100

ically (e.g., DYNASMART, INTEGRATION), or macroscopically(e.g., INDY, MARPLE).

As part of simulation-based DTA models, route choice modelstypically describe optimizing travel behavior (i.e., minimizing gen-eralized travel costs). In these models, travelers may select their routesbefore departure, anticipating known (recurring) network conditions(referred to as pretrip route choice). Or, travelers adjust routes dur-ing their trip, responding to the network conditions they (unexpect-edly) encounter (referred to as en route route choice). Unexpectednetwork conditions include, for instance, regular travel time varia-tions, adverse weather conditions, incidents, and accidents. In thepretrip route choice model, routes are stored, and vehicles can betracked from origin to destination. Travelers cannot deviate fromtheir pretrip chosen routes but can possibly iteratively update pre-trip chosen routes such that each traveler chooses his or her best route(user equilibrium state). In the en route route choice model, travel-ers can continuously adjust their routes by choosing only the nextlink to their destination. However, their routes are unlikely to be thebest routes in terms of actual travel time because no equilibrium stateis reached.

In reality, the distinction between minimizing costs pretrip anden route is not definite, because travelers are most likely to considerboth making pretrip route choice decisions and deviating from thisroute in response to information received about a more attractive route(e.g., via a variable message sign, route guidance panels, or radio).These different kinds of behavior also may be expressed in parallel,because some travelers receive information about current networkconditions (e.g., in-car navigation system users) such that they mayupdate their routes, whereas others do not. Therefore, in variousreal-life cases, it would be necessary to combine both model types,where people follow a certain route but still have the opportunity todeviate from that route. For example, in the case of route guidance,a route can be prescribed to travelers, and they may prefer to followthat route until they feel that another route would be better, accord-ing to observed current traffic conditions. Another example wouldbe prescribed routes in evacuation planning, where each evacuee isordered to follow a certain route. Depending on the enforcementand the current threat level, travelers will follow these instructions,completely ignore them, or do something in between. These situationswould coincide with modeling pretrip route choice, en route routechoice, or a combination of the two. As a last example, in several DTAmodels that include queuing and spillback, gridlocks are a potentialproblem. The problem arises mainly with intermediate route flowsthat have not yet converged to a user equilibrium state and thereforethe flow rate on some routes in a specific iteration is too high. Grid-locks may occur in practice but typically are resolved by travelersturning around or taking detours. This en route route choice behavioris typical and is not modeled in DTA models that usually have onlypretrip route choice.

Hybrid Route Choice Modeling in Dynamic Traffic Assignment

Adam J. Pel, Michiel C. J. Bliemer, and Serge P. Hoogendoorn

Dynamic traffic assignment (DTA) models typically describe travelersselecting their routes before departure (pretrip) or during the trip (enroute). However, in reality, people follow a certain route but have theopportunity to deviate from that route. An analytical hybrid routechoice model is proposed that unifies pretrip and en route route choicein a tractable way. It enables modeling intermediate states where trav-elers make pretrip route choice decisions and may deviate from thisroute if they receive information about a more attractive route, forinstance, because of unforeseen adverse traffic conditions. The hybridroute choice model is widely applicable to various planning and man-agement applications in DTA and makes the DTA model more realisticin cases such as route guidance problems, where the combination of pre-scribed routes and en route route choice is evident. Furthermore, theproposed route choice model is generic because different dynamic traf-fic flow models can be used in the model, analytical or simulation-based.Also, two common problems in DTA related to gridlock and time-varyingnetwork conditions are solved in the hybrid route choice model.

Dynamic traffic assignment (DTA) models focus on estimatingtime-varying network conditions by describing the route choicebehavior of travelers on an infrastructure network and how the traf-fic dynamically flows over the network. Peeta and Ziliaskopoulos(1) and more recently Sisiopiku and Li (2) give comprehensiveoverviews of DTA approaches, including a discussion of current andfuture challenges in DTA research and applications.

Two classes of DTA models generally are distinguished: analyticaland simulation-based. Analytical models are directly solved by usingwell-known optimization techniques (e.g., mathematical programmingor control theory approaches) or by formulating the model as a varia-tional inequality problem. Examples include the models proposed byRan and Boyce (3), Chen and Hsueh (4), and Bliemer and Bovy (5).These models usually are limited to relatively small infrastructurenetworks because they use solution procedures that do not takeadvantage of the specific characteristics of the transportation prob-lems. In contrast, simulation-based models are designed specificallyfor transportation problems and can handle large, realistic networks.Simulation-based DTA models are widely available and can define theproblem microscopically (e.g., PARAMICS, AIMSUN2), mesoscop-

Department of Transport and Planning, Faculty of Civil Engineering and Geosciences,Delft University of Technology, P.O. Box 5048, 2600 GA Delft, Netherlands. Dualaffiliation for M. C. J. Bliemer: University of Sydney, Faculty of Business and Eco-nomics, Institute of Transport and Logistics Studies (ITLS), 144 Burren Street,Newtown, New South Wales 2006, Australia. Corresponding author: A. J. Pel,a.j.pel@tudelft.nl.

Transportation Research Record: Journal of the Transportation Research Board,No. 2091, Transportation Research Board of the National Academies, Washington,D.C., 2009, pp. 100–107.DOI: 10.3141/2091-11

Pel, Bliemer, and Hoogendoorn 101

In this paper, an analytical model that combines pretrip and enroute route choice is introduced in which travelers follow routes butcan deviate if necessary. In this hybrid route choice model, the pretrip-computed route flow rates are updated online (i.e., during executionof the dynamic traffic flow model) at every network intersection forall routes in the dynamic route choice sets. An additional term is intro-duced into the generalized route cost function to include the travel-ers’ reluctance to deviate from their initial routes. A single parameterwill then dictate their actual route choice behavior: completely pre-trip, completely en route, or somewhere in between. It enables com-puting an equilibrium assignment by allowing pretrip route decisionsonly, a nonequilibrium situation with only en route decisions, or anystate in between.

This paper is structured as follows. First, a concise overview isgiven of previous approaches of both pretrip and en route route choicemodeling in DTA models. Then, the mathematical formulation ofthe proposed hybrid route choice model is discussed. Next, severalillustrative examples are given. A case study is presented to showthe feasibility of the model in real-life DTA applications. Finally, it isconcluded that the proposed hybrid route choice model is widelyapplicable because of its generic setup and also is capable of solvingcommon problems with possible gridlock and time-varying networks.

ROUTE CHOICE MODELING APPROACHES IN DTA MODELS

Pretrip Route Choice

In pretrip route choice models, it is assumed that travelers choose theirroutes from origin to destination at the time of departure and do notswitch routes while traveling. It relates to nonequilibrium pretripassignment because the chosen route may not be the fastest or thecheapest when network conditions deviate from expected condi-tions. A difference in network conditions would yield an incentive tochange to a different route if the traveler were aware of the prevailingconditions.

An iterative procedure is used that allows travelers to choose adifferent route on the basis of experienced route travel times andcosts in the next iteration, instead of en route. Repeating this processleads to a user equilibrium assignment in which no traveler can uni-laterally switch routes and be better off (Wardrop’s equilibrium law).Pretrip route choice models in an iterative equilibrium frameworkare widely available and are being used for many DTA applications,but mainly for long-term planning purposes in which travelers areassumed to have information about future traffic conditions based onpast experience.

En Route Route Choice

The assumption that travelers cannot deviate from their (pretrip)chosen route is relaxed in the case of en route route choice. Travel-ers observe current traffic conditions when they travel and makeroute choice decisions based on the current traffic state. Hence, theymay deviate from the route originally planned at the start of the trip.Such en route route choice behavior is likely to be more realistic thanpretrip route choice behavior and is used mainly for traffic manage-ment. It is assumed that travelers have limited information and thatthe available information mainly relates to the current traffic condi-tions. Therefore, it is often assumed that instead of basing their deci-sions on the actual travel costs, travelers choose their routes on thebasis of instantaneous travel costs, predicted travel costs, or routeguidance. No iterative procedure is applied. Instead, a one-shotsimulation is assumed.

Previous approaches in en route route choice modeling explain trav-elers’ en route decisions heuristically, for instance, by applying a setof fuzzy rules (6), a recurrent neural network (7), or a fuzzy network(8) or describing en route route choice as a discrete choice model orprobabilistic model where travelers may either continue their pretriproutes or comply and follow the en route instructed route (9, 10). Com-pared with these former approaches, the analytical route choiceapproach proposed here has the advantage of being (mathematically)tractable and enables modeling intermediate states, in which travelersdo not choose the en route fastest route or the pretrip route but some-thing in between, making a trade-off between continuing the pretriproute and possibly saving travel time by switching routes.

HYBRID ROUTE CHOICE MODEL

A transport network G = (N, A), is given in which N is the set of net-work nodes and A the set of network links (arcs). The modeling timehorizon is given by set T. Furthermore, a set of origin nodes R ⊂ Nand destination nodes S ⊂ N are given. Travel demand (in vehiclesper hour) for a time period K ⊂ T is given for each origin–destination(O-D) pair (r, s) ∈ RS and is denoted for each departure timeinstant k by –Drs(k). The origin and destination nodes are assumed tobe connected with so-called connector links to the network, whichare included in set A.

First, suppose that all travelers have been prescribed a certainroute q. Let Prs(k) be the set of routes that are relevant for O-D pair(r, s) at departure time k (Figure 1b). The demand rate of travelersfrom r to s at departure time k with prescribed route q is given by

D k k D kq qrs( ) = ( ) ( )�π ( )1

Prs (k)

q

(b)(a)

Dq (k)

r sn

Drs (t )

p

Anin

uapq (t )

Anout

nvaq (t ) uaq (t )

a

FIGURE 1 Model variables for (a) nodes and links and (b) routes.

102 Transportation Research Record 2091

In other words, the total travel demand for O-D pair (r, s), which isgiven by –Drs(k), can be distributed according to prescribed route ratesπ~q(k) over the routes q ∈ Prs(k), where evidently ∑q∈Prs(k)π~q(k) = 1.These prescribed route rates may be determined, for example, by aprevious iteration in a DTA model or given exogenously by a routeguidance device or an evacuation plan.

Throughout the paper it is assumed that each route has its ownindex, and once a route is defined, its start and end points also areknown. Therefore, to keep the notation short, indices for origins,destinations, and nodes are left out in case they are implicitly knownthrough the route index. In a DTA model in which one aims to reacha dynamic user equilibrium state, these prescribed route rates aregiven for each O-D pair (r, s) and each q ∈Prs(k) as

For other states, mapping procedures other than the logit model canbe used to determine the prescribed route rates π~q(k) from the gen-eralized costs c~q(k). In this equation, the generalized costs consist ofthe actual experienced route travel times in the previous iteration anda possible route overlap factor to include the effect of correlationbetween routes on route choice behavior:

The actual experienced route travel times can be computed as adynamic sum of consecutive link travel times along the route:

where

δaq(k, t) = dynamic link–route incidence indicator, equal to 1 ifflow on route q departing at time instant k reaches linka at time instant t (equal to 0 otherwise);

θa(t) = link travel time for vehicles entering link a at timeinstant t;

ηq = route overlap factor, taken as the C-logit factor or thepath-size factor (11, 12); and

α̃ and β̃ = behavioral parameters to be estimated.

Even though the routes q have been prescribed to travelers, trav-elers may not comply. If traffic conditions are such that travelers arebetter off (or perceive they will be better off) by deviating to anotherroute, they might do so. If x(t) denotes the current traffic conditions,then the information I which travelers receive on the current condi-tions is I = I(x(t)). Then, travelers have an expected travel time τbased on this information, τ = τ(I). Expected travel time can be pre-dicted travel time, where travelers consider the expected future traf-fic dynamics, or instantaneous travel time, where the current trafficstate is expected to continue for the remainder of the trip. Arguably,route choice is based on a combination of these factors, becausetravelers in fact consider both (certain) local traffic information and(uncertain) predicted traffic information for links farther downstreamthe route. The instantaneous travel time is used here; however, it canbe easily changed to predicted travel time (or a combination) withoutaffecting the hybrid route choice model.

Travelers take into account the instantaneous route travel cost foreach relevant route from the current location to the destination when

�τ δ θq aqa A

T

ak k t t( ) = ( ) ( )∈∑∫ , ( )

04

� � � �c k kq q q( ) = ( ) +ατ βη ( )3

��

�πq

q

q

q P k

kc k

c krs

( ) =− ( )( )

− ( )( )′′∈ ( )∑

exp

exp(22)

making any en-route route choice decisions. All travelers also havea prescribed route q that they may wish to consider. Travelers with thesame prescribed route q can be seen as belonging to the same class oftravelers. Hence, the formulation in this section is actually a multi-class formulation in which each class is a distinct route. The instanta-neous route travel costs cpg(t) are formulated for a route p ∈ Pns(t)from node n to destination s for travelers with prescribed route q(i.e., class q travelers) as follows:

The instantaneous route travel time τp(t) can be computed as

where δap is the static link–route incidence indicator (because instan-taneous travel times are considered here) that equals 1 if link abelongs to route p and zero otherwise, and the route overlap factorηp is defined as in Equation 3.

The structure of Equation 5 is similar to that of Equation 3 exceptfor the last term, which is introduced to account for travelers’ pos-sible reluctance to deviate from the pretrip route q. The term ξpq thusindicates the difference between routes p and q (i.e., the nonoverlap-ping part of the routes). If the difference is small, then route p moreor less follows the prescribed route q, and if the difference is large,then route p deviates significantly from route q. This difference fac-tor can be defined by computing the relative length of route p that isdistinct to route q:

where �a is the length of link a. Here, the difference factor is mea-sured in route length because of good results with analogous over-lap factors (e.g., commonality and pathsize factors). Arguably, othermeasures—such as travel time—can be used. Additional researchand data analysis can show which measure is more appropriate.

The parameter ω ∈ [0, 1� in Equation 5 determines how easilytravelers will deviate from their prescribed route. If ω = 0, then thelast term drops out, and the traveler will completely ignore the pre-scribed route and decide which link to take next at each node. In thelimiting case when ω approximates 1, the last term becomes domi-nating, and travelers will follow the prescribed route exactly and notdeviate from this route, regardless of current traffic conditions. Forall other values, 0 < ω << 1, travelers will show some preference tofollow the prescribed route but may deviate if current traffic condi-tions favor other routes. The behavioral preferences in trade-offs aredetermined by the parameters α, β, and ω.

Given the generalized instantaneous cost function in Equation 5,the probability of choosing route p ∈ Pns(t) from current node n todestination s at time instant t is determined by

Note that the route choice sets Pns(t) are time-dependent, because thechoice set includes all routes from node n to destination s relevant

π pqpq

p q

p P t

tc t

c tns

( ) =− ( )( )

− ( )( )′′∈ ( )∑

exp

exp(88)

ξδ δ

δpq

aq ap aa A

ap aa A

=−( )

∈

∈

∑∑1

7�

�( )

τ δ θp apa A

at t( ) = ( )∈∑ ( )6

c t tpq p p pq( ) = ( ) + +−

⎛⎝⎜

⎞⎠⎟

∈[ ]ατ βη ωω

ξ ω1

0 1 5, ( )

at time t. Therefore, these sets are repeatedly generated during modelexecution on the basis of the current traffic conditions.

Because travelers do not have to follow route p strictly, only thefirst link of this route is of interest. A new decision will be made atthe next node. The link inflow rate for travelers with prescribedroute q is determined by multiplying the class q travel “demand” bythe probabilities in Equation 8. The class q travel demand for linksstarting at the origin node n ∈ R is given by Dq(t) in Equation 1,whereas for other nodes n ∈N \R this travel demand is determinedby the outflowing vehicles from the links upstream to node n. Math-ematically, for all a ∈ An

out, the route-specific inflow rate at timeinstant t of vehicles with prescribed route q choosing route p (or atleast the first link) is computed as

where Anout is the set of links with tail node n and An

in is the set of linkswith head node n (Figure 1a). The class q outflow rates va′q(t) are inde-pendent of the route taken to arrive at node n. Also, it is not importantto know which route the link inflow rates are following; only the firstlink of route p is of importance. Hence, the total link inflow rate fortravelers with prescribed route q is

The mapping from uaq(t) to vaq(t) is determined by the dynamictraffic flow model used. It can be an analytical dynamic networkloading (DNL) procedure (13) or a (micro)simulation. The traffic flowmodel propagates the traffic flow over the link and takes into accountpossible capacity and spillback constraints.

The total link inflow and outflow rates are merely summations overall classes of prescribed routes:

By definition, the cumulative inflows and outflows (in vehicles) attime instant t are given by

Assuming that the first-in, first-out (FIFO) property holds (and ittypically does for analytical queuing models with a single vehicletype), the link travel times can be determined by

For simplicity, the hybrid route choice model is formulated herefor a single vehicle type. Multiple vehicle types (e.g., cars, buses,and trucks) can be modeled by adding the index m to the variables

θa a at V U t t( ) = ( )( ) −−1 15( )

V t v ta a

t( ) = ( )∫ dt0

14( )

U t u ta a

t( ) = ( )∫ dt0

13( )

v t v ta aq

p P tr s RS rs

( ) = ( )∈ ( )( )∈∑∑

,

( )12

u t u ta aq

q P tr s RS rs

( ) = ( )∈ ( )( )∈∑∑

,

( )11

u t u taq apq

p P tns

( ) = ( )∈ ( )∑ ( )10

u t

t D t n R

t v tapq

ap pq q

ap pq a q( ) =

( ) ( ) ∈

( ) (′

δ π

δ π

if

)) ∈

⎧⎨⎪

⎩⎪ ′∈∑ if

i

n N Ra An

\( )

n

9

in the formulas above. The dynamic travel demand is given by vehi-cle type; the travel times, generalized route costs, route flow rates,and link inflow and outflow rates are computed for each vehicletype; but the total link flows must be aggregated over all vehicletypes. Note that by this procedure it is implied that FIFO holds onlywithin each vehicle type and not across vehicle types, which is a rea-sonable assumption. Most (micro)simulators and the DNL modelproposed by Bliemer can account for multiple vehicle types (13).

Pretrip Route Choice Model (Special Case � → 1)

The pretrip route choice model is illustrated as a special case of thehybrid route choice model in which ω approaches boundary value 1.In the limiting case that ω → 1, the generalized costs are predomi-nantly determined by the route difference factor ξpq. This value willequal zero if p = q and is greater than zero otherwise. Therefore, theroute choice probabilities πpq(t) will be 1 if p = q and zero otherwise.Equations 9 and 10 simplify to

Equations 1 through 4 and 11 through 16 define the usual pretrip routechoice model.

En Route Route Choice Model (Special Case � � 0)

If ω = 0 is chosen, then the en route route choice model results. Theroute difference ξpq is no longer relevant; therefore, the prescribedroute q no longer plays a role in travelers’ route choice behavior andcan be dropped as an index. However, the travelers’ destinationsremain important; hence the index s is used (instead of q) to makesure that all travelers reach their destinations. Equations 9 and 10simplify to

Equations 5 through 8, 11 through 15, and 17 define the en route routechoice model.

MODEL APPLICATION

For illustration purposes, the hybrid route choice model describedabove was applied to the network taken from Chen (14) (Figure 2a).The example network contains two origins r, one destination s, andnine links. Excluding circular routes, travelers departing from theleftmost origin choose from four possible routes, whereas travelersfrom the other origin have two possible routes. For simplicity, thelink characteristics of all network links are set to be equal, wherecapacity = 2,000 veh/h, free speed = 100 km/h, length = 10 km, andqueue density = 200 veh/km. The connector links differ in capacity(infinite) and length (2 km).

Three assignments were computed, varying travelers’ informa-tion; these assignments are discussed in the following sections. The

u t

t D t n R

tas

ap prs

p P t

ap p

ns

( ) =

( ) ( ) ∈

(∈ ( )∑ δ π

δ π

if

)) ( ) ∈

⎧

⎨⎪⎪

⎩⎪⎪ ∈ ( )

′′∈

∑ ∑p P t

as

a Ansn

v t n N Ri

ifn

\(177)

u tD t a

aq

q( ) =( ) if link is the first link on rroute

if link is the previous l

p

v t aa q′ ( ) ′ iink on route p

⎧⎨⎪

⎩⎪( )16

Pel, Bliemer, and Hoogendoorn 103

104 Transportation Research Record 2091

discussion refers to the paths marked in Figure 2b. In Figure 3, theline style in the plots distinguishes the flow rates and travel timeson the four paths. The DNL model applied to this example is theanalytical procedure that includes dynamic queuing and spillback,explained by Bliemer (13).

Pretrip User Equilibrium (Full Future Information)

The pretrip user equilibrium assignment corresponds to the case inwhich travelers have full information about (and will anticipate)future traffic conditions. This type of anticipative travel behavioroften is assumed in long-term planning applications, for instance,

network design problems and land use modeling. For the assign-ment, set ω → 1 and let the DTA model iteratively converge to adynamic user equilibrium (DUE). As shown in Figure 3a, the actualexperienced path travel times (dark graphs) are equal for all pathswith inflow larger than zero and not higher than the path travel timeson any unused path, reflecting the DUE state.

Pretrip User Equilibrium with En Route RouteChoice (Historical and Current Information)

The pretrip user equilibrium assignment with en route route choiceprescribes pretrip routes (where they would lead to an equilibrium)

1 2

3 4r s

r

(b)(a)

FIGURE 2 Example (a) network and (b) paths.

00

500

1000

1500

2000

2500

3000

10 20 30 40 50 60 70 80

time [min]

flow

rat

e [v

eh/h

]

0

10

20

30

40

50

60

70

80

trav

el ti

me

[min

]

0 10 20 30 40 50 60 70 80

time [min]

00

500

1000

1500

2000

2500

3000

10 20 30 40 50 60 70 80

time [min]

(b)

(a)

flow

rat

e [v

eh/h

]

0

10

20

30

40

50

60

70

80

trav

el ti

me

[min

]

0 10 20 30 40 50 60 70 80

time [min]

FIGURE 3 Flow rates and travel times from application of hybrid route choice model: (a) pretrip user equilibrium(� → 1), (b) pretrip user equilibrium with en route route choice (� � 0.7).

(continued on next page)

to travelers but also allows travelers to deviate from their routeswhile en route in case a more attractive route is available based oncurrent traffic conditions. It corresponds to the case in which trav-elers have historical information (e.g., personal experience) and cur-rent information (e.g., from dynamic route information panels orradio) about traffic conditions.

Depending on the setting of the parameter ω, travelers will con-sider more or less the current conditions to deviate from the pre-scribed pretrip route. Here the DTA model was run for a singleiteration for ω = 0.7 and ω = 0.3. For ω = 0.7 (plotted in Figure 3b),path inflows generally follow pretrip route inflows (Figure 3a), andflows deviate to another path only when the instantaneous traveltime on that path (lighter graphs) is lower than the instantaneous traveltime on the current route (even though the actual path travel time[dark graphs] may be higher). This effect is larger for smaller valuesof ω, as seen from the plots for ω = 0.3 (Figure 3c). With decreasingω, the flow rates resemble the route flows en route (Figure 3d).

The pretrip route flows may not result in the user equilibrium statebut lead to a system optimum assignment. This assignment is appro-priate in dynamic traffic management applications, such as routeguidance problems and controlled emergency evacuation, where itis assumed that travelers have prescribed routes based on the sys-

tem optimum and current information about the traffic conditions.Although pretrip route flows based on system optimum potentiallylead to lower system costs, it is no longer ensured if route choiceen route is allowed. However, the hybrid route choice model can beused to investigate the efficiency of the route guidance system givendifferent levels of traveler compliance.

En Route Route Choice (Current Information)

The route choice en route assignment applies to the case in whichtravelers have information about (and can only respond to, notanticipate) only current traffic conditions. This type of reactivebehavior usually is assumed in situations where travelers are con-fronted with unexpected traffic conditions and no management (inparticular, route guidance) is available (yet). It may be the casefor an incident, accident, or voluntary emergency evacuation (andin-car navigation systems in which the instructed route is updated inresponse to current traffic conditions).

For the second assignment, ω = 0 was set and the DTA modelwas run for a single iteration. Because travelers respond to instan-taneous path travel times (gray graphs), travel times are equal for all

/ / / flow rate or actual travel time on respectively path 1, 2, 3, 4

/ / / instantaneous travel time on respectively path 1, 2, 3, 4

00

500

1000

1500

2000

2500

3000

10 20 30 40 50 60 70 80

time [min]

flow

rat

e [v

eh/h

]

0

10

20

30

40

50

60

70

80

trav

el ti

me

[min

]

0 10 20 30 40 50 60 70 80

time [min]

00

500

1000

1500

2000

2500

3000

10 20 30 40 50 60 70 80

time [min]

(c)

(d)

flow

rat

e [v

eh/h

]

0

10

20

30

40

50

60

70

80

trav

el ti

me

[min

]

0 10 20 30 40 50 60 70 80

time [min]

FIGURE 3 (continued) Flow rates and travel times from application of hybrid route choice model: (c) pretripuser equilibrium with en route route choice (� � 0.3), and (d) en route route choice (� � 0).

Pel, Bliemer, and Hoogendoorn 105

106 Transportation Research Record 2091

used paths and not higher than the path travel times on any unusedpath (Figure 3d). Note that the actual path travel times (black graphs)will most likely not be equal for all used paths (i.e., DUE is notreached).

APPLICATION

To illustrate the feasibility of the hybrid route choice model on a rea-sonably large real-life network, the model was programmed inMatlab and implemented in the EVAQ evacuation traffic simulationmodel described by Pel et al. (15). A case study was conducteddescribing a flood evacuation in the area of Zeeland, Netherlands(Figure 4). In total, the more than 200,000 people who live on the560 km2 peninsula are forced to evacuate in a limited amount of time.The network consists of approximately 150 nodes and 500 directedlinks. In total 51 zones contain an origin, and the endangered areacan be exited to 4 safe destinations. The aim of the study was todesign and evaluate different evacuation strategies (consisting ofan instructed departure time window, safe destination, and evac-uation route for all inhabitants) to minimize the expected numberof casualties as well as the duration of the evacuation.

Because of the hybrid route choice model presented in this paper,in the model application, travelers can follow prescribed pretripevacuation routes to prescribed safe destinations (exit points) butalso may deviate and make en route decisions to change their routesand destination, making it realistic. Furthermore, the hybrid routechoice model enables modeling link failure (e.g., links that becomeinaccessible because of flooding), which is not possible in otherevacuation models. (In other models, travelers need to follow thepretrip routes and cannot deviate from these routes during the load-ing process, so the DNL model comes to a halt when links can nolonger be used during simulation.) Both these latter two features are

a consequence of the hybrid route choice model and enhance theapplication domain of the EVAQ evacuation traffic model.

With a time step of 10 s applied in the case study traffic simulation(with a simulated time horizon of 30 h), the running time on a PC withWindows XP and a 2.2-GHz processor ranged from 5 to 12 min com-puter processing unit (CPU) time and required 70 to 370 MB of RAM,depending on the traffic assignment, as seen from the table below:

RAM Usage Assignment CPU Time (s) (MB)

Pretrip route choice 322 304(special case ω → 1)

Pretrip + en route route 721 370choice (0 < ω < 1)

En route route choice 396 74(special case ω = 0)

Here, pretrip route choice assignment corresponds to a mandatoryevacuation in which travelers follow prescribed routes. The com-bined pretrip and en route route choice assignment corresponds to arecommended evacuation in which travelers are instructed to followprescribed routes but may choose to deviate from these routes ifanother route is (sufficiently) more attractive based on current traf-fic conditions. The en route route choice assignment corresponds toa voluntary evacuation in which travelers choose routes during theirtrips in response to current traffic conditions. The CPU time forthe hybrid route choice model does not grow exponentially but isapproximately the summation of CPU times for the pretrip case andthe en route case. The reason is that the individual traffic flows fol-lowing a prescribed route are tracked (not tracked in the en routecase), and the route choice set generation during the DNL procedureis needed because travelers may deviate from their routes (omittedin the pretrip case).

Note that the CPU time for the hybrid route choice model doesnot grow exponentially; it is approximately the summation of CPU

FIGURE 4 Zeeland evacuation network.

time for the pretrip and the en route route choice cases, because here,neither of the mentioned factors is in place. The same applies for thememory requirements. For the pretrip and en route route choice assign-ment, CPU time and RAM usage are proportional to the number ofprescribed pretrip routes, because most link and node variables arecomputed for each class of travelers with the same prescribed route q.

DISCUSSION AND CONCLUSIONS

The proposed hybrid route choice model combines pretrip and enroute route choice and allows the modeling of intermediate states. Itis widely applicable to various DTA planning and managementapplications and makes the DTA model more realistic in cases suchas route guidance problems, where the combination of prescribedpretrip routes and en route route choice is evident. Furthermore,the route choice model described here is generic because differentdynamic traffic flow models, both analytical and simulation-based,can be used.

Two common problems in DTA related to gridlock and time-varying network conditions are solved in the hybrid route choicemodel. First, DTA models typically merely propagate travelers overthe given routes, and travelers cannot deviate from their routes dur-ing the loading process. In models that use queuing and spillback,this approach may lead to gridlocks. Gridlocks cause significantproblems in the model because propagation halts; thus travel timescannot be computed and no equilibrium can be determined.

The proposed hybrid route choice model allows for en route routechoice decisions such that in the case of a gridlock, travelers maydecide (with some penalty) to deviate to a different route (e.g., turnaround and circumvent the gridlock). The DTA model is not halted,and travel times can be computed. Note that these higher travel costs(due to detours and penalties for deviating from the initial route)will lead to different pretrip route choice decisions such that in theend an equilibrium still can be determined (where the equilibriumsituation does not have gridlock or circular routes). Because thepretrip route choice model is based on experienced traffic conditions(whereas the en route route choice model is based on current trafficconditions), the equilibrium state for pretrip assignment is not equalto the equilibrium state for the assignment with pretrip and en routeroute choice. However, the Wardrop user equilibrium still can bereached by fading out the en route route choice over subsequentiterations (i.e., ω → 1 as duality gap → 0).

For the second problem, the hybrid route choice model enablesmodeling a time-dependent network in which travelers cannot fore-see local adverse conditions and therefore can only respond to themas they occur and not unrealistically anticipate them. Local adverseconditions can be caused by, for instance, incidents, accidents, or theeffects of a natural disaster (as in the emergency evacuation applica-tion described earlier). This model merit holds for all time-varyingnetwork conditions, such as free speeds, capacities, and flow direc-tion if contraflow is applied during evacuation. Also, it can modellink failure, which usually cannot be handled for reasons similar tothose for gridlock.

Finally, the proposed model has the same computational com-plexity as the pretrip route choice model, which also must keep track

of all routes for all O-D pairs; however, it requires additional com-putation time and memory to construct and store route sets Pns(t).Hence, the greater flexibility in route choice modeling comes at theprice of increased computation time and slightly increased memoryrequirements, as shown and discussed in the model application.

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The Transportation Network Modeling Committee sponsored publication of thispaper.

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