English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We consider a dynamic model of traffic that has received a lot of attentionin the past few years. Users control infinitesimal flow particles aiming totravel from a source to destination as quickly as possible. Flow patterns varyover time, and congestion effects are modeled via queues, which form wheneverthe inflow into a link exceeds its capacity. Despite lots of interest, somevery basic questions remain open in this model. We resolve a number of them:  - We show uniqueness of journey times in equilibria.  - We show continuity of equilibria: small perturbations to the instance or tothe traffic situation at some moment cannot lead to wildly differentequilibrium evolutions.  - We demonstrate that, assuming constant inflow into the network at thesource, equilibria always settle down into a "steady state" in which thebehavior extends forever in a linear fashion.  One of our main conceptual contributions is to show that the answer to thefirst two questions, on uniqueness and continuity, are intimately connected tothe third. Our result also shows very clearly that resolving uniqueness andcontinuity, despite initial appearances, cannot be resolved by analytictechniques, but are related to very combinatorial aspects of the model. Toresolve the third question, we substantially extend the approach of Cominettiet al., who show a steady-state result in the regime where the input flow rateis smaller than the network capacity.

Continuity, Uniqueness and Long-Term Behavior of Nash Flows Over Time