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How to communicate travel times?

The model: The central authority broadcasts at time t the signal based on information collected up until then. Every agent i makes its decision ("a") as to which resource to use based on its policy ("omega"). The decisions of all agents generate the new congestion profile ("n"), which then leads to the current cost profile ("c").

In transportation applications, sensor data are heterogeneous, noisy, and unlabelled. Outside of many other challenges, there is the little-studied question of how to aggregate the data and provide the aggregated information such that the transportation system is stable, in a very precise, closed-loop fashion. Consider the following example: there is a ring-road around Dublin with 11 often congested radial roads leading to the city center. If the Dublin City Council tell drivers that travel time on one radial road is 10 minutes and on the next one it is 25 minutes, the former radial road may become congested, while the latter may become underutilised. That is: the forecast will become invalidated upon broadcasting it to the users; the present state will change following the broadcast. This is clearly not desirable, as it leads to the congestion alternating between the options. Although such instability is intrinsic to the provision of a single performance indicator per radial road, notice that the single performance indicator itself is an arbitrary aggregate of a time series of past travel times.
The VaVeL team at IBM Research – Ireland has proposed a variety of approaches, which provide the information aggregated differently, such as:

  •     an interval based on the minimum and maximum over a time-window
  •     an interval based on exponential smoothing of the values and measures of the variance
  •     an interval obtained by optimising over all subintervals of the interval given by the minimum and maximum over a time-window.

In the accompanying papers (,,, they provide closed-loop analyses of the related stochastic models and proofs of a stability result in those models (“distribution of drivers across roads converges in distribution, under certain assumptions”). The models are rather general: they allow for the link performance functions of the Highway Capacity Manual, they allow for the evolution of a heterogeneous population of drivers, governed by a Markov chain, and in some cases, for distributional robustness in the decision-making. Both in theory and simulations, these perform considerably better than any approach, where a single number per road segment is provided.