Mathematical models predict how we wait in line, traffic

As New Jersey drivers approach the George Washington Bridge to enter New York City, a digital sign flashes overhead with estimates of the delays on the upper and lower levels of the bridge. Most drivers choose the level with the shortest predicted wait. But a few savvy drivers choose the other level, expecting that the digital signs are lagging and that conditions will change by the time they arrive at the bridge. 'Most people are waiting averse, so they tend to choose the shorter line - but occasionally, they'll choose the longer one,' said Jamol Pender , assistant professor in Cornell's School of Operations Research and Information Engineering. 'We really wanted to understand how delays in queue length or waiting time information affect the system dynamics, and so we developed a probabilistic way of calculating which line they will choose.' In collaboration with Richard H. Rand , p rofessor of mathematics and mechanical and aerospace engineering , and Elizabeth Wesson , visiting assist ant professor of mathematics, Pender simulated probabilistic models that demonstrate that drivers obey digital signs that direct them toward less-congested routes. But if these signs do not update quickly enough to keep pace with the realities on the highway, drivers will continue to pile onto the suggested route long after it has reached critical mass, creating new and unexpected congestion. Worse, when these digital signs finally update, a wave of drivers will cram onto the other level - kicking off a vicious cycle of back-and-forth bridge traffic that can cripple a commute.