zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Equilibrium model and algorithm of urban transit assignment based on augmented network. (English) Zbl 1177.90082
Summary: The passenger flow assignment problem for the urban transit network is relatively complicated due to the complexity of the network structure and many factors influencing the passengers’ route and line choices. In the past three decades, many models have been proposed to solve the passenger flow assignment problem. However, the common-line problem remains challenging in transit flow assignment. In this paper, the characteristics of the urban transit network is analysed and a new technique of augmented network is proposed to represent the urban transit system. The purpose is to eliminate the complex common-line problem when modeling transit passenger flow assignment. Through this augmentation technique, the urban transit system can be represented by an augmented network-it then behaves like a simple network and can be used as a generalized network for traffic assignment or network analysis. This paper presents a user equilibrium model for the urban transit assignment problem based on such a technique. A numerical example is also provided to illustrate the approach.
MSC:
90B20Traffic problems
References:
[1]Dafermos S C. Relaxation algorithm for the general asymmetric traffic equilibrium problem. Transportation Sci, 1982, 16: 231–240 · doi:10.1287/trsc.16.2.231
[2]Smith M J. An algorithm for solving asymmetric equilibrium problem with a continuous cost-flow function. Transport Res, 1983, 18B: 432–448
[3]Sheffi Y. Urban transportation networks: Equilibrium analysis with mathematical programming methods. New Jersey: Prentice-Hall, Englewood Cliffs, 1985
[4]Huang H J. A study on Logit assignment which excludes all cyclic flows. Transportation Res, 1998, 32B: 401–412 · doi:10.1016/S0191-2615(98)00008-3
[5]Yang H, Huang H J. The multi-class, multi-criteria traffic network equilibrium and system optimum problem. Transport Res, 2004, 38B: 1–15 · doi:10.1016/S0191-2615(02)00074-7
[6]Dial R B. Transit pathfinder algorithms. Highway Research Record, 1967, 205: 67–85
[7]Fearnside K, Draper D P. Public transport assignment–A new approach. Traffic Eng Control, 1971, 298–299
[8]Le Clercq F. A public transport assignment model. Traffic Eng Control, 1972, 91–96
[9]De Cea J, Fernández E. Transit assignment for congested public transport systems: An equilibrium model. Transport Sci, 1993, 27(2): 133–147 · Zbl 0788.90030 · doi:10.1287/trsc.27.2.133
[10]Wu J H, Florian M, Marcotte P. Transit equilibrium assignment: A model and solution algorithms. Transport Sci, 1994, 28(3): 193–203 · Zbl 0814.90025 · doi:10.1287/trsc.28.3.193
[11]Lam W H K, Gao Z Y, Chan K S, et al. A stochastic user equilibrium assignment model for congested transit networks. Transport Res, 1999, 33B: 351–368 · doi:10.1016/S0191-2615(98)00040-X
[12]Cominetti R, Correa J. Common-lines and passenger assignment in congested transit networks. Transport Sci, 2001, 35(3): 250–267 · Zbl 1160.90328 · doi:10.1287/trsc.35.3.250.10154
[13]Cepeda M, Cominetti R, Florian M. A frequency-based assignment model for congested transit networks with strict capacity constraints: Characterization and computation of equilibria. Transport Res, 2006, 40B: 437–459 · doi:10.1016/j.trb.2005.05.006
[14]Chriqui C, Robillard P. Common bus lines. Transport Sci, 1975, 9: 115–121 · doi:10.1287/trsc.9.2.115
[15]Spiess H, Florian M. Optimal strategies: A new assignment model for transit network. Transport Res, 1989, 23B: 83–102 · doi:10.1016/0191-2615(89)90034-9
[16]Nguyen S, Pallottino S. Hyperpaths and shortest hyperpaths, combinatiorial optimization. In: Lecture Note in Mathematics. Berlin: Springer-Verlag, 1989. 258–271
[17]Kurauchi F, Bell M G H, Schmöcker J D. Capacity constrained transit assignment with common lines. J Math Model Algorithm, 2003, 2(4): 309–327 · Zbl 1048.90033 · doi:10.1023/B:JMMA.0000020426.22501.c1
[18]Si B F, Long J C, Gao Z Y. Optimization model and algorithm for mixed traffic of urban road network with flow interference. Sci China Ser E-Tech Sci, 2008, 51(12): 2223–2232 · Zbl 1258.90023 · doi:10.1007/s11431-008-0248-9