DelayFlow Centrality
Definition
DelayFlow that incorporates travel time delay and commuter flow volume.
DelayFlow centrality are more similar with degree centrality and betweenness centrality with correlation scores above 0.5. Time delay is incurred for commuters to find alternative means to reach destinations when a node is down. To determine the extent of delay caused to the people affected, we compute texp(i,j), the expected time taken to travel from node i to node j, and talt(i,j), the time taken to travel from node i to node j using an alternative means of transportation (e.g. bus). The time delay factor lij is then defined to be talt(i,j)/texp(i,j). We assume that texp and talt are static throughout the day. The time delay factor lij is asymmetric as both texp(i,j) and talt(i,j) are asymmetric. The larger the lij value (>1), the greater the time delay. Let hij denote the number of commuters from node i to node j per hour, and hjk(i) denote the number of commuters from node j to node k through node i per hour.
where 
is the total commuter flow of the transportation
network and 
[CHENG, Y.-Y. 2013]
DelayFlow centrality are more similar with degree centrality and betweenness centrality with correlation scores above 0.5. Time delay is incurred for commuters to find alternative means to reach destinations when a node is down. To determine the extent of delay caused to the people affected, we compute texp(i,j), the expected time taken to travel from node i to node j, and talt(i,j), the time taken to travel from node i to node j using an alternative means of transportation (e.g. bus). The time delay factor lij is then defined to be talt(i,j)/texp(i,j). We assume that texp and talt are static throughout the day. The time delay factor lij is asymmetric as both texp(i,j) and talt(i,j) are asymmetric. The larger the lij value (>1), the greater the time delay. Let hij denote the number of commuters from node i to node j per hour, and hjk(i) denote the number of commuters from node j to node k through node i per hour.
is the total commuter flow of the transportation
network and [CHENG, Y.-Y. 2013]
Software
References
- CHENG, Y.-Y., LEE, R. K.-W., LIM, E.-P. & ZHU, F. DelayFlow centrality for identifying critical nodes in transportation networks. Proceedings of the 2013 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining, 2013. ACM, 1462-1463.