Mathematics and the Zipper Lane

On Tuesday, July 8, the Zipper Lane, the reversible rush hour car pool lanes from central Oahu to Honolulu, will go from HOV-2 to HOV-3. Some viewers asked why the state Department of Transportation would try something that didn't work when it was tried a few years ago. One even asked if it was a plot to hurt carpoolers, on the theory that they're among the strongest supporters of rail. Conspiracy plots always entertain, don't they? But the real reason for the change is mathematics, and mathematics may also cause the new policy to fail. Let me explain. HOV-3 attracted few takers the first time, so the state compromised and went to HOV-2. That worked better, as indeed it has worked better in many cities. It works so well that some days the sheer number of two-occupant vehicles makes the Zipper Lane slower than the regular lanes. We've all seen that from time to time. That phenomenon has intensified to the point where the math impels the state to resort to a second attempt at HOV-3. The problem, of course, is that there many families with two people traveling the same direction -- usually the husband and wife both working in town but sometimes a parent taking a child to school on the way to work -- but few families where three are headed the same way. So now, in order to continue zipping along in the car pool space, pairs of people from the same family will need to find some acquaintance or stranger to join for the ride into town. (If you are in this fix, and want helps, call 692-7695 or email Rideshare@hawaii.gov. You might also consider getting into the vanpool program. For information on that, call 596-8297.) The problem arises if, as another viewer suggested, the number of people who find a third rider turns out to be less than the number of current HOV-2 riders who do not find an extra passenger, are forced back into the regular lanes, and then decide, screw it, they'll both drive in separately for the flexibility. Suppose there are 10 vehicles, Group A, now moving through the Zipper Lane for which third riders are found, 10 people now driving solo in the regular lanes -- and 10 other vehicles, Group B, now moving through the Zipper Lane for which third riders are not found and the remaining two begin driving separate vehicles solo in the regular lanes. Let's do the math. In this scenario, Group A will pull 10 vehicles out of the regular lanes without adding any vehicles to the Zipper Lane. Group B will pull 10 vehicles out of the Zipper Lanes and add 20 vehicles to the regular lanes. So, the Zipper Lane will wind up with 10 fewer vehicles, while the regular lanes will wind up with 10 additional vehicles. The success or failure of the policy will depend on whether Group A and Group B really are equal or whether there are more Group B vehicles. There is little question that the Zipper Lane  will become less congested. The issue is how much worse the regular lanes will get. In order for them not to get worse, HOV-3 has to pull a car out for every HOV-2 car that goes back in. Traffic planners think like this. They do studies, too, and sometimes learn things that strike the rest of us as counterintuitive. For example, as speeds slow on Interstate highways, those roads can carry more vehicles, because the space between them is reduced. But this stops working at a particular speed -- I think it's around 40 mph but I can't recall for sure -- and after that, any further slowing actually reduces a road's vehicle capacity.