Citation
Congestion toll pricing models and methods for variable demand networks

Material Information

Title:
Congestion toll pricing models and methods for variable demand networks
Creator:
Yildirim, Mehmet Bayram
Place of Publication:
[Gainesville, Fla.]
Publisher:
University of Florida
Publication Date:
Language:
English

Subjects

Subjects / Keywords:
Cost functions ( jstor )
Elasticity of demand ( jstor )
Linear programming ( jstor )
Market prices ( jstor )
Optimal solutions ( jstor )
Pricing ( jstor )
Toll booths ( jstor )
Tolls ( jstor )
Transportation ( jstor )
Travel time ( jstor )
Computer networks -- Management ( lcsh )
Dissertations, Academic -- Industrial and Systems Engineering -- UF ( lcsh )
Industrial and Systems Engineering thesis, Ph. D ( lcsh )
Telecommunication -- Traffic -- Management ( lcsh )
Genre:
government publication (state, provincial, terriorial, dependent) ( marcgt )
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Summary:
ABSTRACT: General variable demand (GVD) traffic assignment problems estimate the traffic volumes on each link and the flows and demands between each origin destination pair. In GVD models, demand is a function of the generalized trip cost on the network. We define two optimization models for GVD traffic assignment problems. In the user equilibrium, each user maximizes his/her own net user benefit. However, this results in the suboptimal utilization of the transportation network. When the total net user benefit is maximized, the most efficient utilization of the network is achieved and the system optimal flows and demands are realized. Our goal is to characterize the set of all tolls which will make the tolled user equilibrium problem have the same flows and demands as the system optimal ones. The set of all such toll vectors is defined as the first best toll set. Given that there are constraints on tolling some portions of the network, a first best toll pricing scheme might not be feasible. Under such circumstances, a second best toll pricing scheme can be utilized. The appropriate models for second best pricing schemes are mathematical programs with equilibrium constraints (MPECs). Since MPECs are very difficult to solve, obtaining alternative toll vectors by adding side constraints and resolving the MPEC is not desirable.
Summary:
ABSTRACT (cont.): Given a second best solution, we show that there exists a non-empty second best toll set. Given the first or second best toll set, one can define additional objectives and constraints and solve either linear programs or mixed integer programs to obtain alternative toll vectors. This process is known as the "toll pricing framework" (TPF). We generalize the TPF for the first best fixed demand traffic assignment models to GVD models in order to find alternative first best and second best toll vectors. Two natural choices of such vectors are MINTB and MINMAX toll vectors. The MINTB problem minimizes the number of toll booths whereas MINMAX problem minimizes the maximum toll on the network.
Summary:
KEYWORDS: Pricing, First Best, Second Best, Varable Demand Traffic Assignment Problems, Elastic Demand, Combined Distribution Assignment Model, Toll Pricing Framework
Thesis:
Thesis (Ph. D.)--University of Florida, 2001.
Bibliography:
Includes bibliographical references.
System Details:
System requirements: World Wide Web browser and PDF reader.
System Details:
Mode of access: World Wide Web.
General Note:
Title from title page of source document.
General Note:
Document formatted into pages; contains xi, 154 p.; also contains graphics.
General Note:
Includes vita.
Statement of Responsibility:
by Mehmet Bayram Yildirim.

Record Information

Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
Copyright Yildirim, Mehmet Bayram. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Embargo Date:
12/15/2002
Resource Identifier:
028626624 ( ALEPH )
51340927 ( OCLC )

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

PAGE 17

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

PAGE 18

D Cost per Trip Generalized Number Of Trips Demand Average Cost Marginal Cost M B C A C A c su tt B C C1-&,:-//+J) (E-+2&-)(& C!$%&'# # ! .!"##!)& "#-#&E-+2&-),%$0&. !!"#) (+0+ %(%)C((!") &'!#(%! "0,"(!"+0+%*&% -## E+!% .!") &1( +#% +%#!%*&% !& 0+#E+!%!") &1( +-#& 2(H!10(2!") (-&0,!/%(! !"%(%)C(# "0, "##!"##!)%/!) +/%(!,(%&&!%" 0!"-#&E-+2&-) ! . %(%)#!# &1-!" !!" !!"-#&##"%-+2" &1 !%++(!" )%-(!%* .!"!%++, "!%++# & #!%%)/-!2 *%&)-+
PAGE 19

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

PAGE 20

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

PAGE 21

+!&%( &##!).!"&-#""%-&!& C" #& #2S$"+(%(J/ ' /&%!& C" #(& #2BS, (BB>. (1%JA9/&## (#(!&%-"1"%-/ (!%++<= + (#,(1+%-/ (0"+# & ++%$!%-#!"+ (#*!"/ RA *%& #/ +/&)!. (!"#/ & / !%*+ (# &-#)%&C(!+, (-#&# &$++(1!%/ !%++*%&1 ((1 ()/&%0+0+%*#&0, ,A, +-&# ( )/+)(! !%( %* % &(1 &%4!# +!"%-1"!"9!(#0#(!H&# &" (9/&)(! !%(%(!"G!#%* /&(1%(!"%(1%(1!& C(!$%&'#"%$(%-& 1(1&#-+!#. /&%/%# &% /&(1/&%4!(B@>$ #(%!)/+)(!< $#%( ( !+(1O?P ( &&#%(! +,O?;P=,"&$�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

PAGE 22

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

PAGE 23

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

PAGE 24

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A %(+*
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

PAGE 28

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�& +#!%" #!-#&E-+2&-))%+#.*!" ##!)%#!#/&!-&22!%++#.##!)%/!) +M%$#.,,. H&#!2#! #%+-!%(.$++2 !! (, (!"( )!& C ##1()(!/&%2+)#.!"!& 0+) (# (%#!# 0 &%0&!) (!"-#%(1#!%(!%++#(!%2!)0 &(1<&" (! ( )" -#&O@.@;P (OP=,%!!" !!"#")#( )#( !%(+/(#%(!"(#! (! (%-#M%$#,(&#%(OA;P.1($OP=. & (&(0 # (O@P ((1 ( (1OA?P#"%$!" !!"#")) '# !"-#&/&%2+)" 0!"# )M%$# #!"##!)#%+-!%(*%& 2%!!+('%& #(1+J#!( !%((!$%&',-&!"&)%&.!"#/&%/&!# +#%%2#&02! +,O;A.;>P. #( (1ODBP.! +,O.?.AP ( (%2( O;P*%&1(& +(!$%&'#,

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,? %++ &(1 "%& *%& 9 ) ( !$%&'# H( # . (%(#&!"/&!-&2-#&%/!) +!/&%2+): <
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"*%++%$(1# &#-+!*&%)&1(%&G! +,OP9/&##(1 (!&)#%* !"/%+"&
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? (E+!#!" !#&2!"-#&E-+2&-)
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A 2+;,: < =. < = ( < =*%&!"/ + ##%*!")%+, MODEL ' '( '() ' * # + # + # < = &%(09, < =. < = ( < =*%&!")%+#!" !$%(#& &+#! ( 2+;,, ##-)!" ! < = ( < = &+( &,"&#-+!(1##!) ( -#&/&%2+)#" 0 %(09(%(+( &%24!0 (+( &%(#!& (!#,"-# %(#!& (!E+H !%( -!%) ! ++"%+# ()-+!/+&#$++9#! !!"+% + %/!) , ;,, #!) &%2+) "##!)/&%2+) ##-)#!" !!"&# (!& +/+ (((1 -!"%&! $""%(!&%+#!"!& (#/%&! !%(##!).!"-# (C(!##!)#1( (2 )/+)(!,(!"1(& +0 & 2+) ()%+.$"(!"##!)%24!0# )()7 !%(%*!"!%! +##!)%#!. (C(!(!$%&'-!+7 !%(# "02 " 0(1M%$# () (#$"" &%(##!(!$!" &&%/F##%(/&(/+, (H(!"##!)/&%2+)P." /!&A,

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> !L< =K & K< +, = < I = *< I = *L< =K ' K< =
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D -))(1-/!"#E!%(#$1!. & I L 'I K !I
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@
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; (#-" #H(!%2 ,!!" (%!2 2!" #!%* ++#-"0!%&#. :K K ,%& 10(0!%&
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; %)!!"/&%%*%*!"#+)) #(!##)+ &!%!"%(2 &( ( ) ( O?BP*%&!"H9) ( #, &%) &&%/F#&#!&(/+.$'(%$!" !(!"E-+2&-).!"-!+7 / !"#*%& (%&1(J#!( !%(/ &" 0!"# )!& 0+!) (!"-(-#%(# %(%!" 0+%$&!& 0+!)#,"(9!%&%++ &0&H#!" !!"1(& +7%#! 0&#%(%*!"#/&(/+"%+#,! .2 / !"*%&%))%! . /2*+(' #%(/ !" . (7&%%!"&$#.
PAGE 43

; !" &#-))%0&!" &#%(!"-!+7/ !"#.!"(E+!(!"%&%++ & "%+# # (E+!,"%(+-#%(%*!"%&%++ &!"(*%++%$#, (%!"&$%&#.!"#%&%++ & (2(!&/&!2# (1!" !0& %))%!& "# (E-+2&-)9 !+$"(!"1(& +7/ !"%#!#. (+-(1!%++#.E+#!"1(& +72(H! !!"H( +) (+0+, 10 ( +!&( !0!%++#!#&/!%($"(!"%))%!M%$#I & +#%'(%$(, ! (!
PAGE 44

;; 10(
PAGE 45

;? 1(& ++ 0 + 2+,* $&H9!%I .$$%-+*%&!"-#&#!%/ 9 !+!" # ) )%-(! ((0+#/ (1*"N#"#!& 0+(1%( ##!)%/!)7 !& 0+(!$%&',"(I #H9.-#&#$++/&09 !+!"# ) )%-(!%* %#!#!" &9/&((1(!"##!)%/!) +#%+-!%(,#)+ & &1-)(! "%+#*%&!" I )-+!/+&#,%$.%(#&!"#/ + #$"&
PAGE 46

;A %! +#%!" !.*%&!"!%++#!!%2(%(!&0 +.#%)* #2+!<0 & 2+!=( < =#&E-&, ;,,A #!&! %++ ! %$. ##-)!" !
PAGE 47

;> &%%*:,"##%20%-#*&%)!"H(!%(%* &#! #! %++ &(1 & )$%&' *%& %+# *!&H((1!"!%++#!.!"H9) (H&#!2#!!%++/&(1*& )$%&' O?BP (29!(!%!")%+. ##-)(1 %*!"#%+-!%(# *%&!"J (J)%+#,# (2#((1-&;,.!" *& )$%&' (2#-)) &7 #*%++%$#: ,%+0!"J!%%2! (!"##!)%/!) +#%+-!%(?P (2-#*%&!"##!/, ,H( !%++#!$""#!" / &!%*!"&
PAGE 48

;D Solve the system problem to obtain (,,,) vt Should the users pay exactly the same constraint costs as in the system optimal problem? Define the toll set by part of (,,,)GVDWvt Define the toll set by (,,) part of (,)GVDWvt Define and optimize an objective function over the toll set, possibly intersected with other constraints No Yes 1-&;,:&#!#!%++&(1& )$%&', &*&!%2(1 !0 #$++ #/%#!0,)()7#!"(-)2&%*!%++ 2%%!"#. (!"8)()7#!") 9)-)!%++%(!"!& (#/%&! !%( (!$%&',%!!" ! (0 +!%++0!%&(+-(1!%++0!%&/&%-# !"# )!%++&0(-,# &#-+!.J (J*%&)-+ !%(# & (%!0&(!&#!(1*%&!"(!$%&'#."%$0&." 0(1#%) +!&( !0!%++ 0!%&#)1"!"+/!"!& C/+ ((&!%/&%/%#G&(!!%++/&(1#")#*%& 0 &%-##( &%#, (!"*%++%$(1#!%(#.$/&#(!#/ + ##%*!")%+.H( !"!%++#!*%& ")%+. (++-#!& !!"!%++/&(1*& )$%&'2(-)& + 9 )/+#,

PAGE 49

;@ ;,,D + #! ) ( %+# "+ #!) (<=)%+# #/ + #%*!")%+,"-#!" !%++#!*%&!")%+ (2&0*&%)!"!%++#!*%&!")%+ *!& #%)) (/-+ !%(#, "##!))%+$!"+ #!) ( ##-)#!" !!"1% +%*!& (#/%&! !%( /+ ((&##!%) 9)7!"(!-#&2(H!O;.;@.A.P$""#!"G&( 2!$(!"!%! +(!$%&'-#&2(H!. < ( = )( . (!"##!)%#!. < = , (#! !!"##!)/&%2+)
PAGE 50

;B #(1)) ;,;%*!")%+.$ (9!(!"(%!%(%*!%++/&(1 !%!"+ #!) (!& C ##1()(!)%+#,%& 10(0!%&,DA;(!"-#& /&%2+).#%!"&# A,ASG&(, 2+;, +#%%(! (#!"-#&2(H!*%& !"%/!) +) (+0+#,

PAGE 51

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
PAGE 52

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