Public Transport

, Volume 7, Issue 1, pp 77–99

A tool for measuring and visualizing connectivity of transit stop, route and transfer center in a multimodal transportation network

  • Sabyasachee Mishra
  • Timothy F. Welch
  • Paul M. Torrens
  • Cheng Fu
  • Haojie Zhu
  • Eli Knaap
Original Paper

DOI: 10.1007/s12469-014-0091-2

Cite this article as:
Mishra, S., Welch, T.F., Torrens, P.M. et al. Public Transp (2015) 7: 77. doi:10.1007/s12469-014-0091-2


Agencies at the federal, state and local level are aiming to enhance the public transportation system (PTS) as one alternative to alleviate congestion and to cater to the needs of captive riders. To effectively act as a viable alternative transportation mode, the system must be highly efficient. One way to measure efficiency of the PTS is connectivity. In a multimodal transportation system, transit is a key component. Transit connectivity is relatively complex to calculate, as one has to consider fares, schedule, capacity, frequency and other features of the system at large. Thus, assessing transit connectivity requires a systematic approach using many diverse parameters involved in real-world service provision. In this paper, we use a graph theoretic approach to evaluate transit connectivity at various levels of service and for various components of transit, such as nodes, lines, and transfer centers in a multimodal transportation system. Further, we provide a platform for computing connectivity over large-scale applications, using visualization to communicate results in the context of their geography and to facilitate public transit decision-making. The proposed framework is then applied to a comprehensive transit network in the Washington-Baltimore region. Underpinning the visualization, we introduce a novel spatial data architecture and Web-based interface designed with free and open source libraries and crowd-sourced contextual data, accessible on various platforms such as mobile phones, tablets and personal computers. The proposed methodology is a useful tool for both riders and decision-makers in assessing transit connectivity in a multimodal transit network in a number of ways such as the identification of under-served transit areas, prioritization and allocation of funds to locations for improving transit service.


Transit connectivity Graph theory Public transportation Multimodal transportation system GIS 

List of symbols

\( D_{l}^{i} \)

Inbound distance of link l

\( D_{l}^{o} \)

Outbound distance of link l from node n to destination


Frequency of line l


Daily hours of operation of l

\( L_{{n,n_{1} }} \)

Shortest distance between node n1 to n

\( P_{l,n}^{i} \)

Inbound connecting power of link l

\( P_{l.n}^{o} \)

Outbound connecting power of link l

\( P_{l,n}^{t} \)

Total connecting power of line l at node n


Set of stops in region R


Set of stops in line l


Set of stops in region center σ


Average speed of link l


Initial stop

\( t_{{n_{1} ,n}} \)

Transfer time from n1 to n

\( \delta_{{n_{1} ,n_{2} }} \)

Total number of paths between n1 and n2

\( \delta_{{n_{1} ,n_{2} }} (n) \)

Number of paths exist between n1 and n2 those pass through n

\( \delta_{np} \)

A binary indicator variable for determining the degree centrality, which takes the value of 1 when node p is dependent on n, and 0 otherwise

\( \theta_{R} \)

Connectivity index for region R

\( \theta_{l} \)

Connectivity index for line l

\( \theta_{n} \)

Connectivity index for node n

\( \rho_{{n_{1} ,n}} \)

Passenger acceptance rate from node n1 to n

\( \rho_{R} \)

Density measure for region R


Parameter for passenger acceptance rate


Parameter for passenger acceptance which is sensitive to travel time






Network system


Node dependent on n


Scaling factor coefficient for capacity of line l


Scaling factor coefficient for speed of line l


Scaling factor coefficient for distance of line l


Activity density of line l, at node n

\( \vartheta \)

Scaling factor for activity density

\( E_{l,n}^{z} \)

Number of households in zone z containing line l and node n

\( E_{l,n}^{z} \)

Employment for zone z containing line l and node n

\( \varTheta_{l,n}^{z} \)

Area of z containing line l and node

\( \varTheta_{l}^{n} \)

Number of lines l at node n

Supplementary material

12469_2014_91_MOESM1_ESM.docx (1.6 mb)
Supplementary material 1 (DOCX 1642 kb)

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Sabyasachee Mishra
    • 1
  • Timothy F. Welch
    • 2
  • Paul M. Torrens
    • 3
  • Cheng Fu
    • 3
  • Haojie Zhu
    • 4
  • Eli Knaap
    • 5
  1. 1.Department of Civil and Environmental Engineering and Intermodal Freight Transportation InstituteUniversity of MemphisMemphisUSA
  2. 2.School of City and Regional PlanningGeorgia Institute of TechnologyAtlantaUSA
  3. 3.Department of Geographical Sciences and Institute for Advanced Computer StudiesUniversity of MarylandCollege ParkUSA
  4. 4.Department of Geographical SciencesUniversity of MarylandCollege ParkUSA
  5. 5.National Center for Smart Growth Research and Education, 054 Preinkert FieldhouseUniversity of MarylandCollege ParkUSA