Transitions between quasi-stationary states in traffic systems: Cologne orbital motorways as an example

Traffic systems can operate in different modes. In a previous work, we identified these modes as different quasi-stationary states in the correlation structure. Here, we analyze the transitions between such quasi-stationary states, i.e., how the system changes its operational mode. In the longer run this might be helpful to forecast the time evolution of correlation patterns in traffic. We take Cologne orbital motorways as an example, we construct a state transition network for each quarter of 2015 and find a seasonal dependence for those quasi-stationary states in the traffic system. Using the PageRank algorithm, we identify and explore the dominant states which occur frequently within a moving time window of 60 days in 2015. To the best of our knowledge, this is the first study of this type for traffic systems.

Identifying strongly correlated groups of sections in a large motorway network

In a motorway network, correlations between the different links, i.e. between the parts of (different) motorways, are of considerable interest. Knowledge of fluxes and velocities on individual motorways is not sufficient, rather, their correlations determine or reflect, respectively, the functionality of and the dynamics on the network as a whole. These correlations are time dependent as the dynamics on the network is highly non-stationary, as it strongly varies during the day and over the week. Correlations are indispensable to detect risks of failure in a traffic network. Discovery of alternative routes less correlated with the vulnerable ones helps to make the traffic network robust and to avoid a collapse. Hence, the identification of, especially, groups of strongly correlated road sections is needed. To this end, we employ an optimized $k$-means clustering method. A major ingredient is the spectral information of certain correlation matrices in which the leading collective motion of the network has been removed. We identify strongly correlated groups of sections in the large motorway network of North Rhine-Westphalia (NRW), Germany. The groups classify the motorway sections in terms of spectral and geographic features as well as of traffic phases during different time periods. The representation and visualization of the groups on the real topology, i.e. on the road map, provides new results on the dynamics on the motorway network. Our approach is very general and can also be applied to other correlated complex systems.

Regularities and Irregularities in Order Flow Data

We identify and analyze statistical regularities and irregularities in the recent order flow of different NASDAQ stocks, focusing on the positions where orders are placed in the orderbook. This includes limit orders being placed outside of the spread, inside the spread and (effective) market orders. We find that limit order placement inside the spread is strongly determined by the dynamics of the spread size. Most orders, however, arrive outside of the spread. While for some stocks order placement on or next to the quotes is dominating, deeper price levels are more important for other stocks. As market orders are usually adjusted to the quote volume, the impact of market orders depends on the orderbook structure, which we find to be quite diverse among the analyzed stocks as a result of the way limit order placement takes place.