Marginal Revolution pointed to this piece arguing for a different form of congestion pricing: pay for priority at lights.
The only way I can imagine this being implementable would be having bidders submit their intended destination on leaving the house, or having a standing route-bid, with a schedule of offers for different total commute times. The traffic management system would have to reoptimize the sequence of lights in real time to take account of incoming bids and traffic volumes. Most decent grid systems already have some kind of optimization algorithm working somewhere in the background, ensuring that folks on a one-way set of streets meet a string of green lights - so streets get greens, then avenues, then streets. The system would then spit back to the GPS the commuter's optimized route. The optimization problem doesn't sound trivial. I'd expect some kind of loss function minimizing a weighted sum of divergence from its default light sequence (which presumably minimized total waiting time) and divergence from maximal fee collection. Running it just on willingness to pay would probably get the mayor booted out of office - too many folks would be too annoyed at rich folk motorcades going by.
I'm not sure whether I like the idea. It would implement a form of congestion charging, and I favour congestion charging. I'd worry a bit about folks trying to free ride on the typical commuting routes of richer folks. In Christchurch, aggregate willingness to pay of Sumner folks to get to downtown/home in rush hour would be high, so I'd take a slight divergence from my regular route to free-ride on their priority lights. That would mess things up a bit. Perhaps the system could avoid that by randomizing routes: Monday's paid route from the rich suburb to downtown would be different from Tuesday's. And then there'd be a counter-industry of folks who'd tweet updates of the daily priority route.
I'd also worry about the incentives facing the city in setting the algorithm. We know that red light cameras, ostensibly meant for safety, resulted in shorter yellow lights so that cities could collect more fines (while increasing the risk of accidents). I'm now imagining sitting at a red light, middle of the night, with nobody else around in either direction, while the system waits to see if I'll input a bid. Minor downgrades of the baseline algorithm to make the paid experience more valuable would not be surprising.