Dynamic user equilibrium with side constraints for a traffic network: Theoretical development and numerical solution algorithm
► The paper formulates the dynamic user equilibrium (DUE) with side-constraints on dynamic traffic volume representing traffic management objective or strict link capacity. ► The paper provides the proofs of constraint qualification and existence of DUE with side-constraints. ► The papers derives th...
Uloženo v:
| Vydáno v: | Transportation research. Part B: methodological Ročník 45; číslo 7; s. 1035 - 1061 |
|---|---|
| Hlavní autoři: | , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Kidlington
Elsevier Ltd
01.08.2011
Elsevier |
| Edice: | Transportation Research Part B: Methodological |
| Témata: | |
| ISSN: | 0191-2615, 1879-2367 |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| Abstract | ► The paper formulates the dynamic user equilibrium (DUE) with side-constraints on dynamic traffic volume representing traffic management objective or strict link capacity. ► The paper provides the proofs of constraint qualification and existence of DUE with side-constraints. ► The papers derives the analytical closed-form of the link control for ensuring that dynamic traffic volumes under DUE condition satisfy the side-constraint on link volumes. ► The paper proposed a computational algorithm for solving DUE-SC and deriving the link control parameters.
This paper investigates a traffic volume control scheme for a dynamic traffic network model which aims to ensure that traffic volumes on specified links do not exceed preferred levels. The problem is formulated as a dynamic user equilibrium problem with side constraints (DUE-SC) in which the side constraints represent the restrictions on the traffic volumes. Travelers choose their departure times and routes to minimize their generalized travel costs, which include early/late arrival penalties. An infinite-dimensional variational inequality (VI) is formulated to model the DUE-SC. Based on this VI formulation, we establish an existence result for the DUE-SC by showing that the VI admits at least one solution. To analyze the necessary condition for the DUE-SC, we restate the VI as an equivalent optimal control problem. The Lagrange multipliers associated with the side constraints as derived from the optimality condition of the DUE-SC provide the traffic volume control scheme. The control scheme can be interpreted as additional travel delays (either tolls or access delays) imposed upon drivers for using the controlled links. This additional delay term derived from the Lagrange multiplier is compared with its counterpart in a static user equilibrium assignment model. If the side constraint is chosen as the storage capacity of a link, the additional delay can be viewed as the effort needed to prevent the link from spillback. Under this circumstance, it is found that the flow is incompressible when the link traffic volume is equal to its storage capacity. An algorithm based on Euler’s discretization scheme and nonlinear programming is proposed to solve the DUE-SC. Numerical examples are presented to illustrate the mechanism of the proposed traffic volume control scheme. |
|---|---|
| AbstractList | This paper investigates a traffic volume control scheme for a dynamic traffic network model which aims to ensure that traffic volumes on specified links do not exceed preferred levels. The problem is formulated as a dynamic user equilibrium problem with side constraints (DUE-SC) in which the side constraints represent the restrictions on the traffic volumes. Travelers choose their departure times and routes to minimize their generalized travel costs, which include early/late arrival penalties. An infinite-dimensional variational inequality (VI) is formulated to model the DUE-SC. Based on this VI formulation, we establish an existence result for the DUE-SC by showing that the VI admits at least one solution. To analyze the necessary condition for the DUE-SC, we restate the VI as an equivalent optimal control problem. The Lagrange multipliers associated with the side constraints as derived from the optimality condition of the DUE-SC provide the traffic volume control scheme. The control scheme can be interpreted as additional travel delays (either tolls or access delays) imposed upon drivers for using the controlled links. This additional delay term derived from the Lagrange multiplier is compared with its counterpart in a static user equilibrium assignment model. If the side constraint is chosen as the storage capacity of a link, the additional delay can be viewed as the effort needed to prevent the link from spillback. Under this circumstance, it is found that the flow is incompressible when the link traffic volume is equal to its storage capacity. An algorithm based on Euler's discretization scheme and nonlinear programming is proposed to solve the DUE-SC. Numerical examples are presented to illustrate the mechanism of the proposed traffic volume control scheme. ► The paper formulates the dynamic user equilibrium (DUE) with side-constraints on dynamic traffic volume representing traffic management objective or strict link capacity. ► The paper provides the proofs of constraint qualification and existence of DUE with side-constraints. ► The papers derives the analytical closed-form of the link control for ensuring that dynamic traffic volumes under DUE condition satisfy the side-constraint on link volumes. ► The paper proposed a computational algorithm for solving DUE-SC and deriving the link control parameters. This paper investigates a traffic volume control scheme for a dynamic traffic network model which aims to ensure that traffic volumes on specified links do not exceed preferred levels. The problem is formulated as a dynamic user equilibrium problem with side constraints (DUE-SC) in which the side constraints represent the restrictions on the traffic volumes. Travelers choose their departure times and routes to minimize their generalized travel costs, which include early/late arrival penalties. An infinite-dimensional variational inequality (VI) is formulated to model the DUE-SC. Based on this VI formulation, we establish an existence result for the DUE-SC by showing that the VI admits at least one solution. To analyze the necessary condition for the DUE-SC, we restate the VI as an equivalent optimal control problem. The Lagrange multipliers associated with the side constraints as derived from the optimality condition of the DUE-SC provide the traffic volume control scheme. The control scheme can be interpreted as additional travel delays (either tolls or access delays) imposed upon drivers for using the controlled links. This additional delay term derived from the Lagrange multiplier is compared with its counterpart in a static user equilibrium assignment model. If the side constraint is chosen as the storage capacity of a link, the additional delay can be viewed as the effort needed to prevent the link from spillback. Under this circumstance, it is found that the flow is incompressible when the link traffic volume is equal to its storage capacity. An algorithm based on Euler’s discretization scheme and nonlinear programming is proposed to solve the DUE-SC. Numerical examples are presented to illustrate the mechanism of the proposed traffic volume control scheme. |
| Author | Lam, William H.K. Zhong, R.X. Sumalee, A. Friesz, T.L. |
| Author_xml | – sequence: 1 givenname: R.X. surname: Zhong fullname: Zhong, R.X. email: cezhong@gmail.com organization: Department of Civil and Structural Engineering, The Hong Kong Polytechnic University, Hong Kong SAR, China – sequence: 2 givenname: A. surname: Sumalee fullname: Sumalee, A. email: ceasumal@polyu.edu.hk organization: Department of Civil and Structural Engineering, The Hong Kong Polytechnic University, Hong Kong SAR, China – sequence: 3 givenname: T.L. surname: Friesz fullname: Friesz, T.L. email: tfriesz@psu.edu organization: Department of Industrial and Manufacturing Engineering, Pennsylvania State University, USA – sequence: 4 givenname: William H.K. surname: Lam fullname: Lam, William H.K. email: cehklam@polyu.edu.hk organization: Department of Civil and Structural Engineering, The Hong Kong Polytechnic University, Hong Kong SAR, China |
| BackLink | http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=24371095$$DView record in Pascal Francis http://econpapers.repec.org/article/eeetransb/v_3a45_3ay_3a2011_3ai_3a7_3ap_3a1035-1061.htm$$DView record in RePEc |
| BookMark | eNp9kT-P3CAQxa3oImXvkg-QjiZKtc6ADbaTKrr8lVZKsz3CeMiyscEHeE_b5LMH315SpLjigRDzfgNvrosr5x0WxWsKJQUq3h3LFPqSAaUl8BKgflZsaNt0W1aJ5qrYAO3olgnKXxTXMR4BoKqBborfn85OTVaTJWIgeLfY0fbBLhO5t-lAoh2QaO9iCsq6FInxgSiST8Zkk8N078Ov92R_QB8wWa1GMuAJRz9P6BJRbiBumTA83EQ_Lsl6R9T404fMn14Wz40aI7563G-K_ZfP-9tv292Pr99vP-62um7btDWNMrQH09Rc9FVft2JgyGsDTAPltDasMqLFrhUdN4NWBkxLEQYcesYMr26KtxfsHPzdgjHJyUaN46gc-iXKthMMGkG7XLm7VAacUcs52EmFs0TE_GcXe3mSlap5Xs5Za955s1lN1pxFoeKSgqDykKaMe_PYWMWcgMkMbeM_LKurhkK3PrC51OngYwxopLZJrVmtwY8ZKNcxy6PMY5YPbYHLPObspP85_8Kf8ny4eDBHfrIYZNQWncbBBtRJDt4-4f4DrHLExA |
| CODEN | TRBMDY |
| CitedBy_id | crossref_primary_10_1016_j_trb_2019_11_002 crossref_primary_10_1016_j_trpro_2019_05_028 crossref_primary_10_1080_21680566_2024_2341012 crossref_primary_10_1016_j_tre_2021_102305 crossref_primary_10_1016_j_trpro_2014_10_070 crossref_primary_10_1016_j_tre_2024_103486 crossref_primary_10_1080_23249935_2013_871094 crossref_primary_10_1016_j_physa_2013_06_004 crossref_primary_10_1093_imanum_drx056 crossref_primary_10_1016_j_trc_2021_103190 crossref_primary_10_1016_j_physa_2016_01_034 crossref_primary_10_1016_j_trb_2017_09_008 crossref_primary_10_1007_s00245_025_10284_0 crossref_primary_10_1016_j_trb_2019_05_005 crossref_primary_10_1109_ACCESS_2020_2964644 crossref_primary_10_1002_atr_195 crossref_primary_10_1007_s40534_017_0128_8 crossref_primary_10_1016_j_trb_2017_11_013 crossref_primary_10_1137_18M1234795 crossref_primary_10_1002_atr_1203 crossref_primary_10_1287_opre_2023_0577 crossref_primary_10_3141_2498_01 crossref_primary_10_1016_j_trpro_2017_05_051 crossref_primary_10_1287_trsc_2022_1147 crossref_primary_10_1007_s11067_019_09471_8 crossref_primary_10_1007_s11067_014_9228_8 crossref_primary_10_1016_j_trb_2025_103207 crossref_primary_10_1016_j_trc_2020_02_005 crossref_primary_10_1016_j_ejor_2021_11_025 crossref_primary_10_1080_21680566_2013_779793 crossref_primary_10_1007_s10107_013_0689_1 crossref_primary_10_1371_journal_pone_0188874 crossref_primary_10_1109_TITS_2022_3208317 crossref_primary_10_1139_cjce_2014_0231 |
| Cites_doi | 10.1016/j.trc.2008.10.002 10.1080/18128600608685654 10.1287/opre.41.1.179 10.1080/01441640600979403 10.1109/JPROC.2003.819610 10.1016/j.trb.2008.01.006 10.1016/j.trb.2010.05.003 10.1155/S0161171284000831 10.1016/S0191-2615(01)00041-8 10.1016/S0191-2615(02)00091-7 10.1016/j.trb.2005.03.002 10.1287/trsc.33.4.341 10.1080/18128600902717483 10.1016/j.trb.2008.07.005 10.1016/j.trb.2004.04.005 10.1016/0191-2615(95)00016-7 10.1023/A:1012896228490 10.1016/j.trb.2004.10.002 10.1090/S0002-9939-1974-0348698-5 10.1002/nav.20250 10.1016/j.trb.2010.07.001 10.1016/S0191-2615(01)00011-X 10.1016/S0191-2615(99)00024-7 10.1016/S0377-0427(00)00305-8 10.1287/trsc.34.4.402.12322 10.1016/S0191-2615(98)00024-1 10.1016/S0191-2615(03)00077-8 10.1137/1037043 10.1287/trsc.1030.0045 10.1007/s11067-005-6663-6 10.1016/j.trb.2007.10.002 10.1080/18128600802630281 10.1016/S0191-2615(02)00092-9 10.1007/s11067-007-9022-y 10.1016/S0191-2615(00)00039-4 10.1016/S0191-2615(00)00049-7 10.1016/0191-2615(88)90023-9 10.1057/palgrave.jors.2602543 10.1016/S0191-2615(97)00041-6 |
| ContentType | Journal Article |
| Copyright | 2011 Elsevier Ltd 2015 INIST-CNRS |
| Copyright_xml | – notice: 2011 Elsevier Ltd – notice: 2015 INIST-CNRS |
| DBID | AAYXX CITATION IQODW DKI X2L 7ST C1K SOI |
| DOI | 10.1016/j.trb.2011.05.004 |
| DatabaseName | CrossRef Pascal-Francis RePEc IDEAS RePEc Environment Abstracts Environmental Sciences and Pollution Management Environment Abstracts |
| DatabaseTitle | CrossRef Environment Abstracts Environmental Sciences and Pollution Management |
| DatabaseTitleList | Environment Abstracts |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Economics Engineering Applied Sciences |
| EISSN | 1879-2367 |
| EndPage | 1061 |
| ExternalDocumentID | eeetransb_v_3a45_3ay_3a2011_3ai_3a7_3ap_3a1035_1061_htm 24371095 10_1016_j_trb_2011_05_004 S0191261511000543 |
| GroupedDBID | --K --M -~X .DC .~1 0R~ 123 1B1 1RT 1~. 1~5 29Q 4.4 457 4G. 5VS 7-5 71M 8P~ 9JO AAAKF AAAKG AACTN AAEDT AAEDW AAFJI AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AARIN AAXUO ABDEX ABDMP ABFNM ABLJU ABMAC ABMMH ABPPZ ABUCO ABXDB ABYKQ ACDAQ ACGFS ACNCT ACRLP ADBBV ADEZE ADMUD AEBSH AEKER AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AHRSL AIEXJ AIKHN AITUG AJBFU AJOXV AKYCK ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ AOMHK APLSM ASPBG AVARZ AVWKF AXJTR AZFZN BKOJK BLXMC CS3 EBS EFJIC EFLBG EJD EO8 EO9 EP2 EP3 FDB FEDTE FGOYB FIRID FNPLU FYGXN G-2 G-Q GBLVA HAMUX HMY HVGLF HZ~ H~9 IHE J1W KOM LY1 LY7 M3Y M41 MO0 MS~ N9A O-L O9- OAUVE OHT OZT P-8 P-9 P2P PC. PRBVW Q38 R2- RIG ROL RPZ SDF SDG SDP SDS SES SET SEW SPCBC SSB SSD SSO SSS SSZ T5K WUQ XPP ~G- 9DU AATTM AAXKI AAYWO AAYXX ABWVN ACLOT ACRPL ADNMO AEIPS AFJKZ AGQPQ AIIUN ANKPU APXCP CITATION EFKBS ~HD AFXIZ AGCQF AGRNS BNPGV IQODW SSH DKI X2L 7ST C1K SOI |
| ID | FETCH-LOGICAL-c488t-f7af1b0f7456b3b486d2e54f02c01514f23f68e98695fdcaf0f81e0dedb22f53 |
| ISICitedReferencesCount | 37 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000293436200008&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0191-2615 |
| IngestDate | Tue Oct 07 09:15:50 EDT 2025 Sun Mar 30 03:31:12 EDT 2025 Mon Jul 21 09:14:02 EDT 2025 Sat Nov 29 05:58:17 EST 2025 Tue Nov 18 21:54:40 EST 2025 Fri Feb 23 02:27:33 EST 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 7 |
| Keywords | Traffic volume control Dynamic user equilibrium (DUE) Traffic assignment with side constraint Lagrange multiplier Traffic management and control Pontryagin minimum principle Stress analysis User Transportation Theoretical study Algorithm Equilibrium Traffic assignment Formulation Traffic management Example Traffic control Numerical simulation |
| Language | English |
| License | https://www.elsevier.com/tdm/userlicense/1.0 CC BY 4.0 |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c488t-f7af1b0f7456b3b486d2e54f02c01514f23f68e98695fdcaf0f81e0dedb22f53 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
| PQID | 896207619 |
| PQPubID | 23462 |
| PageCount | 27 |
| ParticipantIDs | proquest_miscellaneous_896207619 repec_primary_eeetransb_v_3a45_3ay_3a2011_3ai_3a7_3ap_3a1035_1061_htm pascalfrancis_primary_24371095 crossref_citationtrail_10_1016_j_trb_2011_05_004 crossref_primary_10_1016_j_trb_2011_05_004 elsevier_sciencedirect_doi_10_1016_j_trb_2011_05_004 |
| PublicationCentury | 2000 |
| PublicationDate | 2011-08-01 |
| PublicationDateYYYYMMDD | 2011-08-01 |
| PublicationDate_xml | – month: 08 year: 2011 text: 2011-08-01 day: 01 |
| PublicationDecade | 2010 |
| PublicationPlace | Kidlington |
| PublicationPlace_xml | – name: Kidlington |
| PublicationSeriesTitle | Transportation Research Part B: Methodological |
| PublicationTitle | Transportation research. Part B: methodological |
| PublicationYear | 2011 |
| Publisher | Elsevier Ltd Elsevier |
| Publisher_xml | – name: Elsevier Ltd – name: Elsevier |
| References | Larsson, Patriksson, Rydergren (b0105) 2004; 38 Lu, Mahmassani, Zhou (b0125) 2009; 43 Noiri (b0160) 1974; 46 Nie, Zhang (b0150) 2010; 10 Buskens, Maurer (b0025) 2000; 120 Lindsey (b0115) 2004; 38 Carey, Ge (b0035) 2003; 37 Huang, Lam (b0090) 2002; 36 Aboudolas, Papageorgiou, Kosmatopoulos (b0005) 2009; 17 Mun (b0135) 2007; 27 Nie, Zhang (b0145) 2005; 5 Hartl, Sethi, Vickson (b0085) 1995; 37 Larsson, Patriksson (b0100) 1999; 33 Friesz, Bernstein, Suo, Tobin (b0055) 2001; 1 Larsson, Patriksson (b0095) 1995; 29 Chow (b0045) 2009; 5 Minoux (b0130) 1986 Szeto, Lo (b0185) 2006; 2 Xu, Wu, Florian, Marcotte, Zhu (b0200) 1999; 33 Papageorgiou, Diakaki, Dinopoulou, Kotsialos, Wang (b0165) 2003; 96 Yang, Meng, Lee (b0215) 2004; 38 Lo, Szeto (b0120) 2002; 36 Roger, Johnson (b0170) 1985 Ross (b0180) 1988; 22 Wie, Tobin, Carey (b0195) 2002; 36 Carey (b0040) 2008; 60 Friesz, Bernstein, Smith, Tobin, Wie (b0050) 1993; 41 Leoni (b0110) 2009 Tong, Wong (b0190) 2010; 6 Yang, Huang (b0220) 2005 Nie, Zhang (b0140) 2002; 39 Astarita, V., 1996. A continuous time link model for dynamic network loading based on travel time function. In: Proceedings of 13th International Symposium on Transportation and Traffic Theory, pp. 79–102. Friesz (b0070) 2010 Zhu, Marcotte (b0225) 2000; 34 Gentile, Meschini, Papola (b0080) 2005; 39 Rose (b0175) 1984; 7 Adida, Perakis (b0010) 2007; 54 Yang, Meng (b0205) 1998; 32 Friesz, Mookherjee (b0060) 2006; 40 Friesz, Kim, Kwon, Rigdon (b0075) 2011; 45 Yang, Bell, Meng (b0210) 2000; 34 Ban, Liu, Ferris, Ran (b0020) 2008; 42 Nie (b0155) 2011; 45 Carey, McCartney (b0030) 2002; 36 Friesz, Mookherjee, Yao (b0065) 2008; 42 Adida (10.1016/j.trb.2011.05.004_b0010) 2007; 54 10.1016/j.trb.2011.05.004_b0015 Larsson (10.1016/j.trb.2011.05.004_b0100) 1999; 33 Nie (10.1016/j.trb.2011.05.004_b0155) 2011; 45 Friesz (10.1016/j.trb.2011.05.004_b0055) 2001; 1 Friesz (10.1016/j.trb.2011.05.004_b0070) 2010 Chow (10.1016/j.trb.2011.05.004_b0045) 2009; 5 Nie (10.1016/j.trb.2011.05.004_b0140) 2002; 39 Yang (10.1016/j.trb.2011.05.004_b0220) 2005 Carey (10.1016/j.trb.2011.05.004_b0030) 2002; 36 Yang (10.1016/j.trb.2011.05.004_b0205) 1998; 32 Ross (10.1016/j.trb.2011.05.004_b0180) 1988; 22 Noiri (10.1016/j.trb.2011.05.004_b0160) 1974; 46 Ban (10.1016/j.trb.2011.05.004_b0020) 2008; 42 Carey (10.1016/j.trb.2011.05.004_b0035) 2003; 37 Aboudolas (10.1016/j.trb.2011.05.004_b0005) 2009; 17 Larsson (10.1016/j.trb.2011.05.004_b0095) 1995; 29 Roger (10.1016/j.trb.2011.05.004_b0170) 1985 Wie (10.1016/j.trb.2011.05.004_b0195) 2002; 36 Xu (10.1016/j.trb.2011.05.004_b0200) 1999; 33 Tong (10.1016/j.trb.2011.05.004_b0190) 2010; 6 Nie (10.1016/j.trb.2011.05.004_b0150) 2010; 10 Zhu (10.1016/j.trb.2011.05.004_b0225) 2000; 34 Minoux (10.1016/j.trb.2011.05.004_b0130) 1986 Rose (10.1016/j.trb.2011.05.004_b0175) 1984; 7 Lo (10.1016/j.trb.2011.05.004_b0120) 2002; 36 Papageorgiou (10.1016/j.trb.2011.05.004_b0165) 2003; 96 Friesz (10.1016/j.trb.2011.05.004_b0050) 1993; 41 Friesz (10.1016/j.trb.2011.05.004_b0065) 2008; 42 Hartl (10.1016/j.trb.2011.05.004_b0085) 1995; 37 Friesz (10.1016/j.trb.2011.05.004_b0075) 2011; 45 Lu (10.1016/j.trb.2011.05.004_b0125) 2009; 43 Carey (10.1016/j.trb.2011.05.004_b0040) 2008; 60 Friesz (10.1016/j.trb.2011.05.004_b0060) 2006; 40 Gentile (10.1016/j.trb.2011.05.004_b0080) 2005; 39 Yang (10.1016/j.trb.2011.05.004_b0215) 2004; 38 Larsson (10.1016/j.trb.2011.05.004_b0105) 2004; 38 Leoni (10.1016/j.trb.2011.05.004_b0110) 2009 Mun (10.1016/j.trb.2011.05.004_b0135) 2007; 27 Yang (10.1016/j.trb.2011.05.004_b0210) 2000; 34 Huang (10.1016/j.trb.2011.05.004_b0090) 2002; 36 Szeto (10.1016/j.trb.2011.05.004_b0185) 2006; 2 Buskens (10.1016/j.trb.2011.05.004_b0025) 2000; 120 Nie (10.1016/j.trb.2011.05.004_b0145) 2005; 5 Lindsey (10.1016/j.trb.2011.05.004_b0115) 2004; 38 |
| References_xml | – volume: 36 start-page: 83 year: 2002 end-page: 95 ident: b0030 article-title: Behaviour of a whole-link travel time model used in dynamic traffic assignment publication-title: Transportation Research Part B – year: 1986 ident: b0130 article-title: Mathematical Programming: Theory and Algorithms – volume: 17 start-page: 163 year: 2009 end-page: 174 ident: b0005 article-title: Store-and-forward based methods for the signal control problem in large-scale congested urban road networks publication-title: Transportation Research Part C – year: 1985 ident: b0170 article-title: Matrix Analysis – volume: 42 start-page: 823 year: 2008 end-page: 842 ident: b0020 article-title: A link-node complementarity model and solution algorithm for dynamic user equilibria with exact flow propagations publication-title: Transportation Research Part B – volume: 41 start-page: 179 year: 1993 end-page: 191 ident: b0050 article-title: A variational inequality formulation of the dynamic networks user equilibrium problem publication-title: Operations Research – volume: 33 start-page: 233 year: 1999 end-page: 264 ident: b0100 article-title: Side constrained traffic equilibrium models-analysis, computation and applications publication-title: Transportation Research Part B – volume: 96 start-page: 2043 year: 2003 end-page: 2067 ident: b0165 article-title: Review of road traffic control strategies publication-title: Proceedings of the IEEE – volume: 54 start-page: 767 year: 2007 end-page: 795 ident: b0010 article-title: A nonlinear continuous time optimal control model of dynamic pricing and inventory control with no backorders publication-title: Naval Research Logistics – volume: 36 start-page: 421 year: 2002 end-page: 443 ident: b0120 article-title: A cell-based variational inequality formulation of the dynamic user optimal assignment problem publication-title: Transportation Research Part B – volume: 33 start-page: 341 year: 1999 end-page: 353 ident: b0200 article-title: Advances in the continuous dynamic network loading problem publication-title: Transportation Science – year: 2009 ident: b0110 article-title: A First Course in Sobolev Spaces – volume: 22 start-page: 421 year: 1988 end-page: 435 ident: b0180 article-title: Traffic dynamics publication-title: Transportation Research Part B – volume: 46 start-page: 120 year: 1974 end-page: 124 ident: b0160 article-title: On weakly continuous mappings publication-title: Proceedings of the American Mathematical Society – volume: 60 start-page: 395 year: 2008 end-page: 410 ident: b0040 article-title: A framework for user equilibrium dynamic traffic assignment publication-title: Journal of the Operational Research Society – volume: 5 start-page: 85 year: 2009 end-page: 106 ident: b0045 article-title: Dynamic system optimal traffic assignment-a state-dependent control theoretic approach publication-title: Transportmetrica – volume: 39 start-page: 319 year: 2005 end-page: 338 ident: b0080 article-title: Macroscopic ARC performance models with capacity constraints for within-day dynamic traffic assignment publication-title: Transportation Research Part B – volume: 36 start-page: 253 year: 2002 end-page: 273 ident: b0090 article-title: Modeling and solving the dynamic user equilibrium route and departure time choice problem in network with queues publication-title: Transportation Research Part B – volume: 45 start-page: 329 year: 2011 end-page: 342 ident: b0155 article-title: A cell-based Merchant–Nemhauser model for the system optimum dynamic traffic assignment problem publication-title: Transportation Research Part B – reference: Astarita, V., 1996. A continuous time link model for dynamic network loading based on travel time function. In: Proceedings of 13th International Symposium on Transportation and Traffic Theory, pp. 79–102. – volume: 32 start-page: 247 year: 1998 end-page: 260 ident: b0205 article-title: Departure time, route choice and congestion toll in a queuing network with elastic demand publication-title: Transportation Research Part B – volume: 40 start-page: 207 year: 2006 end-page: 229 ident: b0060 article-title: Solving the dynamic network user equilibrium problem with state-dependent time shifts publication-title: Transportation Research Part B – volume: 45 start-page: 176 year: 2011 end-page: 207 ident: b0075 article-title: Approximate network loading and dual-time-scale dynamic user equilibrium publication-title: Transportation Research Part B – volume: 38 start-page: 17 year: 2004 end-page: 38 ident: b0105 article-title: A column generation procedure for the side constrained traffic equilibrium problem publication-title: Transportation Research Part B – volume: 34 start-page: 402 year: 2000 end-page: 414 ident: b0225 article-title: On the existence of solutions to the dynamic user equilibrium problem publication-title: Transportation Science – volume: 7 start-page: 809 year: 1984 end-page: 816 ident: b0175 article-title: Weak continuity and strongly closed sets publication-title: International Journal of Mathematics and Mathematical Science – volume: 37 start-page: 905 year: 2003 end-page: 926 ident: b0035 article-title: Comparing whole-link travel time models used in DTA publication-title: Transportation Research Part B – volume: 39 start-page: 729 year: 2002 end-page: 751 ident: b0140 article-title: Delay-function-based link models: their properties and computational issues publication-title: Transportation Research Part B – volume: 10 start-page: 49 year: 2010 end-page: 71 ident: b0150 article-title: Solving the dynamic user optimal assignment problem considering queue spillback publication-title: Networks and Spatial Economics – volume: 2 start-page: 31 year: 2006 end-page: 52 ident: b0185 article-title: Dynamic traffic assignment: properties and extensions publication-title: Transportmetrica – volume: 37 start-page: 181 year: 1995 end-page: 218 ident: b0085 article-title: A survey of the maximum principles for optimal control problems with state constraints publication-title: SIAM Review – volume: 38 start-page: 293 year: 2004 end-page: 314 ident: b0115 article-title: Existence, uniqueness, and trip cost function properties of user equilibrium in the bottleneck model with multiple user classes publication-title: Transportation Science – year: 2005 ident: b0220 article-title: Mathematical and Economic Theory of Road Pricing – volume: 27 start-page: 231 year: 2007 end-page: 249 ident: b0135 article-title: Traffic performance models for dynamic traffic assignment: an assessment of existing models publication-title: Transport Reviews – volume: 120 start-page: 85 year: 2000 end-page: 108 ident: b0025 article-title: SQP-methods for solving optimal control problems with control and state constraints: adjoint variables, sensitivity analysis and real-time control publication-title: Journal of Computational and Applied Mathematics – volume: 1 start-page: 319 year: 2001 end-page: 347 ident: b0055 article-title: Dynamic network user equilibrium with state-dependent time lags publication-title: Networks and Spatial Economics – volume: 34 start-page: 255 year: 2000 end-page: 275 ident: b0210 article-title: Modeling the capacity and level of service of urban transportation networks publication-title: Transportation Research Part B – volume: 43 start-page: 345 year: 2009 end-page: 364 ident: b0125 article-title: Equivalent gap function-based reformulation and solution algorithm for the dynamic user equilibrium problem publication-title: Transportation Research Part B – volume: 42 start-page: 407 year: 2008 end-page: 437 ident: b0065 article-title: Securitizing congestion: the congestion call option publication-title: Transportation Research Part B – volume: 6 start-page: 97 year: 2010 end-page: 120 ident: b0190 article-title: Heuristic algorithms for simulation-based dynamic traffic assignment publication-title: Transportmetrica – year: 2010 ident: b0070 article-title: Dynamic Optimization and Differential Games – volume: 5 start-page: 89 year: 2005 end-page: 115 ident: b0145 article-title: A comparative study of some macroscopic link models used in dynamic traffic assignment publication-title: Networks and Spatial Economics – volume: 29 start-page: 433 year: 1995 end-page: 455 ident: b0095 article-title: An augmented lagrangian dual algorithm for link capacity side constrained traffic assignment problems publication-title: Transportation Research Part B – volume: 38 start-page: 477 year: 2004 end-page: 493 ident: b0215 article-title: Trial-and-error implementation of marginal-cost pricing on networks in the absence of demand functions publication-title: Transportation Research Part B – volume: 36 start-page: 897 year: 2002 end-page: 918 ident: b0195 article-title: The existence, uniqueness and computation of an ARC-based dynamic network user equilibrium formulation publication-title: Transportation Research Part B – volume: 17 start-page: 163 issue: 2 year: 2009 ident: 10.1016/j.trb.2011.05.004_b0005 article-title: Store-and-forward based methods for the signal control problem in large-scale congested urban road networks publication-title: Transportation Research Part C doi: 10.1016/j.trc.2008.10.002 – volume: 2 start-page: 31 issue: 1 year: 2006 ident: 10.1016/j.trb.2011.05.004_b0185 article-title: Dynamic traffic assignment: properties and extensions publication-title: Transportmetrica doi: 10.1080/18128600608685654 – volume: 41 start-page: 179 issue: 2 year: 1993 ident: 10.1016/j.trb.2011.05.004_b0050 article-title: A variational inequality formulation of the dynamic networks user equilibrium problem publication-title: Operations Research doi: 10.1287/opre.41.1.179 – volume: 27 start-page: 231 issue: 2 year: 2007 ident: 10.1016/j.trb.2011.05.004_b0135 article-title: Traffic performance models for dynamic traffic assignment: an assessment of existing models publication-title: Transport Reviews doi: 10.1080/01441640600979403 – volume: 96 start-page: 2043 issue: 12 year: 2003 ident: 10.1016/j.trb.2011.05.004_b0165 article-title: Review of road traffic control strategies publication-title: Proceedings of the IEEE doi: 10.1109/JPROC.2003.819610 – year: 1986 ident: 10.1016/j.trb.2011.05.004_b0130 – volume: 42 start-page: 823 issue: 9 year: 2008 ident: 10.1016/j.trb.2011.05.004_b0020 article-title: A link-node complementarity model and solution algorithm for dynamic user equilibria with exact flow propagations publication-title: Transportation Research Part B doi: 10.1016/j.trb.2008.01.006 – volume: 45 start-page: 176 issue: 1 year: 2011 ident: 10.1016/j.trb.2011.05.004_b0075 article-title: Approximate network loading and dual-time-scale dynamic user equilibrium publication-title: Transportation Research Part B doi: 10.1016/j.trb.2010.05.003 – volume: 7 start-page: 809 issue: 4 year: 1984 ident: 10.1016/j.trb.2011.05.004_b0175 article-title: Weak continuity and strongly closed sets publication-title: International Journal of Mathematics and Mathematical Science doi: 10.1155/S0161171284000831 – volume: 36 start-page: 897 issue: 10 year: 2002 ident: 10.1016/j.trb.2011.05.004_b0195 article-title: The existence, uniqueness and computation of an ARC-based dynamic network user equilibrium formulation publication-title: Transportation Research Part B doi: 10.1016/S0191-2615(01)00041-8 – volume: 37 start-page: 905 issue: 10 year: 2003 ident: 10.1016/j.trb.2011.05.004_b0035 article-title: Comparing whole-link travel time models used in DTA publication-title: Transportation Research Part B doi: 10.1016/S0191-2615(02)00091-7 – volume: 40 start-page: 207 issue: 3 year: 2006 ident: 10.1016/j.trb.2011.05.004_b0060 article-title: Solving the dynamic network user equilibrium problem with state-dependent time shifts publication-title: Transportation Research Part B doi: 10.1016/j.trb.2005.03.002 – year: 2009 ident: 10.1016/j.trb.2011.05.004_b0110 – volume: 33 start-page: 341 issue: 4 year: 1999 ident: 10.1016/j.trb.2011.05.004_b0200 article-title: Advances in the continuous dynamic network loading problem publication-title: Transportation Science doi: 10.1287/trsc.33.4.341 – year: 2010 ident: 10.1016/j.trb.2011.05.004_b0070 – volume: 5 start-page: 85 issue: 2 year: 2009 ident: 10.1016/j.trb.2011.05.004_b0045 article-title: Dynamic system optimal traffic assignment-a state-dependent control theoretic approach publication-title: Transportmetrica doi: 10.1080/18128600902717483 – volume: 43 start-page: 345 issue: 3 year: 2009 ident: 10.1016/j.trb.2011.05.004_b0125 article-title: Equivalent gap function-based reformulation and solution algorithm for the dynamic user equilibrium problem publication-title: Transportation Research Part B doi: 10.1016/j.trb.2008.07.005 – volume: 39 start-page: 319 issue: 10 year: 2005 ident: 10.1016/j.trb.2011.05.004_b0080 article-title: Macroscopic ARC performance models with capacity constraints for within-day dynamic traffic assignment publication-title: Transportation Research Part B doi: 10.1016/j.trb.2004.04.005 – volume: 29 start-page: 433 issue: 6 year: 1995 ident: 10.1016/j.trb.2011.05.004_b0095 article-title: An augmented lagrangian dual algorithm for link capacity side constrained traffic assignment problems publication-title: Transportation Research Part B doi: 10.1016/0191-2615(95)00016-7 – volume: 1 start-page: 319 issue: 3–4 year: 2001 ident: 10.1016/j.trb.2011.05.004_b0055 article-title: Dynamic network user equilibrium with state-dependent time lags publication-title: Networks and Spatial Economics doi: 10.1023/A:1012896228490 – volume: 39 start-page: 729 issue: 8 year: 2002 ident: 10.1016/j.trb.2011.05.004_b0140 article-title: Delay-function-based link models: their properties and computational issues publication-title: Transportation Research Part B doi: 10.1016/j.trb.2004.10.002 – year: 1985 ident: 10.1016/j.trb.2011.05.004_b0170 – volume: 46 start-page: 120 issue: 1 year: 1974 ident: 10.1016/j.trb.2011.05.004_b0160 article-title: On weakly continuous mappings publication-title: Proceedings of the American Mathematical Society doi: 10.1090/S0002-9939-1974-0348698-5 – volume: 54 start-page: 767 issue: 7 year: 2007 ident: 10.1016/j.trb.2011.05.004_b0010 article-title: A nonlinear continuous time optimal control model of dynamic pricing and inventory control with no backorders publication-title: Naval Research Logistics doi: 10.1002/nav.20250 – volume: 45 start-page: 329 issue: 2 year: 2011 ident: 10.1016/j.trb.2011.05.004_b0155 article-title: A cell-based Merchant–Nemhauser model for the system optimum dynamic traffic assignment problem publication-title: Transportation Research Part B doi: 10.1016/j.trb.2010.07.001 – volume: 36 start-page: 421 issue: 5 year: 2002 ident: 10.1016/j.trb.2011.05.004_b0120 article-title: A cell-based variational inequality formulation of the dynamic user optimal assignment problem publication-title: Transportation Research Part B doi: 10.1016/S0191-2615(01)00011-X – volume: 34 start-page: 255 issue: 4 year: 2000 ident: 10.1016/j.trb.2011.05.004_b0210 article-title: Modeling the capacity and level of service of urban transportation networks publication-title: Transportation Research Part B doi: 10.1016/S0191-2615(99)00024-7 – volume: 120 start-page: 85 issue: 1 year: 2000 ident: 10.1016/j.trb.2011.05.004_b0025 article-title: SQP-methods for solving optimal control problems with control and state constraints: adjoint variables, sensitivity analysis and real-time control publication-title: Journal of Computational and Applied Mathematics doi: 10.1016/S0377-0427(00)00305-8 – volume: 34 start-page: 402 issue: 4 year: 2000 ident: 10.1016/j.trb.2011.05.004_b0225 article-title: On the existence of solutions to the dynamic user equilibrium problem publication-title: Transportation Science doi: 10.1287/trsc.34.4.402.12322 – volume: 33 start-page: 233 issue: 4 year: 1999 ident: 10.1016/j.trb.2011.05.004_b0100 article-title: Side constrained traffic equilibrium models-analysis, computation and applications publication-title: Transportation Research Part B doi: 10.1016/S0191-2615(98)00024-1 – volume: 38 start-page: 477 issue: 6 year: 2004 ident: 10.1016/j.trb.2011.05.004_b0215 article-title: Trial-and-error implementation of marginal-cost pricing on networks in the absence of demand functions publication-title: Transportation Research Part B doi: 10.1016/S0191-2615(03)00077-8 – volume: 37 start-page: 181 issue: 2 year: 1995 ident: 10.1016/j.trb.2011.05.004_b0085 article-title: A survey of the maximum principles for optimal control problems with state constraints publication-title: SIAM Review doi: 10.1137/1037043 – volume: 38 start-page: 293 issue: 3 year: 2004 ident: 10.1016/j.trb.2011.05.004_b0115 article-title: Existence, uniqueness, and trip cost function properties of user equilibrium in the bottleneck model with multiple user classes publication-title: Transportation Science doi: 10.1287/trsc.1030.0045 – volume: 5 start-page: 89 issue: 1 year: 2005 ident: 10.1016/j.trb.2011.05.004_b0145 article-title: A comparative study of some macroscopic link models used in dynamic traffic assignment publication-title: Networks and Spatial Economics doi: 10.1007/s11067-005-6663-6 – volume: 42 start-page: 407 issue: 5 year: 2008 ident: 10.1016/j.trb.2011.05.004_b0065 article-title: Securitizing congestion: the congestion call option publication-title: Transportation Research Part B doi: 10.1016/j.trb.2007.10.002 – volume: 6 start-page: 97 issue: 2 year: 2010 ident: 10.1016/j.trb.2011.05.004_b0190 article-title: Heuristic algorithms for simulation-based dynamic traffic assignment publication-title: Transportmetrica doi: 10.1080/18128600802630281 – volume: 38 start-page: 17 issue: 1 year: 2004 ident: 10.1016/j.trb.2011.05.004_b0105 article-title: A column generation procedure for the side constrained traffic equilibrium problem publication-title: Transportation Research Part B doi: 10.1016/S0191-2615(02)00092-9 – volume: 10 start-page: 49 issue: 1 year: 2010 ident: 10.1016/j.trb.2011.05.004_b0150 article-title: Solving the dynamic user optimal assignment problem considering queue spillback publication-title: Networks and Spatial Economics doi: 10.1007/s11067-007-9022-y – year: 2005 ident: 10.1016/j.trb.2011.05.004_b0220 – ident: 10.1016/j.trb.2011.05.004_b0015 – volume: 36 start-page: 83 issue: 1 year: 2002 ident: 10.1016/j.trb.2011.05.004_b0030 article-title: Behaviour of a whole-link travel time model used in dynamic traffic assignment publication-title: Transportation Research Part B doi: 10.1016/S0191-2615(00)00039-4 – volume: 36 start-page: 253 issue: 3 year: 2002 ident: 10.1016/j.trb.2011.05.004_b0090 article-title: Modeling and solving the dynamic user equilibrium route and departure time choice problem in network with queues publication-title: Transportation Research Part B doi: 10.1016/S0191-2615(00)00049-7 – volume: 22 start-page: 421 issue: 6 year: 1988 ident: 10.1016/j.trb.2011.05.004_b0180 article-title: Traffic dynamics publication-title: Transportation Research Part B doi: 10.1016/0191-2615(88)90023-9 – volume: 60 start-page: 395 issue: 3 year: 2008 ident: 10.1016/j.trb.2011.05.004_b0040 article-title: A framework for user equilibrium dynamic traffic assignment publication-title: Journal of the Operational Research Society doi: 10.1057/palgrave.jors.2602543 – volume: 32 start-page: 247 issue: 4 year: 1998 ident: 10.1016/j.trb.2011.05.004_b0205 article-title: Departure time, route choice and congestion toll in a queuing network with elastic demand publication-title: Transportation Research Part B doi: 10.1016/S0191-2615(97)00041-6 |
| SSID | ssj0003401 |
| Score | 2.1918762 |
| Snippet | ► The paper formulates the dynamic user equilibrium (DUE) with side-constraints on dynamic traffic volume representing traffic management objective or strict... This paper investigates a traffic volume control scheme for a dynamic traffic network model which aims to ensure that traffic volumes on specified links do not... |
| SourceID | proquest repec pascalfrancis crossref elsevier |
| SourceType | Aggregation Database Index Database Enrichment Source Publisher |
| StartPage | 1035 |
| SubjectTerms | Applied sciences Dynamic user equilibrium (DUE) Dynamic user equilibrium (DUE) Traffic volume control Traffic management and control Traffic assignment with side constraint Pontryagin minimum principle Lagrange multiplier Exact sciences and technology Ground, air and sea transportation, marine construction Lagrange multiplier Pontryagin minimum principle Traffic assignment with side constraint Traffic management and control Traffic volume control Transportation planning, management and economics |
| Title | Dynamic user equilibrium with side constraints for a traffic network: Theoretical development and numerical solution algorithm |
| URI | https://dx.doi.org/10.1016/j.trb.2011.05.004 http://econpapers.repec.org/article/eeetransb/v_3a45_3ay_3a2011_3ai_3a7_3ap_3a1035-1061.htm https://www.proquest.com/docview/896207619 |
| Volume | 45 |
| WOSCitedRecordID | wos000293436200008&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVESC databaseName: Elsevier SD Freedom Collection Journals 2021 customDbUrl: eissn: 1879-2367 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0003401 issn: 0191-2615 databaseCode: AIEXJ dateStart: 19950201 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1Lj9MwELZKiwQIIVhAlMfKB05EifJsHG4FulpgtULQQ2-W49hsV21amrRaLvxKfhDj2HGzCFaAxMFWZTV13PlsfzMezyD03OdcRmIUuiINEjcGRuvmhOduIIqY54QpUtAkm0hPT8lsln3o9b63d2F2i7QsycVFtv6vooY2ELa6OvsX4rY_Cg3wGYQONYgd6j8S_BudY95R5gdHfNnOG6_-7dJ4o8-Lxj-9anJD1JX2olSZIlQsCafUXuHGF8NecSz2rkXNaUO51Qc9C6cdi8MWn1cb6GHZpbs2dLqGmYksdOYBcd3UzivVjU5h3S7Bezu2cRX-6M28_cHVkpnA_mPbeKR0_cYKPvVObOuJxrmxJjnH3nuva9_QBtuOfcNevNl7OTV20CxwQfnTB-JCr90kzVwVkK67uOtYlQbEaWelDvwo6ez6SjP-5Y6ijRvnXr3JTcBXZYSL99undWr8pF5KvZOKwgdMOLqGBmGaZKSPBuO3k9k7yxCi2Dd5MvUg2tP2xu_wp45-x5dur1kFYpE6_col_WiwEWvBOzRpehfdMfoNHmtc3kM9UR6gG-319-oA3epEwLyPvhm0YoVW3EErVmjFCq24g1YMaMUMG7Rig9aXuINV3MEqBqxii1XcYhVbrD5A06PJ9PWxa1KCuBx2mtqVKZNB7ssUeH8e5TEZFaFIYumHHHhtEMswkiMiMjLKEllwJn1JAuEXosjDUCbRQ9QvV6V4hHAaJQHL8ohwyWPGkhx4LgkjxknOUpGOhshv_3fKTbh8NdYFbf0izymIiipRUT-hIKohemEfWetYMVd9OW6FSQ3Z1SSWAvKueuzwkuBtRyqwaAD60hDhFgkUdgp1_MdKsdpWlGSjsLFaDtGkQYh9VghRq_UgpzsasTiB6iuUptuIzaGkUNZQ1Kyhaq7Qs3r5-N-G8ATd3M_zp6hfb7biGbrOd_W82hyaufIDIx8BIA |
| linkProvider | Elsevier |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Dynamic+user+equilibrium+with+side+constraints+for+a+traffic+network%3A+Theoretical+development+and+numerical+solution+algorithm&rft.jtitle=Transportation+research.+Part+B%3A+methodological&rft.au=Zhong%2C+R.X.&rft.au=Sumalee%2C+A.&rft.au=Friesz%2C+T.L.&rft.au=Lam%2C+William+H.K.&rft.date=2011-08-01&rft.pub=Elsevier+Ltd&rft.issn=0191-2615&rft.eissn=1879-2367&rft.volume=45&rft.issue=7&rft.spage=1035&rft.epage=1061&rft_id=info:doi/10.1016%2Fj.trb.2011.05.004&rft.externalDocID=S0191261511000543 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0191-2615&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0191-2615&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0191-2615&client=summon |