in German and North American traffic data contains nothing at all to contradict this analogy; i.e., the evidence indicates that queues grow when bottlenecks become active and that instabilities are the result and not the cause of queues.