Wednesday, October 27, 2010

Queuing and road pricing in traffic

Queuing theory is often based on the poisson model.  Under the cover of the theory is the idea of random arrival of customers at a fixed service time queue, people arriving at the bank, for example, how likely is it that I will have three people in front of me.

In city traffic one gross model of the queue is to model the traffic cloud as a grid with an typical service time for random arrival of cargo and passengers to use the grid.  This is sort of a novel approach, but points out some thing regarding traffic grids.  If the amount of commuters piled up is a Poisson, then there is a significant liklihood of long waits, long wait that make planning ad hoc movement at risk.  In other words, when something goes a little out of whack in the firm, then on the firm must risk an out of band movement of cargo, then it cannot really guarantee queue waits.  Long transaction time across town have a differentially bad effect on businesses who rely on ad hoc transactions, it differentially favors economies of scale.

Adding capacity never works, the probability distribution always equilbriates to poison.  What works is synchronizing traffic, dynamically.  The transaction times are always adjusted by dynamic road pricing, so the queue becomes a narrow bell curve.  That is how you get the big multiplier with traffic technology.  The ultimate goal is to price me from the edge of the city, HOT lanes, light priorities, reserved parking space; all bundled into a virtual path.

The key here is low transaction times and a bit of futures pricing, getting users to buy space 10 or 15 minutes a head of time, again using technology and traffic sourcing applications.

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