On the convergence of Bell's logit assignment formulation

S. C. Wong

Transportation Research Part B: Methodological, 1999, vol. 33, issue 8, 609-616

Abstract: In Bell M.G.H. (1995. Transportation Research B 29, 287-295), a new logit assignment formulation was developed, which considered all possible paths in the network while still retaining the absence of a need for path enumeration. In his formulation, it presumes that the sum of a geometric series of the weights matrix always converges and hence can be computed as the inversion of a matrix. In this paper, we investigate the convergence properties of this geometric series by means of an eigensystem interpretation which states that the series converges if and only if all the eigenvalues associated with the weights matrix fall into the unit circle in a complex plane. It is found that the geometric series converges unconditionally for acyclic networks, but not necessarily does so for general networks.

Date: 1999
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0191-2615(99)00015-6
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:transb:v:33:y:1999:i:8:p:609-616

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Transportation Research Part B: Methodological is currently edited by Fred Mannering

More articles in Transportation Research Part B: Methodological from Elsevier
Bibliographic data for series maintained by Catherine Liu ().