Modeling temporal networks using random itineraries

We propose a procedure to generate dynamical networks with bursty, possibly repetitive and correlated temporal behaviors. Regarding any weighted directed graph as being composed of the accumulation of paths between its nodes, our construction uses random walks of variable length to produce time-extended structures with adjustable features. The procedure is first described in a general framework. It is then illustrated in a case study inspired by a transportation system for which the resulting synthetic network is shown to accurately mimic the empirical phenomenology

Graph Orientation and Flows Over Time

Flows over time are used to model many real-world logistic and routing problems. The networks underlying such problems -- streets, tracks, etc. -- are inherently undirected and directions are only imposed on them to reduce the danger of colliding vehicles and similar problems. Thus the question arises, what influence the orientation of the network has on the network flow over time problem that is being solved on the oriented network. In the literature, this is also referred to as the contraflow or lane reversal problem. We introduce and analyze the price of orientation: How much flow is lost in any orientation of the network if the time horizon remains fixed? We prove that there is always an orientation where we can still send $\frac{1}{3}$ of the flow and this bound is tight. For the special case of networks with a single source or sink, this fraction is $\frac12$ which is again tight. We present more results of similar flavor and also show non-approximability results for finding the best orientation for single and multicommodity maximum flows over time

Identifying public transport gaps using time-dependent accessibility levels

One of the concerns that has aroused much scholarly attention in transport geography lately is the extent to which public transport provision enables the less privileged population segments, especially those without privately owned motorized vehicles, to participate in activities that are deemed normal within the society they live in. This study contributes to this line of inquiry by proposing a methodology for identifying public transit gaps, a mismatch between the socially driven demand for transit and the supply provided by transit agencies. The methodology draws on the latest accomplishments in the field of modeling time-continuous, schedule-based public transport accessibility. Accessibility levels to key destinations are calculated at regular time intervals, and synoptic metrics of these levels over various peak and off-peak time windows are computed for weekdays and weekends. As a result, a temporally reliable picture of accessibility by public transport is constructed. The obtained index of public transport provision is compared to a public transport needs index based on the spatial distribution of various socio-demographics, in order to highlight spatial mismatches between these two indices. The study area consists of Flanders, which is the northern, Dutch-speaking region of Belgium. The results indicate that mainly suburban areas are characterized by high public transport gaps. Due to the time-variability of public transport frequencies, these gaps differ over time