Go back to Carlos Daganzo's Publications PageThis paper presents a continuum model of merge operations and shows how it can be used to describe traffic dynamics on a closed-loop freeway (a "beltway"). The paper shows that it is possible for traffic on a beltway to start a process of self- destruction from which it cannot recover without outside intervention. If allowed to continue indefinitely, the end result of such a process is a gridlocked traffic stream without any motion. A related phenomenon sometimes occurs in roundabouts when priority is given to the entering traffic.
Our result only hinges on three critical assumptions: (i) if a merge is congested, merging vehicles will "force" gaps and trickle into the freeway in a given ratio with freeway vehicles, (ii) vehicles stay on the freeway until they reach their specific destinations, and (iii) when on the freeway, vehicles take up some space that may depend on flow.
The paper then describes the collapse process and shows that there is a "relaxation time" or "half-life" during which the freeway flow declines by a factor of 1/2. The half-life can be estimated by a simple formula; it can be considerably less than 1 hour for 3-lane freeways. Because speed is very sensitive to flow when flow is reduced from its maximum level, the decline in speed is much more sudden: we estimate that speeds drop by a factor of six during the first half-life.
Although a state of complete gridlock should never be
reached if there are alternative routes, because drivers would
begin to exit before reaching their destinations, the low flows
and speeds that would result would still negate the advantage of
the beltway over the surface streets. The good news is that the
collapse process can be reversed, or better prevented altogether,
by restricting the ratio of input flow to mainline flow below a
critical level. The paper also identifies such level and
describes the recovery process.
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