  We present novel online mechanisms for traffic intersection auctions in which
users bid for priority service. We assume that users at the front of their lane
are requested to declare their delay cost, i.e. value of time, and that users
are serviced in decreasing order of declared delay cost. Since users are
expected to arrive dynamically at traffic intersections, static pricing
approaches may fail to estimate user expected waiting time accurately, and lead
to non-strategyproof payments. To address this gap, we propose two Markov chain
models to determine the expected waiting time of participants in the auction.
Both models take into account the probability of future arrivals at the
intersection. In a first model, we assume that the probability of future
arrivals is uniform across lanes of the intersection. This queue-based model
only tracks the number of lower- and higher-bidding users on access lanes, and
the number of empty lanes. The uniformness assumption is relaxed in a second,
lane-based model which accounts for lane-specific user arrival probabilities at
the expense of an extended state space. We then design a mechanism to determine
incentive-compatible payments in the dynamic sense. The resulting online
mechanisms maximize social welfare in the long run. Numerical experiments on a
four-lane traffic intersection are reported and compared to a static
incentive-compatible mechanism. Our findings show that static
incentive-compatible mechanisms may lead users to misreport their delay costs.
In turn, the proposed online mechanisms are shown to be incentive-compatible in
the dynamic sense.
