Dynamic Traffic Routing, Assignment, and Assessment of Traffic Networks

Glossary

Car-following model:

A mathematical representation (traffic flow model) for driver longitudinal motion behavior.

Dynamic traffic assignment:

Traffic assignment considering the temporal dimension of the problem.

Link or arc:

A roadway segment with homogeneous traffic and roadway characteristics (e.g. same number of lanes, base lane capacity, free-flow speed, speed-at-capacity, and jam density). Typically networks are divided into links for traffic modeling purposes.

Marginal link travel time:

The increase in a link’s travel time resulting from an assignment of an additional vehicle to this link.

Road pricing:

Road pricing is an economic concept in which drivers are charged for the use of the road facility.

Route or path:

A sequence of roadway segments (links or arcs) used by a driver to travel from his/her point of origin to his/her destination.

Static traffic assignment:

Traffic assignment ignoring the temporal dimension of the problem.

Synthetic O-D estimation:

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Appendix

Term Abbreviations

ANN:

Artificial Neural Networks

ATIS:

Advanced Traveler Information System

AVI:

Automatic Vehicle Identification

AVL:

Automatic Vehicle Location

DTA:

Dynamic Traffic Assignment

FHWA:

Federal Highway Administration

GA:

Genetic Algorithm

GPS:

Global Positioning System

HCM:

Highway Capacity Manual

HOV:

High Occupancy Vehicle

ITS:

Intelligent Transportation Systems

LDV:

Light Duty Vehicle

LMC:

Link Marginal Cost

LP:

Linear Programming

MOE:

Measure of Effectiveness

NLP:

Non-Linear Programming

O-D:

Origin – Destination

PMC:

Path Marginal Cost

SO:

System Optimum

SOV:

Single Occupancy Vehicle

TT:

Travel Time

UE:

User Equilibrium

VMS:

Variable Message Sign

Variable Definitions

v _i :

Traffic volume on route i

N :

Set of network nodes

A :

Set of network arcs (links)

R :

Set of origin centroids

S :

Set of destination centroids

k _rs :

Set of paths connecting O-D pair (r–s); r ∈ R, s ∈ S

x _a :

Flow on arc (a)

x _b :

Flow on arc (b)

t _a :

Travel time on arc (a)

t _b :

Travel time on arc (b)

${\boldsymbol{f}}_{\boldsymbol{k}}^{\boldsymbol{rs}}$ :

Flow on path (k) connecting O-D pair (r-s)

${\boldsymbol{f}}_{\boldsymbol{l}}^{\boldsymbol{mn}}$ :

Flow on path (l) connecting O-D pair (m-n)

${\boldsymbol{c}}_{\boldsymbol{k}}^{\boldsymbol{rs}}$ :

Travel time on path (k) connecting O-D pair (r-s)

q _rs :

Trip rate between origin (r) and destination (s)

${\boldsymbol{\delta}}_{\boldsymbol{a},\boldsymbol{k}}^{\boldsymbol{rs}}$ :

Indicator variable, = 1 if arc (a) is on path (k) between O-D pair (r-s), and 0 otherwise

x :

Vector of flows on all arcs, D (…, x_a,…)

t :

Vector of travel times on all arcs, D (…, t_a,…)

f ^rs :

Vector of flows on all paths connecting O-D pair r-s, = $\left(\dots, {f}_k^{rs},\dots \right)$

f :

Matrix of flows on all paths connecting all O-D pairs, = (…, f ^rs,…)

c ^rs :

Vector of travel times on all paths connecting O-D pair r-s, = (…, c^rs,…)

c :

Matrix of travel times on all paths connecting all O-D pairs, D (…, c^rs,…)

q :

Origin-destination matrix (with elements = q_rs)

Δ ^rs :

Link-path incidence matrix (with ${\delta}_{a,k}^{rs}$ elements) for O-D pair r-s, as discussed below

Δ :

Matrix of link-path incidence matrices (for all O-D pairs), = (…, Δ^rs, …)

z :

Objective function

L :

Lagrange (transformation of the) objective function

u _rs :

Dual variable associated with the flow conservation constraint for O-D pair (r-s)

t _{i, k} :

Observed average travel time along link i within the kth sampling interval

t ˜ _{I, k} :

Smoothed average travel time along link i in the kth sampling interval

${\boldsymbol{s}}_{\boldsymbol{i},\boldsymbol{k}}^2$ :

Variance of the observed travel times relative to the observed average travel time in the kth sampling interval

${\tilde{\boldsymbol{s}}}_{\boldsymbol{i},\boldsymbol{k}}^2$ :

Variance of the observed travel times relative to the smoothed travel time in the kth sampling interval

n _{i, k} :

Number of valid travel time readings on link i in the kth sampling interval

α :

Exponential smoothing factor that varies as a function of the number of observations n_{i, k} within the sampling interval

β :

Constant that varies between 0 and 1

T _ij :

Number of trips between production zone i and attraction zone j

P _i :

Number of trip productions from the origin zone

A _j :

Number of trip attractions to the destination zone

F _ij :

Impedance factor between production zone i and attraction zone j

K _ij :

Socio-economic adjustment factor for trips between production zone i and attraction zone j

c _ij :

Generalized cost of inter-zonal travel between production zone i and attraction zone j

t _ij :

Prior information on the number of trips between production zone i and attraction zone j

Va :

Traffic flow on link (a)

${\boldsymbol{V}}_{\boldsymbol{a}}^{\prime }$ :

Complementary traffic flow on link (a)

${\boldsymbol{p}}_{\boldsymbol{ij}}^{\boldsymbol{a}}$ :

Probability of traffic flow between origin (i) and destination (j) to use link (a)

T _r :

Total demand departing during time-slice (r)

t _r :

Total seed matrix demand departing during time-slice (r)

T _rij :

Traffic demand departing during time-slice (r) traveling between origin (i) and destination (j)

t _rij :

Seed traffic demand departing during time-slice (r) traveling between origin (i) and destination (j)

l _rij :

Lagrange multiplier for departure time-slice, origin, and destination combination (rij)

V _sa :

Observed volume on link (a) during time-slice (s)

${\boldsymbol{p}}_{\boldsymbol{rij}}^{\boldsymbol{sa}}$ :

Probability of (a) demand between origin (i) and destination (j) during time-slice (r) is observed on link (a) during time-slice (s)

d ( t _i ) :

Vehicle delay at time (t_i)

u ( t _i ) :

Vehicle instantaneous speed at time (t_i)

u _f :

Free-flow speed

S ( t _i ) :

Vehicle full and partial stops at time (t_i)

MOE _e :

Instantaneous fuel consumption or emission rate

${\boldsymbol{K}}_{\boldsymbol{i},\boldsymbol{j}}^{\boldsymbol{e}}$ :

Model regression coefficient for MOE (e) at speed power (i) and acceleration power (j)

${\boldsymbol{L}}_{\boldsymbol{i},\boldsymbol{j}}^{\boldsymbol{e}}$ :

Model regression coefficient for MOE (e) at speed power (i) and acceleration power (j) for positive accelerations

${\boldsymbol{M}}_{\boldsymbol{i},\boldsymbol{j}}^{\boldsymbol{e}}$ :

Model regression coefficient for MOE (e) at speed power (i) and acceleration power (j) for negative accelerations

u :

Vehicle instantaneous speed

a :

Vehicle instantaneous acceleration rate

q :

Traffic stream flow (veh/h)

k :

Traffic stream density (veh/km)

u :

Traffic stream space-mean speed (km/h)

u _f :

Expected traffic stream free-flow speed (km/h)

u _c :

Expected traffic stream speed-at-capacity (km/h)

k _j :

Expected traffic stream jam density (veh/km)

q _c :

Expected traffic stream capacity (veh/km)

c ₁ :

Model coefficient (km/veh)

c ₃ :

Model constant (h/km² -veh)

c ₂ :

Model constant (h^-1)