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Article: On the convergence of Bell's logit assignment formulation
Title | On the convergence of Bell's logit assignment formulation |
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Authors | |
Issue Date | 1999 |
Publisher | Pergamon. 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? |
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. | 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 Identifier | http://hdl.handle.net/10722/70999 |
ISSN | 2015 Impact Factor: 3.769 2015 SCImago Journal Rankings: 3.905 |
ISI Accession Number ID | |
References |
DC Field | Value | Language |
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dc.contributor.author | Wong, SC | en_HK |
dc.date.accessioned | 2010-09-06T06:28:00Z | - |
dc.date.available | 2010-09-06T06:28:00Z | - |
dc.date.issued | 1999 | en_HK |
dc.identifier.citation | Transportation Research Part B: Methodological, 1999, v. 33 n. 8, p. 609-616 | en_HK |
dc.identifier.issn | 0191-2615 | en_HK |
dc.identifier.uri | http://hdl.handle.net/10722/70999 | - |
dc.description.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. | 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.language | eng | en_HK |
dc.publisher | Pergamon. The Journal's web site is located at http://www.elsevier.com/locate/trb | en_HK |
dc.relation.ispartof | Transportation Research Part B: Methodological | en_HK |
dc.title | On the convergence of Bell's logit assignment formulation | en_HK |
dc.type | Article | en_HK |
dc.identifier.openurl | http://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+formulation | en_HK |
dc.identifier.email | Wong, SC:hhecwsc@hku.hk | en_HK |
dc.identifier.authority | Wong, SC=rp00191 | en_HK |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1016/S0191-2615(99)00015-6 | en_HK |
dc.identifier.scopus | eid_2-s2.0-0032695172 | en_HK |
dc.identifier.hkuros | 47780 | en_HK |
dc.relation.references | http://www.scopus.com/mlt/select.url?eid=2-s2.0-0032695172&selection=ref&src=s&origin=recordpage | en_HK |
dc.identifier.volume | 33 | en_HK |
dc.identifier.issue | 8 | en_HK |
dc.identifier.spage | 609 | en_HK |
dc.identifier.epage | 616 | en_HK |
dc.identifier.isi | WOS:000082263800005 | - |
dc.publisher.place | United Kingdom | en_HK |
dc.identifier.scopusauthorid | Wong, SC=24323361400 | en_HK |