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Article: On the convergence of Bell's logit assignment formulation

TitleOn the convergence of Bell's logit assignment formulation
Authors
Issue Date1999
PublisherPergamon. The Journal's web site is located at http://www.elsevier.com/locate/trb
Citation
Transportation Research Part B: Methodological, 1999, v. 33 n. 8, p. 609-616 How to Cite?
AbstractIn 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. | In Bell M.G.H., 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.
Persistent Identifierhttp://hdl.handle.net/10722/70999
ISSN
2015 Impact Factor: 3.769
2015 SCImago Journal Rankings: 3.905
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorWong, SCen_HK
dc.date.accessioned2010-09-06T06:28:00Z-
dc.date.available2010-09-06T06:28:00Z-
dc.date.issued1999en_HK
dc.identifier.citationTransportation Research Part B: Methodological, 1999, v. 33 n. 8, p. 609-616en_HK
dc.identifier.issn0191-2615en_HK
dc.identifier.urihttp://hdl.handle.net/10722/70999-
dc.description.abstractIn 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. | In Bell M.G.H., 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.en_HK
dc.languageengen_HK
dc.publisherPergamon. The Journal's web site is located at http://www.elsevier.com/locate/trben_HK
dc.relation.ispartofTransportation Research Part B: Methodologicalen_HK
dc.titleOn the convergence of Bell's logit assignment formulationen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0191-2615&volume=33B&spage=609 &epage= 616&date=1999&atitle=On+the+convergence+of+Bell%27s+logit+assignment+formulationen_HK
dc.identifier.emailWong, SC:hhecwsc@hku.hken_HK
dc.identifier.authorityWong, SC=rp00191en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1016/S0191-2615(99)00015-6en_HK
dc.identifier.scopuseid_2-s2.0-0032695172en_HK
dc.identifier.hkuros47780en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0032695172&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume33en_HK
dc.identifier.issue8en_HK
dc.identifier.spage609en_HK
dc.identifier.epage616en_HK
dc.identifier.isiWOS:000082263800005-
dc.publisher.placeUnited Kingdomen_HK
dc.identifier.scopusauthoridWong, SC=24323361400en_HK

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