A simulation-based multiclass, multimodal traffic assignment model with departure time for evaluating traffic control plans of planned special events

  


    




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Transportation Research Procedia 00 (2017) 000–000

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Transportation Research Procedia 25C (2017) 1352–1379 www.elsevier.com/locate/procedia

World Conference on Transport Research - WCTR 2016 Shanghai. 10-15 July 2016

A simulation-based multiclass, multimodal traffic assignment model with departure time for evaluating traffic control plans of planned special events Yun-Zhu Lin a,*, Wei-Hao Chen aa

Department of Civil Engineering, Chung Yuan Christian University, 200 Chung Pei Road, Chung Li District, Taoyuan, 32023, Taiwan

Abstract Different types of traffic control plans can be proposed to reduce the traffic impact of planned special events. The simulationbased, multi-class, multi-modal traffic assignment model with departure time windows can be used to forecast the occurrence time and the level of traffic congestion produced by a planned special event. Using Cube Voyager, a mesoscopic and systematic assessment tool is developed to explore participant behaviours of planned special event for mode and departure time window choices, evaluate event scenarios, and duplicate what happened during previous planned special events for a better understanding of the related issues. Peak traffic volumes and traffic congestion generated by the planned special event are successfully estimated in this study. The impacts of a planned special event and the mitigation measures for various traffic control plans are also established successfully in this study. How far restrictions on turning movements are needed, when traffic control needs to start, and what value there is in the headway of feeder buses needs are also determined in these stage-by-stage traffic control plans. © 2017 The Authors. Published by Elsevier B.V. © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of WORLD CONFERENCE ON TRANSPORT RESEARCH SOCIETY. Peer-review under responsibility of WORLD CONFERENCE ON TRANSPORT RESEARCH SOCIETY. Keywords: mesoscopic transportation planning; dynamic traffic assignment and simulation; planned special event traffic; traffic control plans

1.
     Planned special events (PSE) include sporting events, concerts, festivals, and conventions occurring at permanent multi-use venues as well as less frequent public events occurring at temporary venues, such as parades, fireworks displays, bicycle races, sporting games, motorcycle rallies, and seasonal festivals. Unlike emergency special events

* Corresponding author. Tel.: +886-3-2654210; fax: +886-3-2654299. E-mail address: [email protected] 2214-241X © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of WORLD CONFERENCE ON TRANSPORT RESEARCH SOCIETY.


2352-1465 © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of WORLD CONFERENCE ON TRANSPORT RESEARCH SOCIETY. 10.1016/j.trpro.2017.05.161

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(ESE), PSEs occur at known locations and at scheduled times. PSEs create an increase in travel demands and produce significant site-specific or even regional impacts such as severe traffic congestion or transit overcrowding. Related transportation system operations are also affected, such as freeway operations, arterial and other street operations, transit operations, and pedestrian flow (FHWA, 2009). Authorities must manage the intense travel demands of PSEs to order to maintain transportation system safety, mobility, and reliability. The challenges they face include mitigating potential capacity constraints, accommodating heavy pedestrian flow, and influencing the utility associated with various travel choices. Unlike traditional travel demand models, event-generated travel demand modeling highlights the temporal distribution of travel demands (Yaun et al., 2009; Kuppam et al., 2010). Event time and duration (e.g., specific start time, abrupt end time, continuous operation), event time of occurrence (e.g., day/night, weekday/weekend), participants accommodation (e.g., reserved seating, general admission), and event type (e.g., sports/concert, fair/festival, parade/race) will influence traffic arrival and departure rates (Tringides, 2004). Event-generated travel forecast analysis involves event traffic generation, modal split, and traffic arrival rate (FHWA, 2007). Macroscopic, mesoscopic and microscopic approaches are three basic models of traffic network. They are distinguished primarily by their ability to model the scale of an impact area and the detail level of analysis. Macroscopic traffic models can represent a whole urban region and are useful in analyzing large-scale events. They evaluate congestion using speed-flow curves. However, macroscopic traffic models are not time sensitive. They are difficult to use if a better understanding of queue formation on specific roadway links is desired and very specific traffic control plans want to be implemented. In the other way, microscopic traffic models are useful in analyzing particular roadway segments and corridors where the vehicles have their own characteristics and respond to the presence of other vehicles and to traffic control devices. They simulate individual vehicle trajectories on a detailed network and use behavior models (e.g. car following, gap acceptance) to predict second-by-second driver responses to enroute events. Thus, microscopic traffic models are useful in modeling smaller aspects of a network and in providing very precise results. However, they are inapplicable to represent large geographic areas because they are difficult to be calibrated at the regional level. In between these two modeling approaches are mesoscopic traffic models which can represent larger geographic areas than microscopic traffic models and allow for more precise and time sensitive results than macroscopic traffic models. Mesoscopic traffic models simulate movement of trips along their routes at some detailed resolution (packets) and discretely model traffic queues in network at bottlenecks. Traffic stream performance is still evaluated using aggregate macroscopic (e.g. speed-flow) relationships. According to the efficiency and accuracy of three traffic network models, we think that mesoscopic simulation models are more applicable as a means to build event scenarios and duplicate what happened during previous PSEs to better understand what traffic control actions should be taken in future PSEs. To our knowledge, there have been very few studies in the transportation literature that have jointly modeled these travel decisions
of event-generated travel choices. The purpose of this study is to explore PSE participants’ behaviors regarding mode and departure time window choices and to estimate peak traffic volumes and traffic congestion generated by the event. This will help agencies develop effective traffic control plans to reduce traffic impact of PSE. We propose a mesoscopic simulation model to evaluate traffic impacts generated by PSE and mitigation measures reduced by traffic control plans. Nomenclature

ca ( k )

k 2'

' C rsn jp ( t )

k 2'

k 2' Cˆ prsn ' ( t )

d rsj

Ej Eb

f jprsn ' ( t )

travel time of link a at time interval k at iteration k2’ path travel time from origin r to destination s using private mode j and driving on path p, which departs at time interval t and is expected to arrive at time window n’ at iteration k2’ path travel time from origin r to destination s using bus line p, which departs at time interval t and is expected to arrive at time window n’ at iteration k2’ a travel distance from origin r to destination s using private mode j a passenger car equivalent of private mode j a passenger car equivalent of buses

k 2'

path flows from origin r to destination s using private mode j and driving on path p, which depart

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k 2' fˆprsn ' ( t )

f

rs p

(t )

f

srn

(t )

jp

k 2'

k 2'

k 2'

(t ) k1' gˆ rsn ' ( t ) k1' ' qrsn j (t ) k1'

rsn ' j

qˆ rsn ' (t )k1'

q srj ( n )

k 1'

( n)

k 1'

qˆ

expected to arrive at time window n’ at iteration k2’ (PSE ingress trips) path flows from origin r to destination s driving on path p, which depart at time interval t at path flows from destination s to origin r using private mode j and driving on path p, which depart at time interval t and are
expected to depart at time window n at iteration k2’ (PSE egress trips)

fˆ p ( t )

sr

at time interval t and are
expected to arrive at time window n’ at iteration k2’ (PSE ingress trips) path flows from origin r to destination s using bus line p, which depart at time interval t and are

iteration k2’ (daily trips)

srn

g

path flows from destination s to origin r using bus line p, which depart at time interval t and are expected to depart at time window n at iteration k2’ (PSE egress trips) k1' ' auxiliary variables of PSE ingress trips qrsn j (t ) auxiliary variables of PSE ingress trips qˆ rsn ' (t ) k1' PSE ingress trips from origin r to destination s using private mode j, which depart at time interval t and are expected to arrive at time window n’ at iteration k1’ PSE ingress trips from origin r to destination s using a bus, which depart at time interval t and are expected to arrive at time window n’ at iteration k1’ PSE egress trips from destination s to origin r using private mode j, which are expected to depart at time window n at iteration k1’ PSE egress trips from destination s to origin r using a bus, which are expected to depart at time

q rs (n)

window n at iteration k1’ daily ingress trips from origin r to destination s departing at time window n at iteration k1’

Q rsn '

PSE ingress trips from origin r to destination s and expected to arrive at time window n’

tn* ' − Δ n '

a start time interval for expected arrival time window n’

tn* '

a end time interval for expected arrival time window n’

+ Δn '

ua (k )

inflows of link a at time interval k at iteration k2’

k 2'

(k ) k 2' uˆa ( k )

u

j a

j a

3

u (k )

k 2'

k 2'

uˆ a ( k )
k 2' ua (k )

k 2'

inflows of link a of private mode j at time interval k at iteration k2’ (PSE ingress trips) inflows of link a of buses at time interval k at iteration k2’ (PSE ingress trips) inflows of link a of private mode j at time interval k at iteration k2’ (PSE egress trips) inflows of link a of buses at time interval k at iteration k2’ (PSE egress trips) inflows of link a of daily trips at time interval k at iteration k2’

rsjn ' uapt (k )

k 2'

rsn ' uˆapt ( k )k 2 '

inflows of link a of private mode j at time interval k at iteration k2’, which drive on path p, depart at time interval t, and are expected to arrive at time window n’ (PSE ingress trips from origin r to destination s) inflows of link a of buses at time interval k at iteration k2’, which drive on bus line p, depart at time interval t, and are expected to arrive at time window n’ (PSE ingress trips from origin r to destination s)

srjn

u apt ( k )

k 2'

inflows of link a of private mode j at time interval k at iteration k2’, which drive on path p, depart at time interval t, and are expected to depart at time window n (PSE egress trips from destination s to origin r)

srn

uˆ apt ( k )

k 2'

inflows of link a of buses at time interval k at iteration k2’, which drive on bus line p, depart at

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rs k 2 ' (k ) uapt U

rsn ' j

(t )

k 1'

1355

time interval t, and are expected to depart at time window n (PSE egress trips from destination s to origin r) inflows of link a at time interval k at iteration k2’, which drive on path p and depart at time interval t (daily trips from origin r to destination s) disutility of PSE participants between origin r and destination s using private mode j at iteration

k 1' Uˆ rsn ' ( t )

k1’, which departs at time interval t and is expected to arrive at time window n’ disutility of PSE participants between origin r and destination s using a bus at iteration k1’, which

Tn

departs at time interval t and is expected to arrive at time window n’ a set of time intervals within time window n

Tn

the number of time intervals within time window n

yˆ

feeder bus ticket fare between origin r and destination s

rs

y rsj

variable costs of using private mode j between origin r and destination s

αˆ α α1 α2 α 3jt

a constant of the disutility function for taking a bus departing at time interval t

t 0 jt 0

a constant of disutility function for using private mode j which departs at time interval t a coefficient of disutility function of travel time a coefficient of disutility function of travel costs

β jn '

a coefficient of disutility function of travel distance for using private mode j which departs at time interval t a dispersion parameter that reflects the degree of perception of participants with the variation of

βn'

travel disutility, which uses private mode j and is expected to arrive at time windows n’ a dispersion parameter that reflects the degree of perception of participants with the variation of travel disutility, which uses buses and is expected to arrive at time window n’ the choice split of expected departure time window n of PSE egress trips

γn rsjn ' δ apt (k )

rsn ' δˆapt (k )

(k )

δ

rs apt

δ

srjn apt

k 2'

k 2'

k 2'

if the path flows f jprsn ' ( t )k 2' pass through link a at time interval k, the value equals 1, otherwise the value equals 0 if the path flows fˆprsn ' ( t )k 2' pass through link a at time interval k, the value equals 1, otherwise the value equals 0 if path flows f prs ( t )k 2' pass through link a at time interval k, the value equals 1, otherwise the value equals 0

(k )

k2'

if the path flows f

srn jp

(t )

k 2'

pass through link a at time interval k, the value equals 1, otherwise the

value equals 0 srn

δ apt ( k )

k2'

srn

if the path flows fˆ p

(t )

k 2'

pass through link a at time interval k, the value equals 1, otherwise the

λj

value equals 0 a load factor of private mode j

λˆ k1' ' π rsn (t ) j

a load factor of buses average value of travel times of multiple shortest paths between origin r and destination s using

π ρ

rsn '

(t )

k 1'

private mode j at iteration k1’, which departs at time interval t and is expected to arrive at time window n’ an average value of travel times between origin r and destination s using a bus at iteration k1’, which departs at time interval t and is expected to arrive at time window n’ unit penalty costs for early schedule delay using a bus

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rj

unit penalty costs for early schedule delay using private mode j

 sj

unit penalty costs for late schedule delay using a bus unit penalty costs for late schedule delay using private mode j

' Θ jn ' ( t + π rsn (t )) j

Θ n ' ( t + πˆ

rsn '

(t ))

k 1'

5

schedule delay costs of PSE ingress trips from origin r to destination s using private mode j,

which depart at time interval t and are expected to arrive at time window n’ at iteration k1’ schedule delay costs of PSE ingress trips from origin r to destination s using a bus, which departs

k 1'

at time interval t and are expected to arrive at time window n’ at iteration k1’ 2.
Literature reviews There are several publications that have discussed PSE traffic management (Bertoli, 2008; Carson and Bylsma, 2003; FWHA, 2007a; Frantzeskakis and Frantzeskakis, 2006; Latoski et al., 2003; Yaun et al., 2009; Wojtowicz and Wallace, 2010). However, most focus on guidelines for PSE traffic management. Quite a few also perform realistic applications and case studies. Frantzeskakis and Frantzeskakis (2006) describe how Athens planned and managed their transportation infrastructure to ensure that Olympic participants, spectators, and workers could arrive and depart from their destinations with minimal delays. They developed a traffic simulation and assignment model mainly using the SATURN software. Expected traffic volumes and levels of service for the 2004 Olympic traffic movements were then estimated. Further, arrivals and departures for any combination of user group, venue, and transport mode were determined and then provided for any day and broken into intervals of 30 minutes. They described their successful experiences for how they implemented transportation system management programs after a large number of road and public transportation projects were completed. Thus, the increased capacity of the road network was fully utilized and vehicular movement was decreased as much as possible. Parking control zones, zones of controlled entrance and traffic, Olympic exclusive lanes, and prohibition of conflicting left turns were established according to estimated traffic flows and then implemented successfully. However, detailed models are not presented here. Yaun et al. (2009) developed a multi-class dynamic traffic assignment to support the decision- making for special event transportation planning and management, including simultaneous events held at different places and the 2010 Winter Olympic events. This multi-class DTA model was built on the VISUM platform, and used the Dynamic User Equilibrium (DUE) model embedded within VISUM. The DUE model in VISUM involves a specific focus on pedestrian behavior, route choice, and vehicle pedestrian interactions, including the uneven directional pedestrian flow on sidewalks, the inundation of pedestrians into vehicle space, and the impact of pedestrians on vehicle turning capacities. They lacked event-generated travel demand forecasts, however. Wojtowicz and Wallace (2010) adopted the microsimulation software TransModeler in conjunction with tabletop exercises to present traffic management alternatives for special events to stakeholders, including the evacuation of a minor-league baseball stadium and vehicular egress plans for a large urban indoor arena in New York State's Capital District region. Moreover, they demonstrated that using microsimulation to review possible high-impact, incident scenarios (such as police-controlled intersections, power outages affecting traffic signals, vehicular crashes at the intersection, and overturned truck blocking) could formulate positive improvements to current traffic management procedures. They also lacked event-generated travel demand forecasts. Thus, they focused on a response analysis of traffic incident management. However, a microsimulation model is limited in making consistent route choices for a congested network, as it removes the well-constructed mathematical properties of equilibrium assignment in its static models (Ziliaskopoulos and Peeta, 2002). DTA adequately captures the temporal effects of congestion and the impacts of time-varying demands and supplies of PSEs. In addition, simulation-based DTA models are often more suitable for real-world applications (Peeta and Ziliaskopoulos, 2001; Ziliaskopoulos et al., 2004; Balakrishna, 2006). Simulation-based DTA models have been applied to real-life networks. A number of DTA models (Ben-Akiva et al., 2001; Mahmassani, 2001; Mahut, 2001; Taylor, 2003) have employed mesoscopic supply simulation. Aggregate traffic flow relationships were

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further adopted to model individual vehicle movements. In this study, we apply a simulation-based mesoscopic DTA model to estimate peak traffic volumes generated by a specific event. 3.
A simulation-based PSE travel choice model Trip makers choose their departure times based for expected travel times on their chosen mode and their preferred start/arrival times for their activity (Day, 2008). Departure time and mode choice decisions directly determine the temporal distribution of event-generated demands. These two decisions are inherently connected by the interactions between event timing constraints and expected travel times to and from event venues (Chang and Lu, 2013). Furthermore, because most participants of PSE use the same travel mode when they go to and leave the PSE site. In this study, the simulation of PSE demand choice analytic procedures comprises a multinomial logit model of departure time window/mode choice and a simulation-based dynamic traffic assignment model. Traffic arrival and departure rates during event ingress and egress are estimated in the upper-level model, i.e. the logit model of departure time window/mode choice. According to modal split estimates and vehicle occupancy factors, the number of event-generated trips by personal automobile and public transportation are estimated. The decision ' and of using feeder variables of the upper-level model include the ingress PSE trips of using private modes qrsn j (t ) buses qˆ rsn ' (t ) . They are used to derive the egress PSE trips of using private modes q srj ( n ) and of using feeder

buses qˆ sr ( n ) . Combined with the daily travel demands, these four trips matrices are forwarded to the lower-level model, i.e. the simulation-based dynamic traffic assignment model. The decision variables of the lower-level model include ingress path flows of using private modes f jprsn ' ( t ) , ingress path flows of using feeder buses fˆprsn ' ( t ) , daily p a t h srn flows f prs ( t ) , egress path flows of using private modes f jp ( t ) , and egress path flows of using feeder buses srn

fˆ p (t ) . Then these four sets of time-dependent path flows are conversed to time-dependent link flows. Thus, time-dependent traffic flow patterns, travel times, and travel costs can be obtained and passed to the upper-level model again. These procedures are repeated until a convergence attained. The method of successive averages (MSA), one of the more popular algorithms, is used in attempting to equilibrate these two complex models. 3.1.
Assumptions Consider a transportation network G = (N, A), where N is the set of all nodes, including origin nodes, intersection nodes, and destination nodes, and A is the set of all directed links, including centroid connectors and road links. Event participants are divided into different user classes according to their travel mode and preferred arrival time windows. We assume that the sponsoring organization provides feeder buses to pick up event participants from main transfer stations. Let J denote the set of private travel modes. Let L denote the set of all possible preferred arrival time windows. Let M denote the set of all user classes. Let m1 denote a user class with a specific private travel mode j and preferred arrival time window n’. Let m2 denote a user class with the feeder bus and the preferred arrival time window n’. Hence, there are J ⋅ L + L user classes and we have M = m1 : ( j, l ) ∈ J × L ∪ {m2 : n ∈ L} , where
×

{

}

denotes the Cartesian product. To facilitate the presentation of these essential ideas without loss of generality, the following basic
assumptions are made in this paper: •
The whole simulation period is discretized into n equal time windows T = T1 ∪ T2 ∪ ... ∪ Tn , and Tn is the length of a time window. Each time window is discretized into equal time intervals that are consecutively numbered t ∈Tn = {( n-1) × Tn +1,..., n × Tn } .

•
The choice of departure time window is a pre-trip decision. This assumption is appropriate for assessing transportation policies at a strategic level (Ran et al., 1996; Lam et al., 2006). •
The decision-making process on travel choices for a PSE is rational and follows a hierarchical choice structure. At the first stage of travel choices, the participants first determine the preferred start and end time windows of

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their participation and then select a desirable departure time window and travel mode that will minimize their disutilities from origin to the PSE site. Then, they choose the shortest route in travel time to reach the event site at the second stage of travel choices. •
The modal choices of PSE egress trips are simultaneously considered by the participants when they make the modal choices for PSE ingress trips. When the PSE finishes, they use the same travel mode and depart within a predetermined departure time window to leave the PSE site. Then, they choose the shortest route of travel time to reach their destinations at the third stage of travel choices. •
The parking charge depends on the vehicle type but is independent of parking duration. •
Feeder buses for the PSE have fixed routes, but flexible headways. A set of artificial links are added to connect a set of demand locations and a set of bus stop locations in accordance with the admissibility of a walking distance. 3.2.
The upper-level model: departure time window and travel mode choices Drop-off points of feeder buses are usually near the PSE event site. The travel distance in feeder buses and the walking distance to the site are ignored when we considered the disutility of a PSE participant. Without lost generality, we assume the disutility of a PSE participant using feeder buses is a linear function of path travel time and travel costs. That is, the disutility between origin r and destination s using feeder bus line p which departs at time interval t and is expected to arrive at time window n’ includes average path travel time πˆ rsn ' ( t ) , schedule delay

(

)

costs Θ n" t + πˆ rsn ' ( t ) , and ticket fare yˆ rs . Average path travel time πˆ rsn ' ( t ) represents the average value of travel times of multiple shortest paths between origin r and destination s, which departs at time interval t and is expected to arrive at time window n’. For example, the first five shortest paths are considered. We denote the set of multiple shortest paths as P ' ⊂ P . Schedule delay costs of early or late arrival at destination s can be defined as Eq. (3) (Yang and Meng, 1998; Huang and Lam, 2002).

U

rsn '

(t ) = α 0 + α1π (t ) + α2 ⎡⎢Θn t

rsn '

⎣

πˆ rsn ' (t ) = AVE Cˆ prsn ' (t ) p∈P '

(t + π

rsn '

(t )

) + y ⎤⎦⎥ rs

∀r, s, n ', t

(1)

∀r, s, n ', t

{

(2)

}

⎧ ρ tn* ' − Δ n ' − ⎡t + πˆ rsn ' ( t )⎤ ⎣ ⎦ ⎪ ⎪ rsn ' rsn ' * Θn ' ( t + πˆ ( t ) ) = ⎨σ {t + πˆ ( t ) − tn ' − Δ n ' } ⎪ ⎪0 ⎩

if tn* ' − Δ n ' > t + πˆ rsn ' ( t ) if tn* ' + Δ n ' < t + πˆ rsn ' ( t )

(3)

∀n '

O/W

In contrast, we assume the disutility of a PSE participant using private modes is a linear function of path travel time, travel costs and travel distances without lost generality. That is, the disutility between origin r and destination s using private mode j which departs at time interval t and is expected to arrive at time window n’ includes average ' ' path travel time π rsn ( t ) , variable operation costs of mode y rs , and travel (t ) of , schedule delay costs Θ jn ' t +π rsn j j

(

distance d

)

j

rs . j

(

' ' ' U rsn ( t ) = α0jt + α1π rsn ( t ) + α 2 ⎡⎣Θ jn ' t + π rsn (t ) j j j ' ' π rsn ( t ) = AVE C rsn j jp ( t ) p∈P '

∀r , s, j , n ', t

k 1'

)+ y

rs j

⎤ + α jt d rs ⎦ 3 j

∀r , s, j, n ', t

(4) (5)

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{

}

' ⎧ ρ j tn* ' − Δ n ' − ⎡t + π rsn ( t )⎤⎦ j ⎣ ⎪ ' ' Θ jn ' ( t + π rsn ( t ) ) = ⎪⎨σ j {t + π rsn (t ) − tn*' − Δ n ' } j j ⎪ 0 ⎪ ⎩

1359

' if tn* ' − Δ n ' > t + π rsn (t ) j ' if tn* ' + Δ n ' < t + π rsn (t ) j

∀j , n '

(6)

O/W

' where average path travel time π rsn (t ) represents the average value of travel times of multiple shortest paths j

between origin r and destination s using private mode j, which departs at time interval t and is expected to arrive at time window n’. Travel distance d rsj denotes the distance of the shortest path between origin r and destination s. We now formulate the multinomial logit (MNL) model for the joint choice of mode and departure time window of ingress travel demands (Bhat, 1998). We then have

q

rsn ' j

(t ) =

' U rsn j (t )

−β jn ' e

Q rsn '

λj

∑∑ −β j

qˆ rsn ' ( t ) =

Q rsn ' λˆ

n'

jn '

U rjsn ' ( t )

e

+ ∑ −βn 'e

Uˆ rsn ' ( t )

j

n'

− β n 'e jn '

(7)

∀r , s, n ', t

(8)

n'

Uˆ rsn ' ( t )

∑∑ − β

∀r , s, j, n ', t

U rjsn ' ( t )

e

+ ∑ − β n 'e

Uˆ rsn ' ( t )

n'

And participants make the choice of departure time window of egress travel demands in accordance with the selected travel mode and choice splits of expected departure time window. So we have sr

' q j ( n ) = γ n ∑∑ q rsn (t ) j n'

q

sr

( n ) = γ n ∑∑ qˆ rsn ' ( t ) n'

∀s, r , j, n

(9)

t

∀r , s, n

(10)

t

Note that the expected departure time of egress trips using feeder buses is earlier than the expected departure time of egress trips using private modes because the ending time of the PSE event was too late to take daily buses to travel home. 3.3.
The lower-level model The main advantages of a simulation-based DTA model over an analytical model are based on two characteristics of the former: (1) the realistic modelling of traffic dynamics through vehicle-to-vehicle interactions and (2) the wide range of operational strategies that can be more properly evaluated at the individual vehicle level. In this study, we consequently adopted a mesoscopic and simulation-based dynamic traffic assignment model, Cube Avenue Version 6.1, to load time-varying ingress and egress demands of PSE trips onto a roadway network. Avenue is an optional add-on to Cube Voyager that enables DTA with mesoscopic simulation. Cube Avenue uses a path builder in a capacity-restraint loop to model drivers’ finding their routes and modifying those routes to predict time-dependent costs and flows. In addition, Cube Avenue simulates the movement of vehicles through the network to evaluate the costs generated by a set of routing decisions. Thus, it can reect route choice behaviours and vehicular ow behaviours in the network by considering the time-dependent aspect. The simulation calculates the dynamic user equilibrium path according to the updated travel and delay time from the ow pattern. Cube Avenue algorithms (Citilabs, 2013) are interpreted as follows. The simulation time is divided into smaller time intervals. The travel demand is assumed to be approximately constant during each time slice, but vary between time intervals. The segment-by-segment link and junction times are recalculated on the second and subsequent iterations. Delay for vehicles’ arriving on a link for each time segment can be estimated. Furthermore, dynamic demand is divided into a number of vehicle-packets. Each packet has a start time and a route for each iteration of that assignment. The route is calculated based on the current

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9

estimate for the delays of each time segment and the estimated time of arrival of the packet at each point on its route. Dynamic user equilibrium is achieved through Successive Averages. On each iteration, a new best path is generated along with new packets. Traffic volume is thus equally distributed between all packets. During the ILOOP phase, the path-building algorithm is invoked to calculate routes, and any flows that result from the movement of packets during previous iterations are removed from the volume fields.
The ADJUST phase runs the simulation. The simulation is also run in continuous time (not segment-by-segment). Each link has a storage capacity. At any time, if a packet wishes to move into a link, it must compare the total volume of packets in transit on the destination link. The packets in transit on a link are the packets travelling on the link and plus the packets queuing on the link. If the volume of packets in transit exceeds the storage of the destination link, the packet that is trying to move is blocked and remains queued at its current link until space becomes available. 3.4.
Simulation procedures The simulation procedures for the model are summarized as follows. Step 0: Initial data setting

{ }

Step 0.1: Input the time-window-dependent origin-destination matrix of PSE ingress trips Q rsn ' , the daily time-

⎧ rs ⎫ window-dependent origin-destination matrix ⎨q n ⎬ , and the choice splits of expected departure time window ⎩ ⎭ for PSE egress trips {γ n } .

( )

Step 0.2: Set iteration counter k1’ of the first loop to 1. Set k1’=1. Step 1: Set the initial values of the time-dependent origin-destination matrix for PSE ingress trips

{q

rsn ' j

(t )

k 1'

,q

rsn '

(t )

k 1'

}.

Step 2: Implementation of a simulation-based dynamic traffic assignment

{

' Step 2.1: Update the time-dependent origin-destination matrix for PSE ingress trips q rsn (t ) , q j k 1'

rsn '

(t )

k 1'

} from

the module for the logit model of departure time window/mode choice and calculate PSE egress trips ⎧ k1' sr k1' ⎫ ⎪ sr ⎪ ⎨q j ( n ) , q ( n ) ⎬ . ⎪ ⎪ ⎩ ⎭ sr

q j (n) q

sr

(n)

k 1'

' = γ n ∑∑ q rsn (t ) j n'

k 1'

k 1'

= γ n ∑∑ qˆ rsn ' ( t ) n'

∀s, r , j , n

(11)

∀s, r , n

(12)

t

k 1'

t

Step 2.2: Set the parameters values Set values for the total simulation periods, the length of time intervals, the density of queues, the size of pockets, and the capacity type (inflows or outflows). Step 2.3: Set iteration counter k2’ for the second loop to 1. Step 2.4: Segment-by-segment, perform the dynamic assignment and simulation procedure to load the PSE trips k1' sr k1' ⎫ ⎧ rsn ' k1' rsn ' k1' sr t t ,q ,qj n , qˆ n ⎬ and daily trips q rs ( n ) onto the road network. ⎨q j ⎩ ⎭

()

()

( )

( )

{

}

Step 2.4.1: Set the time interval counter t to 1 and the time window counter n to 1.

10



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k1' rsn ' k1' ⎫ ⎧ ' Step 2.4.2: Assign PSE ingress trips of time interval t ⎨q rsn t ,q t ⎬ to the roadway network and j ⎩ ⎭ determine the corresponding path flows of time interval.

()

∑ f (t ) p

rsn ' jp

∑ fˆ (t ) p

' = q rsn (t ) j

k 2'

rsn ' p

k 2'

=q

rsn '

k 1'

(t )

()

∀r , s, j , n '




(13)

∀r , s, n '




(14)

k 1'

Step 2.4.3: When time interval t is within the time window n, assign one part of daily trips of time window n

{

q

rs

} to the roadway network and determine the corresponding path flows of time interval.

(n)

∑ f (t ) p

rs p

k 2'

1 rs q ( n) Tn

=

(15)

∀r , s

Step 2.4.4: When time interval t is within the time window n, also assign one part of PSE egress trips of time sr k 1' k 1' ⎫ ⎧ sr window n ⎨q j ( n ) , q ( n ) ⎬ to the roadway network and determine the corresponding path flows of time ⎩ ⎭ interval t. srn

k 2'

=

1 sr k 1' q j (n) Tn

k 2'

=

1 sr k 1' q (n) Tn

∑ f (t ) p

jp

srn

∑ f (t ) p

p

∀s, r , j

(16)

∀s, r

(17)

Step 2.4.5: Update link flows of the time interval t according to the path flows obtained at Steps 2.4.2 and 2.4.4. rsjn ' uapt (k ) rsn ' uˆapt (k )

k 2'

rsjn ' = f jprsn ' (t ) ⋅ δ apt (k )

k 2'

k 2' k 2' rsn ' = fˆprsn ' (t ) ⋅ δˆapt (k )

srjn

u apt ( k ) srn

uˆ apt ( k ) rs uapt (k )

k 2'

k 2'

k 2'

k 2'

=f

= f

srn jp

srn p

k 2'

srjn

(t )

k 2'

srn

⋅ δ apt ( k )

rs = f prs ( t ) ⋅ δ apt (k ) k 2'

uaj ( k ) uˆa ( k )

k 2'

k 2'

k 2'

= ∑E j uaj ( k ) j

k 2'

rs

n'

k 2'

n'




(20)




(21) (22)

∀r, s, a, p, k , t k2'

(18) (19)

∀s, r , n, a, p, k , t

.

+ Ebuˆa ( k )

k 2'

j

+∑ E j u a ( k ) +Eb uˆ a ( k ) j

k 2'

k 2'

+ ua ( k )

k 2'

∀a, k

(23)

k 2'

∀j, a, k

(24)

k 2'

∀a, k

(25)

p τ ≤t

rsn ' = ∑∑∑∑ uˆap τ (k ) rs

∀s, r , n, j , a, p, k , t

k 2'

= ∑∑∑∑ uaprsjnτ ' ( k )




∀r, s, n ', a, p, k , t

k 2' k 2' (t ) ⋅ δ apt ( k )

Step 2.4.6: Calculate the link flows ua k

ua ( k )

∀r, s, j, n ', a, p, k , t

p τ ≤t

Yun-Zhu et al. / Transportation (2017) 1352–1379 Lin and Chen/Lin Transportation ResearchResearch ProcediaProcedia 00 (2017)25C 000–000

1362 j

ua (k )

k 2'

ua (k )

k 2'

ua ( k )

srjn

= ∑∑∑∑ u apτ ( k ) sr

srn

n

∀j , a, k

(26)

k 2'

∀a, k

(27)

p τ ≤t

= ∑∑∑ uaprsτ ( k ) rs

k 2'

p τ ≤t

= ∑∑∑∑ u apτ ( k ) sr

k 2'

n

11

k 2'

(28)

∀a, k

p τ ≤t

Step 2.4.7: Update the link travel time ca ( k )k 2' . Step 2.4.8: Check whether the period of time window n is over. If it is, let n = n + 1. Step 2.4.9: Check whether the model period is over. If it is not, let t = t + 1 and go to Step 2.4.2.  t Step 2.5: The time-dependent path flows of PSE trips f rsn jp

dependent path flows of daily trips

{f

rs p

(t )

k 2'

k2'

} are determined.

rsn


fp

t

k2'


f

srn jp

(t )

k 2'

srn


fˆ p

(t )

k 2'

and the time-

Step 2.6: Update path flows and link flows via packet-based implementation. The volumes in the packets generated during the current iteration k2’ will be averaged with the new volume for the old packets. That is,

f jprsn ' ( t )

1 ⎞ rsn ' k 2 ' −1 1 rsn ' k 2 ' ⎛ = ⎜1 − + f jp ( t ) ⎟ f jp ( t ) k 2' ⎝ k 2' ⎠

k 2 ' +1

1 ⎞ ˆ rsn ' k 2 '−1 1 ˆ rsn ' k 2 ' k 2 ' +1 ⎛ = ⎜1 − + fˆprsn ' ( t ) f p (t ) ⎟ f p (t ) k2' ⎝ k2' ⎠ f

srn jp srn

fˆ p

(t )

k 2 ' +1

(t )

k 2' +1

f prs ( t )

k 2' +1

rsjn ' uapt (k )

rsn ' uˆapt (k ) srjn

(29)

∀r , s, n ', p, t

(30)

1 ⎞ srn k 2 '−1 1 srn k 2 ' ⎛ = ⎜1 − + f jp ( t ) ⎟ f jp ( t ) k 2' ⎝ k 2' ⎠

∀s, r , n, j , p, t

(31)

1 ⎞ ˆ srn k 2' −1 1 ˆ srn k 2' ⎛ = ⎜1 − + f p (t ) ⎟ f p (t ) k2' ⎝ k2' ⎠

∀s, r , n, p, t

(32)

1 ⎞ rs k 2'−1 1 rs k 2' ⎛ = ⎜1 − + f p (t ) ⎟ f p (t ) k2' ⎝ k2' ⎠

k 2' +1

k 2' +1

u apt ( k )

∀r , s, j , n ', p, t

k 2' +1

(33)

∀r , s, p, t

1 ⎞ rsjn ' 1 k 2' −1 k 2' rsjn ' k 2' ⎛ f jprsn ' ( t ) δ apt = ⎜1 − + (k ) ∑ ⎟ uapt ( k ) k 2' rsjn ' pt ⎝ k 2' ⎠

∀r , s, n ', a, k , p, t

(35)

srn 1 ⎞ srjn 1 k 2' −1 k 2' srjn k 2' ⎛ f jp ( t ) δ apt ( k ) = ⎜1 − + ∑ ⎟ u apt ( k ) k 2' srjnpt ⎝ k 2' ⎠

∀s, r , j, n, a, k , p, t

(36)

∀s, r , n, a, k , p, t

(37)

∑

k 2' +1

(34)

1 ⎞ rsn ' 1 k 2' −1 k 2' rsn ' k 2' ⎛ fˆprsn ' ( t ) δˆapt = ⎜1 − + (k ) ∑ ⎟ uˆapt ( k ) k 2' rsn ' pt ⎝ k 2' ⎠

srn srn 1 ⎞ srn 1 k 2 '+1 ⎛ k 2 '−1 k 2 ' srn k2' uˆ apt ( k ) fˆ p ( t ) δˆ apt ( k ) = ⎜1 − + ⎟ uˆ apt ( k ) k2' ⎝ k2' ⎠ srnpt rs uapt (k )

∀r , s, j, n ', a, k , p, t

1 ⎞ rs 1 k 2' −1 k 2' k 2' ⎛ rs f prs ( t ) δ apt = ⎜1 − + (k ) ∑ ⎟ uapt ( k ) k 2' rspt ⎝ k 2' ⎠

{

Step 2.7: Calculate the link flows ua ( k )

k 2' +1

, uaj ( k )

k 2' +1

, uˆa ( k )

(23) to (28) and then update the link travel time ca ( k )k 2'+1

k 2' +1

j

, ua ( k )

k 2' +1

∀r , s, a, k , p, t , uˆ a ( k )

k 2' +1

, ua ( k )

(38) k 2' +1

} using Eqs

12

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Step 2.8: Check whether the iteration counter for the second loop converge, i.e. Eq. (39) and/or Eq. (40). If it is not, let k 2' = k 2'+1 and go to Step 2.4.

1 RAAD = A

∑∑ a

ua ( k )

a

GAP =

k 2'+1

a

k

− ua ( k )

ua ( k )

k

∑∑ u ( k )

k 2'+1

ca ( k )

k 2'+1

(39)

≤ ε2

k 2'

∑∑ ua ( k ) a

k 2'

− ∑∑ ua ( k ) a

k 2'

k

k 2'

k

ca ( k )

ca ( k )

k 2'

k 2'

(40)

≤ ε3

Step 3: Implement a multinomial logit model of departure time window/mode choice.  t Step 3.1: Calculate average value of travel time for the multiple shortest paths, πrsn j ' ' π rsn ( t ) = AVE C rsn j jp ( t ) k 1'

k 2'

∀r , s, j, n ', t

p∈P '

πˆ rsn ' ( t ) = AVE Cˆ prsn ' ( t ) k1'

k 2'

(

)

(

k1' k1'

{

and Θn ' t + πˆ rsn ' ( t )

)

k 1' k1'

)

{

}

{

)

' U rsn (t ) j

U

rsn '

(t )

k1'

k 1'

{

}

t

rsn '

(t )

k 1'

(

)

(

)

rsn ' ⎡ k 1' + α 2 ⎢Θ n ' t + π ( t ) ⎣

k1'

k 1'

+ y rsj ⎤⎥ + α3jt d rsj ⎦

rs ⎤ +y ⎥ ⎦

' = g rsn j (t ) k 1'

-β jn 'e

Q rsn '

λj

∑∑ -β j

gˆ rsn ' ( t ) = k 1'

Q rsn ' λˆ

n'

jn '

' U rsn j (t )

e

k 1'

+ ∑ - β n 'e

j

n'

(46) k1'

,grsn t

k1'

.

∀r , s, j , n ', t

(47)

∀r , s, n ', t

(48)

n'

-β n 'eU jn '

(45)

∀r , s, n ', t

k 1'

k 1' Uˆ rsn ' ( t )

ˆ rsn '

∑∑ -β

(t )

(44)

∀n '

∀r, s, j, n ', t

 t Step 3.4: Apply the logit model to calculate auxiliary variables of PSE ingress trips, grsn j ' U rsn j

(43)

∀j, n '

}

k1' k1' ' ' = α0jt + α1π rsn (t ) + α2 ⎡⎢Θ jn ' t + π rsn (t ) j j ⎣

= α 0 + α1 π

(41)

}

k 1' ⎧ ρ t * − Δ − ⎡t + πˆ rsn ' ( t )k1' ⎤ if tn* ' − Δ n ' > t + πˆ rsn ' ( t ) n' ⎣ ⎦ ⎪ n' ⎪ k 1' k 1' k 1' k 1' Θn ' t + πˆ rsn ' ( t ) = ⎨σ t + πˆ rsn ' ( t ) − tn* ' − Δ n ' if tn* ' + Δ n ' < t + πˆ rsn ' ( t ) ⎪ O/W ⎪0 ⎩ Step 3.3: Calculate disutility values for PSE attendances.

(

.

.

k 1' ' ⎧ ρ t * − Δ − ⎡t + π rsn ' ( t )k1' ⎤ if tn* ' − Δ n ' > t + π rsn (t ) n' j j ⎣ ⎦ ⎪ j n' ⎪ k 1' k 1' ' ' if tn* ' + Δ n ' < t + π rsn = ⎨σ j t + π rsn (t ) ( t ) − tn*' − Δ n ' j j ⎪ O/W ⎪0 ⎩

k 1' k 1'

k1'

(42)

' Step 3.2: Calculate schedule delay costs, Θ jn ' t + π rsn (t ) j

(

and πrsn t

∀r , s, n ', t

p∈P '

' Θ jn ' t + π rsn (t ) j

k1'

' U rsn j (t )

e

k 1'

(t )

k 1'

+ ∑ -β n 'e

k 1' Uˆ rsn ' ( t )

n'

Step 4: Update the PSE ingress trips matrix using the successive average method. 1 k 1' +1 k 1' k 1' k 1' ' ' ' ' q rsn ( t ) = q rsn ( t ) + ⎡⎣ g rsn ( t ) − q rsn ( t ) ⎤⎦ ∀r , s, j, n ', t j j j j k1'

(49)

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1 ⎡ rsn ' k1' k 1' gˆ ( t ) − qˆ rsn ' ( t ) ⎤ ⎦ k1' ⎣ Step 5: Update the PSE egress trips matrix. qˆ rsn ' ( t ) sr

q j ( n) q

sr

( n)

k 1' +1

= qˆ rsn ' ( t ) +

k 1' +1

' = γ n ∑∑ q rsn (t ) j

k 1'+1

k 1'

n'

(50)

k 1' +1

∀s, r , j, n

(51)

k 1' +1

∀s, r , n

(52)

t

= γ n ∑∑ qˆ rsn ' ( t ) n

∀r , s, n ', t

13

t

Step 6: Check whether the iteration counter of the first loop converge? i.e. Eq. (53) and/or Eq. (54). If it is not, let k1' = k1'+1 and go to Step 2.3.

max

' q rsn j (t )

r , s , n ',t

' − g rsn j (t )

' q rsn j (t )

r , s , j , n ',t

max

k 1' +1

qˆ rsn ' ( t )

k 1' +1

k 1'

− gˆ rsn ' ( t )

qˆ rsn ' ( t )

k 1'

k 1'

≤ ε1

(53)

≤ ε1

(54)

k 1'

3.5.
Cube models
development In this study, mesoscopic simulation-based dynamic traffic assignment was implemented using ten modules of Cube Voyager Version 6.1. The “logit” module creates time-dependent origin-destination tables of PSE. We apply DYNAMICLOAD techniques to obtain time-dependent path flows on the basis of the given travel demands in the “DTA” module. The framework for this developed model is shown in Figure 1.

14

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Fig. 1. a model framework.

4. Case study 4.1. Data collection of daily trips

Travel Trips (PCUs)

In this study, the 2014 New Year’s Eve celebration in Taoyuan City was used as a case study. Tauyuan City is the seventh largest city in Taiwan. Based on transportation planning of Taoyuan County (2011), the Taoyuan District was divided into 40 traffic analysis zones. Total daily trips to the Taoyuan District are about 213,985 PCUs during the evening to midnight. We abstracted the network data and trips of Taoyuan District from the database of Taoyuan City. Eight centroids were added to represent external traffic analysis zones. The road network was also simplified from the real roadway system in Taoyuan District. Only those road widths are greater than 8 meters. There are 1226 links and 563 nodes. The distribution of the centroids for traffic analysis zones (TAZ) and the road network are shown in Figure 3. A time-dependent profile of daily trips is observed and shown in Figure 2. Rush hour is between 17:00 to 18:00.

60000 50000 40000 30000 20000 10000 0

40842

42966

before 17:59

18:00-18:59

48510

19:00-19:59

42966

20:00~20:59

Time Period Fig. 2. a time-dependent profile of daily trips.

38701

after 21:00

Yun-Zhu Lin et al. / Transportation Research Procedia 25C (2017) 1352–1379 Lin and Chen/ Transportation Research Procedia 00 (2017) 000–000

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15

Fig. 3. a road network of case study.

4.2. Data collection of planned special events trips The event site is located at TAZ 30. Based on the capacity size of the New Year’s Eve celebration in Taoyuan City and historical data, the event attendance for the PSE is predicted. The sponsoring organization estimated around 114,282 participants at the 2013 New Year’s Eve celebration. Based on the advanced knowledge of event attendance at the New Year’s Eve celebration in Taoyuan City and our questionnaire survey, we distributed 114,282 participants from another 47 TAZs to the event site. Event-generated traffic distribution was estimated. We assume travel directions of ingress trips and egress trips were the opposite but their values were equal. The origindestination person-trips matrix is given in Table 1. Referring to the survey results, we further allocated these to the five expected arrival time windows according to the ratios of the EATW of ingress trips in Table 1. Thus, we . The estimated time value is NT$ 144 per derived five time-window-dependent ingress trip matrices
⎡Q rsn ' ⎤

⎣

hour.

⎦ 48×48

Table 1 PSE origin-destination person-trips matrix. Origin/destination Trips Origin Trips Origin/destination Trips Origin/destination Trips Origin/destination Trips

1 566 11 122 21 80 31 6380 41 36274

2 308 12 202 22 278 32 3208 42 2826

3 430 13 326 23 472 33 1498 43 7120

4 286 14 372 24 234 34 1336 44 3390

5 104 15 238 25 700 35 2198 45 7120

6 134 16 392 26 1164 36 2010 46 8928

7 282 17 1142 27 4720 37 554 47 2916

8 308 18 182 28 2404 38 1308 48 1458

9 176 19 572 29 1920 39 0

10 274 20 972 30 5650 40 748 Total 114282

16

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Feeder bus lines and a free motorcycle parking lot were provided by the sponsoring organization to mitigate traffic congestion. Three lines of feeder buses were provided. Bus routes are illustrated in Figure 4. A set of admissible artificial links were added to allow the participants of TAZ 41, 21, 22, 20, 24, 25, and 28 to take the Orange Line to the event site. The participants of TAZ 46 and 31 can take Green Line and those of TAZ 40 and 11 can take Red Line to the event site.

Fig. 4. feeder bus routes.

4.3. Survey of PSE trip behaviour A personal interview and a network survey were conducted with 445 respondents and completed by 402 effective respondents between December 31, 2013 and February 8, 2014. The survey items included individual and household socio-demographics, event participation attributes, and stated preference data so as to explore choice behaviours of travel modes and departure time-windows. This questionnaire survey forced the respondents to choose between conditions for attributes of 15 joint alternatives of travel modes and departure time-windows. That is, these 15 joint alternatives are a combination of five departure time window choices (i.e. departure before 17:59, departure between 18:00 to 18:59, departure between 19:00 to 19:59, departure between 20:00 to 20:59, and departure after 21:00) and three travel mode choices (i.e. motorcycles, cars, and buses). The survey results of expected arrival/departure time windows are summarized as follows. Over 90% PSE trips departed from Taoyuan County. The expected arrival time windows (EATW) of ingress trips and expected departure time windows (EDTW) of egress trips are given in Table 2. In other way, the departure time windows of most participants was before 17:59 at about 35%. Over 55% of the PSE trips departed before 19:00. Over 65% of participants rode a motorcycle to the PSE site, and only 15% of participants drove a car to the site. The detailed data are given in Table 3. The mode split of motorcycles, cars, and buses is around 66%, 15%, and 19%, respectively. The mode splits of motorcycles and buses were higher than with daily trips. The mode splits of cars were lower for daily trips. We think the reasons for this result are: 1) parking spaces for cars are very limited; 2) free parking spaces for motorcycles are adequately provided; 3) and the ending time of the PSE event was too late to take daily buses to travel home. Table 2. Expected arrival/departure time windows. Type Expected arrival time window of ingress profile of PSE trips

Time windows 17:00-17:59 18:00-18:59 19:00-19:59

Split 18% 28% 22%

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Expected departure time window of egress profile of PSE trips using private modes Expected departure time window of egress profile of PSE trips using feeder buses

20:00-20:59 After 21:00 23:00-23:59 24:00-00:59 After 01:00 23:00-23:59 24:00-00:59 After 01:00

17

19% 13% 15% 60% 25% 20% 77% 3%

Table 3. Splits of departure time window and mode choices. Departure Time Window before 17:59 18:00-18:59 19:00-19:59 20:00-20:59 after 21:00 21:00-21:59 22:00-22:59 23:00-23:59 Total Departure Time Window before 17:59 18:00-18:59 19:00-19:59 20:00-20:59 after 21:00 21:00-21:59 22:00-22:59 23:00-23:59 Total

Motorcycles 83 49 48 40 46 24 18 4 266 Motorcycles 20.65% 12.19% 11.94% 9.95% 11.44% 5.97% 4.48% 0.99% 66.17%

Cars 24 17 12 5 2 2 0 0 60 Cars 5.97% 4.23% 2.99% 1.24% 0.50% 0.50% 0.00% 0.00% 14.93%

Buses 33 26 8 6 3 2 1 0 76 Buses 8.21% 6.47% 1.99% 1.49% 0.75% 0.50% 0.25% 0.00% 18.91%

Sum 140 92 68 51 51 28 20 4 402 Sum 34.83% 22.89% 16.92% 12.69% 12.69% 6.97% 4.73% 0.99% 100.00%

We used NLOGIT v4.0 software to calibrate the coefficients of a multinomial logit (MNL) model of departure time windows and mode choices for ingress travel demands. The MNL coefficient estimates are given in Table 4. The log-likelihood value at a convergence of the final MNL specification is -13119.44. The MNL coefficients for the two generic attributes, total travel costs and total travel times, and one alternative specific variable, total distance, are significant with the expected signs. As a goodness-of-fit measure, the adjusted likelihood ratio index is 0.141. Accordingly, the explanatory power of this MNL model is fair. The calibrated time value is NT$ 2.4 per minute. The coefficients and constants of this MNL model are summarized as follows:

{

}

α 0jt = α 0jt j = 1, 2; t = 1,...,5 = {2.3, 2.0,1.63,1.42,1.91, 2.94, 2.59, 2.24,1.37, 0.0}

{

}

(55)

α 0 = α 0 t = 1,...,5 = {2.17, 2.08,1.10, 0.56,1.00}

(56)

α1 = -0.04

(57)

t

t

α 2 = -0.02

{

α = α jt 3

jt 3

(58)

}

j = 1,2; t = 1,...,5 = {-0.09,-0.11,-0.07,-0.07,-0.11,0.0,0.0,0.0,0.0,0.0}

(59)

Table 4. Calibration results of the MNL model of travel mode and departure time window choice of ingress travel demands. Terms

Alternative specific constants

Alternative specification ride a motorcycle and depart before 17:59 ride a motorcycle and depart between 18:00 to 18:59 ride a motorcycle and depart between 19:00 to 19:59 ride a motorcycle and depart between 20:00 to 20:59 ride a motorcycle and depart after 21:00 drive a car and depart before 17:59 drive a car and depart between 18:00 to 18:59 drive a car and depart between 19:00 to 19:59 drive a car and depart between 20:00 to 20:59

Coefficients 2.30 2.00 1.63 1.42 1.91 2.94 2.59 2.24 1.37

t value 4.03** 3.33** 2.76** 2.38** 3.18** 5.05** 4.35** 3.64** 1.94**

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Generic variables

Alternative specific variables

drive a car and depart after 21:00 take a bus and depart before 17:59 take a bus and depart between 18:00 to 18:59 take a bus and depart between 19:00 to 19:59 take a bus and depart between 20:00 to 20:59 take a bus and depart after 21:00 Total travel cost Total travel time ride a motorcycle and depart before 17:59 ride a motorcycle and depart between 18:00 to 18:59 Total ride a motorcycle and depart between 19:00 to 19:59 distance ride a motorcycle and depart between 20:00 to 20:59 ride a motorcycle and depart after 21:00

Number of samples Log-likelihood value at zero LL(0) Log-likelihood value at convergence LL(β) likelihood ratio index ρ2 Adjusted likelihood ratio index ρ2

1369

0.45 0.51 2.17 4.11** 2.08 3.92** 1.10 1.90* 0.56 0.89 Base value -0.02 -7.24** -0.04 -4.47** -0.09 -4.00** -0.11 -3.70** -0.07 -3.08** -0.07 -2.84** -0.11 -3.58** 416 -1126.55 -946.79 0.160 0.141




















Remarks: ** Significant at 5% level, * Significant at 10% level

4.4. Other input data Total simulation periods run from PM 17:00 to AM 2:00 (+1). Ingress periods run from PM 17:00 to PM 24:00. Egress periods run from PM 23:00 to AM 2:00 (+1). Each time window is 1 hour. Each time interval is 10 minutes. The maximum number of iterations is 500. Minimum acceptable values of gap and RADD are 0.01 and 0.005, respectively. Average load factors for motorcycles, cars, and buses are 1.6, 2.2, and 50 persons per vehicle, respectively, and the PCEs for motorcycles and buses is 0.5 and 2.5, respectively. We set the unit penalty costs for early schedule delay of all user classes equal to the time value, NT$ 2.4 per minute. The unit penalty costs for late schedule delay is two times of the unit penalty costs for early schedule delay, i.e., NT$ 4.8 per minute. The ticket fare of feeder buses is NT$ 15. We use fuel costs to estimate variable costs of using private mode. The unit variable cost of using motorcycles and cars is NT$ 0.9 and 3.6 per kilometer. Dispersion parameters that reflects the degree of perception of participants with the variation of travel disutility equal to 1. We referred to our survey results. Five time-window-dependent ingress trip matrices of each mode were calculated according to the ratios of the EATW of ingress trips, i.e., 10%, 30%, 20%, 20%, and 10% for the five ingress periods. Three time-window-dependent egress trip matrices of each private mode were calculated according to the ratios of the EDTW of egress trips, i.e., 10%, 70%, and 20% for the three egress periods. Because the ending time of the PSE event was too late to take daily buses to travel home, the ratio of the EDTW of egress trips using feeder buses is 30% and 70% for the first two egress periods, i.e., 23:00-23:59 and 23:00-23:59. 4.5. Traffic control plans Different types of traffic control plans could be proposed to reduce the traffic impact of the PSE. Stage-by-stage traffic control plans can mitigate any possible adverse impacts that might result from this event. The most common traffic mitigation plans for the PSE are multi-stage road closures, increase in parking fees, and increase in the number of feeder buses. Based on the reality of our case, we propose a two-stage plan to close the roads around the PSE site and a regulation plan for parking fares. Using a series of scenario analyses, we want to know how far the restrictions on turning movements should go and when traffic control should start. At the first stage of road closures, some roads in traffic control Zone 1 (in blue) around the PSE site are barricaded to restrict the number of riders and drivers. At the second stage of road closures of traffic control, some roads in traffic control Zone 2 (in pink) in the vicinity of PSE site are barricaded. The blockade lines for two-stage traffic controls are shown in Figure 5. The start time for traffic control has four values, 17:00, 18:00, 19:00, and 20:00. Parking fees for motorcycles has three values, free, one time NT$ 30, and one time NT$ 50 per day. Parking fees for cars has two values, one time NT$ 80 and NT$ 125 per day. Including a zero alternative, we have three regulation plans for parking fares, i.e., Regulation Plan I (free for motorcycles and NT$ 80 for cars), Regulation

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Plan II (NT$ 30 for motorcycles and NT$ 80 for cars), and Regulation Plan III (NT$ 50 for motorcycles and NT$ 125 for cars). 12 alternatives to the traffic control plans with/without parking fare regulation are also addressed, as shown in Table 5.

Fig. 5. delimitation of two-stage traffic control zones. Table 5. Alternative traffic control plans. Alternatives of Traffic Control TCP 1-1 TCP 1-2 TCP 1-3 TCP 2-1 TCP 2-2 TCP 2-3 TCP 3-1 TCP 3-2 TCP 3-3 TCP 4-1 TCP 4-2 TCP 4-3 TCP 5-1 TCP 5-2 TCP 5-3 Base 1 Base 2 Base 3

Two-stage Road Closure Traffic Control Zone 1 Traffic Control Zone 2 Start at 17:00

Start at 18:00

Start at 17:00

Start at 19:00

Start at 17:00

Start at 20:00

Start at 18:00

Start at 19:00

Start at 18:00

Start at 20:00

-

-

FRP I: FRP II: FRP III: FRP I: FRP II: FRP III: FRP I: FRP II: FRP III: FRP I: FRP II: FRP III: FRP I: FRP II: FRP III: FRP I: FRP II: FRP III:

Fare Regulation Plan (FRP) Parking Fees for Parking Fees for Bus Ticket Cars Motorcycles 0 80 15 30 80 15 50 125 15 0 80 15 30 80 15 50 125 15 0 80 15 30 80 15 50 125 15 0 80 15 30 80 15 50 125 15 0 80 15 30 80 15 50 125 15 0 80 15 30 80 15 50 125 15

4.6. Simulation results We evaluate the effectiveness of proposed TCPs using the proposed simulation-based PSE travel choice model. Quantitative analyses have also been performed, and several criteria are considered as summarized in Table 6. The number of vehicles reaching the destinations (NVRD), average travel time (ATT), and average travel speed (ATS)

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1371

are considered. Note that NVRD is noteworthy to evaluate the effectiveness of TCPs. It means that more PSE participants can arrive the PSE site and more daily trips can reach their destinations. Table 6. Performance of alternative traffic control plans. Alternatives TCP 1-1 TCP 1-2 TCP 1-3 TCP 2-1 TCP 2-2 TCP 2-3 TCP 3-1 TCP 3-2 TCP 3-3 TCP 4-1 TCP 4-2 TCP 4-3 TCP 5-1 TCP 5-2 TCP 5-3 Base 1 Base 2 Base 3

Total Travel Distance (Vehicle-KM) 2468915 2439648 2367221 2388341 2340040 2275950 2429346 2391111 2119037 2398558 2171652 2232802 2122861 2359734 2380941 2396686 2342039 2295080

Total Travel Time (Vehicle-Hour) 143730 153824 135778 152896 147542 141512 147921 144048 119626 142807 116133 156926 120913 142862 142656 166023 146954 141236

Average Travel Speed (KMH) 17.18 (2.74) 15.86 (-0.08) 17.43 (1.18) 15.62 (1.18) 15.86 (-0.08) 16.08 (-0.17) 16.42 (1.98) 16.6 (0.66) 17.71 (1.46) 16.8 (2.36) 18.70 (2.76) 14.23 (-2.02) 17.56 (3.12) 16.52 (0.58) 16.69 (0.44) 14.44 15.94 16.25 -

Total Arrival Vehicles (Vehicle) 250772 245584 240826 239969 233022 215617 248361 241405 196243 243567 206568 218058 197316 238310 235501 236582 235509 229557

(14190) (10075) (11269) (3387) (-2487) (-13940) (11779 (5896 (-33314 (6985) (-28940) (-11499) (-39266) (2801) (5944) -

Average Travel Time (Minutes) 34.39 37.58 33.83 38.23 37.99 39.38 35.74 35.80 36.57 35.18 33.73 43.18 36.77 35.97 36.35 42.11 37.44 36.92

(-7.72 (0.14 (-3.09 (-3.88 (0.55) (2.46) (-6.37) (-1.64) (-0.34) (-6.93) (-3.71) (6.26) (-5.34) (-1.47) (-0.57) -

In the scenario without two-stage road closures and only with fare regulation plan I for parking fares, the NVRD during the simulation time period is largest but the ATT is longest and the ATS is slowest. Conducting any plan of two-stage road closures to improve the congestion of Base 1 case, the NVRD during the simulation time period and the ATS will increase and the AAT will decrease. Comparing Base Plan 1 with corresponding traffic control plans, the average speed of Plan 1-1, Plan 2-1, Plan 3-1, and Plan 4-1 is faster than the average speed of Base Plan 1. The NVRD for these four plans are more than the NVRD for Base Plan 1. The improvement rate for Plan 1-1 is the highest. For lenient price regulation, the first and the second stage of road closures should start at 17:00 and 18:00, respectively. For the same consideration, we think the first and second stage of road closures should start at 17:00 and 20:00 for moderate price regulation. For strict price regulation, the first and the second stages of road closures should start at 17:00 and 18:00. In the scenario with two-stage road closures, the reduction the traffic impact of the PSE for various regulated fares are irregular. Improper timing of road closures will worsen the traffic congestion. The ATT of TCPs 1-2, 2-2, 2-3, and 4-3 increased and the ATS of these four plans decreased. The NVRD of Plans 2-2, 2-3, 3-3, 4-2, 4-3, 5-1, and 5-3 decreased. Those results reveal that the timing of road closures must operate in coordination with the price regulation. In other ways, note that if we only observed ATS and ATT, TCP 4-2 would be the best TCP. TCP 4-2 is actually not so good because NVRD is only 206568. We think the best TCP is TCP 1-1 or TCP 1-3. In this case study, we found that the first and the second stage of road closures should start at 17:00 and 18:00, respectively. Overall, based on the simulation results, imposing such TCPs could significantly increase road efficiency and reduce congestion in the short term. This case study demonstrates the simulation-based DTA model’s ability to evaluate traffic management strategies of the PSE. ATS of each links of TCP 1-1 at the peak period are illustrated in Figure 6. The red lines mean highway traffic is moving at less than 20 kilometers per hour and indicate congestion on that link. The green lines mean highway traffic is moving at more than 25 kilometers per hour and indicate smoothness on that link. The yellow lines mean highway traffic is moving between 20 and 25 kilometers per hour.

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Fig. 6. simulation results of TCP 1-1.

Taking TCP 1-1 as an example and used for demonstration, details the testing results of the logit model as given in Table 7. For those choosing to ride a motorcycle to go to the event site, they should depart before 17:59. For users of other travel modes, they should depart between 18:00 to 18:59. As the traffic congestion worsens, the travel time becomes longer than one hour. Participants who choose to depart at the same time window to their expected arrival time window get less. Thus, they must depart early. Such phenomena are more serious for car users. A comparison of the logit model implementing TCPs 1-1, 1-2, and 1-3 is summarized in Table 8. Price regulation obviously affects the mode choice behavior of participants. For participants who use cars and motorcycles, their travel costs for TCP 1-3 are the highest due to the strict price regulation. Travel demands of cars and motorcycles are the lowest, and travel demands of buses are the highest of these three traffic control plans. Table 7. Test results for the logit model implementing TCP 1-1. Expected Arrival Time Window 17:00-17:59 18:00-18:59 19:00-19:59 20:00-20:59 After 21:00 Total (PCUs) Total (Person-trips) Expected Arrival Time Window 17:00-17:59 18:00-18:59 19:00-19:59

Depart before 17:59

Depart between 18:00 to 18:59

2233.07(100%) 768.71(26.0%) 2188.67(74.0%) 522.57(21.8%) 77.45(3.2%) 12.93(0.3%) 87.02(2.8%) 6.21(0.3%) 0.93(0.00%) 3093.09 2804.47 9897.89 8974.30 Depart before Depart between 17:59 18:00 to 18:59 2885.93(100%) 1014.02(24.1%) 100.16(3.4%)

3191.15(75.9%) 799.91(26.5%)

Depart between Depart between 19:00 to 19:59 20:00 to 20:59 Riding a motorcycle 1798.94(75.0%) 938.84(29.7%) 2124.43(67.2%) 68.71(3.3%) 637.79(30.3%) 2806.49 2762.22 8980.77 8839.10 Depart between Depart between 19:00 to 19:59 20:00 to 20:59 Driving a car 2114.54(70.1%) -

Depart after 21:00

Subtotal

1393.64(66.1%) 1393.64 4459.65 Depart after 21:00 -

2233.07 2957.38 2398.96 3163.22 2107.28 12859.91 41151.71 Subtotal 2885.93 4205.17 3014.61

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20:00-20:59 After 21:00 Total (PCUs) Total (Person-trips) Expected Arrival Time Window 17:00-17:59 18:00-18:59 19:00-19:59 20:00-20:59 After 21:00 Total (PCUs) Total (Person-trips)

17.11(0.7%) 1.27(0.2%) 4018.49 8840.678

137.46(5.3%) 10.64(1.2%) 4139.16 9106.152

468.13(100%) 202.56(26.0%) 20.31(4.8%) 3.49(1.0%) 0.23(0.1%) 694.72 13894.4

575.92(74.0%) 163.02(38.1%) 37.44(10.6%) 2.82(2.1%) 779.20 15584.00

1096.91(42.4%) 1336.54(51.6%) 85.45(9.6%) 393.68(44.4%) 3296.9 1730.22 7253.18 3806.484 Taking a bus 244.03(57.1%) 70.68(20.1%) 240.33(68.3%) 12.95(9.5%) 23.68(17.3%) 327.66 264.01 6553.20 5280.20

1373

395.43(44.6%) 395.43 869.946

2588.02 886.47 13580.2 29876.44

96.98(71.0%) 96.98 1939.60

468.13 778.48 427.36 351.94 136.66 2162.57 43251.40

Table 8. Comparisons of the logit model implementing TCPs 1-1, 1-2 and 1-3. Mode

Motorcycles

Cars

Feeder buses

Departure Time Window Depart before 17:59 Depart between 18:00 to 18:59 Depart between 19:00 to 19:59 Depart between 20:00 to 20:59 Depart after 21:00 Subtotal Depart before 17:59 Depart between 18:00 to 18:59 Depart between 19:00 to 19:59 Depart between 20:00 to 20:59 Depart after 21:00 Subtotal Depart before 17:59 Depart between 18:00 to 18:59 Depart between 19:00 to 19:59 Depart between 20:00 to 20:59 Depart after 21:00 Subtotal Total

TCP 1-1 PCUs Persons 3093.09 9897.89 2804.47 8974.30 2806.49 8980.77 2762.22 8839.10 1393.64 4459.65 12859.91 41151.71 4018.49 8840.68 4139.16 9106.15 3296.90 7253.18 1730.22 3806.48 395.43 869.95 13580.20 29876.44 694.72 13894.40 779.20 15584.00 327.66 6553.20 264.01 5280.20 96.98 1939.60 2162.57 43251.40 28602.68 114279.55

TCP 1-2 PCUs Persons 2259.51 7230.43 2063.71 6603.87 2139.87 6847.58 2167.79 6936.93 1160.34 3713.09 9791.22 31331.90 4516.22 9935.68 4681.98 10300.36 3846.65 8462.63 2037.22 4481.88 467.96 1029.51 15550.03 34210.07 779.72 15594.40 862.60 172520 370.29 7405.80 306.95 6139.00 117.36 2347.20 2436.92 48738.40 27778.17 114280.37

TCP 1-3 PCUs Persons 2101.42 6724.54 1919.71 6143.07 2059.68 6590.98 2107.37 6743.58 1164.89 3727.65 9353.07 29929.82 3070.85 6755.87 3200.64 7041.42 2689.78 5917.53 1468.63 3230.99 353.92 778.62 10783.82 23724.40 946.59 18931.80 1096.21 21924.20 479.57 9591.40 370.71 7414.20 137.76 2755.20 3030.84 60616.80 23167.73 114271.03

Detailed testing results of the logit model for Base 1 are listed in Table 9. Compared with the results of TCP 1-1, participants who choose to depart at the same time windows to their expected arrival time windows get less for Base 1. Because the traffic congestion is successfully mitigated by the road closure, the travel time becomes shorter than one hour. Participants who need to depart early to arrive at the event site during the expected time windows get less. This phenomena mean that the road closure is effective in managing PSE transportation and the timing of road closures indeed will affect the choice behaviors for the departure time window of participants. Table 9. Test results of the logit model for Base 1. Expected Arrival Time Window 17:00-17:59 18:00-18:59 19:00-19:59 20:00-20:59 After 21:00 Total (PCUs) Total (Person-trips) Expected Arrival Time Window 17:00-17:59 18:00-18:59 19:00-19:59 20:00-20:59 After 21:00 Total (PCUs) Total (Person-trips)

Depart before 17:59

Depart between 18:00 to 18:59

1994.32(100%) 902.90(32.6%) 93.93(4.3%) 16.41(0.6%) 1.27(0.1%) 3008.83 9628.26

1867.01(67.4%) 639.63(29.2%) 111.18(3.8%) 8.69(0.4%) 2626.51 8404.83

2597.47(100%) 1210.36(30.9%) 122.90(4.3%) 21.85(0.8%) 1.73(0.2%) 3954.31 8699.48

2700.41(69.1%) 990.37(35.0%) 177.38(6.9%) 14.77(1.6%) 3882.93 8542.45

Depart between Depart between 19:00 to 19:59 20:00 to 20:59 Riding a motorcycle 1458.20(66.5%) 1138.93(39.0%) 1654.18(59.9%) 98.57(5.0%) 703.77(35.7%) 2695.70 2357.95 8626.24 7545.44 Driving a car 1712.70(60.6%) 1342.40(51.9%) 1043.80(40.4%) 120.30(13.3%) 442.21(48.7%) 3175.40 1486.01 6985.88 3269.22

Depart after 21:00

Subtotal

1156.90(58.7%) 1156.90 3702.08

1994.32 2769.91 2191.76 2920.70 1969.20 11845.89 37906.85

328.69(36.2%) 328.69 723.12

2597.47 3910.77 2825.97 2585.43 907.7 12827.34 28220.15

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538.10(100%) 225.30(26.8%) 23.42(4.9%) 4.28(1.1%) 0.34(0.2%) 791.44 15828.8

615.59(73.2%) 198.24(41.2%) 46.25(11.8%) 3.87(2.5%) 863.95 17279

Taking a bus 259.58(53.9%) 86.19(22.0%) 254.35(65.0%) 17.92(11.5%) 26.69(17.1%) 363.69 281.04 7273.8 5620.8

107.55(68.8%) 107.55 2151

23

538.10 840.89 481.24 391.07 156.37 2407.67 48153.40

4.7. Sensitivity analysis We vary unit penalty costs for schedule delay and unit variable cost of using private mode to evaluate the impact of travel costs towards travel choice. In addition, we vary ratios of expected arrival time windows of ingress trips and ratios of expected departure time windows of egress trips to examine the robustness of the traffic control/management schemes towards travel demands. 1. Unit penalty costs for schedule delay We set the unit penalty costs for early schedule delay of all user classes equal to the calibrated time value of the MNL model of departure time windows and mode choices for PSE ingress travel demands. Furthermore, we adopted the investigated value of time of daily trips (IOT, 2011) and the questionnaire results of time value surveyed by our study to set the unit penalty costs for early schedule delay. The unit penalty costs for late schedule delay is also two times of the unit penalty costs for early schedule delay. Detailed data are given in the Table 10. According to the testing results in the Table 10, TCP 1-1 is still the better choice when the unit penalty costs for schedule delay of three modes are the same. Conversely, the unit penalty cost for schedule delay of motorcycles is lower than other two modes. PSE participants who ride motorcycles have a lower value of time than PSE participants who use other modes do. So we can reasonably suppose the price differences of motorcycles parking and cars parking, which can be accepted by PSE participants who ride motorcycles, are smaller. At such a condition, TCP 1-2 is a better choice. 2. Unit variable costs of using private mode Based on the fuel costs in to 2012 to 2016, we estimate the lowest and highest variable costs of using private modes, as shown in Table 11. According to the testing results in the Table 11, we found that the trips of feeder buses will decrease and the trips of cars will increase, as the fuel costs decreases. Furthermore, the trips of feeder buses will increase and the trips of cars and motorcycles will increase, as the fuel costs increases. We take average values of NVRD, ATT, and ATS to be the effectiveness factors of TCPs. If we only observed ATS and ATT, TCP 1-2 would be the best TCP. But NVRD of TCP 1-2 is only 236966. ATS of TCP 1-1 is a little longer than TCP 1-2 has but NVRD of TCP 1-1 is much more than TCP 1-2 has. Consequently, we think the best TCP is TCP 1-1 or TCP 12. 3. Ratios of the EATW of ingress trips Since the simulation results are heavily dependent on the time-dependent OD demands, we set various ratio combinations of the EATW of PSE ingress trips to examine the robustness of the traffic control/management schemes. According to our survey results, we found the expected arrival times of participating New Year’s Eve celebration are spread out over a long period. Two ratio combinations of the EATW of PSE ingress trips are given in Table 12. One is to postpone the peak of EATW. The other is to remove the peak of EATW. According to the testing results in the Table 12, we found that the trips of motorcycles will increase once the ratio of the EATW of ingress trips for the last ingress period increases. But the trips of cars and feeder buses decrease. Robustness of the traffic control/management decreases. If we observed ATS, TCP 2-3 would be the best TCP. From the viewpoint of ATT, TCP 4-2 would be the best TCP. If we only concerned NVRD, TCP 1-1 would be the best TCP. We think TCP 4-2 is the best TCP for compromising these three criteria. Table 10. Comparisons of different unit penalty costs for schedule delay. Alternatives of Traffic Control

Unit Variable Costs of Using Private Modes

Unit Penalty Costs for Early Schedule Delay

Total Travel Total Travel Time Distance (Vehicle-KM) (Vehicle-

Average Speed (KMH)

Total Arrival Vehicles (Vehicle)

Average Travel Time (Minutes)

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Cars

0.9

3.6

TCP 1-1 TCP 1-2 TCP 1-3

Motorcycles 2.40 0.85 1.85 2.40 0.85 1.85 2.40 0.85 1.85

Cars Buses 2.40 2.40 0.85 0.85 3.47 3.47 2.40 2.40 0.85 0.85 3.47 3.47 2.40 2.40 0.85 0.85 3.47 3.47

2,411,315 2,422,853 2,364,196 2,371,337 2,421,452 2,410,911 2,296,276 2,386,867 2,442,281

Hour) 144,171 139,328 152,394 143,083 142,934 141,350 147,587 142,041 147,956

16.73 17.39 15.51 16.57 16.94 17.06 15.56 16.8 16.51

241408 246822 236268 237776 244069 245448 232089 242768 242371

1375

35.83 33.87 38.70 36.11 35.14 34.55 38.15 35.11 36.63

5. Conclusions and Recommendations It is impossible to conduct real-world experiments that truly test a traffic management system for PSEs. Although the knowledge gained in such a test would be valuable, its consequences would include traffic congestion and delays, possibly accidents, and even potential deaths. Review of past incidents and a systematic assessment tool are more helpful to ascertain the effect of various traffic control plans for PSEs. In this study, a combined forecasting model for departure time windows, travel modes, and driving route choices was developed to evaluate the effectiveness of different proposed traffic control plans. The proposed simulation-based PSE travel choice model is seen as be more appropriate for the high-resolution analysis of special events, temporary road closures, and price regulation. Furthermore, the use of the proposed simulation-based PSE travel choice model has proved to be an excellent tool for stakeholders when forecasting time of occurrence and the level of traffic congestion and evaluating the impacts and mitigation measures of proposed alternatives for TCPs. Furthermore, we also have proved the simulation-based PSE travel choice model is an excellent tool to examine the robustness of the traffic control/management schemes towards travel demands. The use of DTA for this model is also a critical feature. DTA adequately captures the temporal effects of congestion and the impacts of time-varying demands and supplies. Therefore, the authorities can more easily gain further useful knowledge of current operating procedures and use that knowledge to discuss and design potential improvements in traffic management for the future.

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Table 11. Comparisons of different unit variable costs of using private mode. Alternatives of Traffic Control

Unit Penalty Costs for Schedule Delay

TCP 1-1

TCP 1-2

2.4

TCP 1-3

TCP 2-1

TCP 2-2

2.4

TCP 2-3

TCP 3-1

TCP 3-2

2.4

TCP 3-3

TCP 4-1

TCP 4-2

2.4

TCP 4-3

TCP 5-1

TCP 5-2

TCP 5-3

2.4

Unit Variable Costs of Average Using Private Modes Speed (KMH) Motorcycles Cars 0.90 3.60 17.18 0.56 2.17 17.38 0.92 3.68 16.47 17.01 Average 0.90 3.60 15.86 0.56 2.17 18.47 0.92 3.68 18.09 Average 17.47 0.90 3.60 17.43 0.56 2.17 16.57 0.92 3.68 17.13 17.04 Average 0.90 3.60 15.62 0.56 2.17 16.76 0.92 3.68 17.22 Average 16.53 0.90 3.60 15.86 0.56 2.17 16.78 0.92 3.68 16.63 16.42 Average 0.90 3.60 16.08 0.56 2.17 16.42 0.92 3.68 16.35 Average 16.28 0.90 3.60 16.42 0.56 2.17 15.25 0.92 3.68 17.76 16.48 Average 0.90 3.60 16.60 0.56 2.17 16.40 0.92 3.68 17.57 16.86 Average 0.90 3.60 17.71 0.56 2.17 17.18 0.92 3.68 17.38 Average 17.42 0.90 3.60 16.80 0.56 2.17 15.94 0.92 3.68 18.27 Average 17.00 0.90 3.60 18.70 0.56 2.17 15.18 0.92 3.68 15.74 Average 16.54 0.90 3.60 14.23 0.56 2.17 15.85 0.92 3.68 17.58 Average 15.89 0.90 3.60 17.56 0.56 2.17 16.73 0.92 3.68 16.34 16.88 Average 0.90 3.60 16.52 0.56 2.17 18.66 0.92 3.68 17.22 Average 17.47 0.90 3.60 16.69 0.56 2.17 16.62 0.92 3.68 16.55 Average 16.62

Total Arrival Vehicles (Vehicle) 250772 245624 241163 245853 245584 214549 250763 236966 240826 236173 236243 237748 239969 244031 198164 227388 233022 246770 240738 240177 215617 239604 223605 226275 248361 235044 252536 245313 241405 238235 249968 243203 196243 237972 243798 226004 243567 240122 252910 245533 206569 232712 243948 227743 218058 227958 238825 228281 197316 250795 240349 229487 238310 191308 249164 226261 235501 244443 239185 239710

Average Trips (Persons) Travel Time (Minutes) Motorcycles Cars 34.39 41151 29876 34.28 40308 32675 35.83 40554 29464 34.83 37.58 31331 34210 34.21 30520 37005 32.30 30743 33586 34.70 33.83 29929 23725 36.76 28784 24815 34.87 29419 23412 35.15 38.23 41350 29957 35.62 40291 32467 37.33 40515 29555 37.06 37.99 31331 34073 35.22 30697 36936 35.85 30922 33702 36.35 39.38 29725 23610 36.36 29727 26193 38.21 29244 23300 37.98 35.74 41111 29899 38.56 40399 32571 32.94 40034 28790 35.74 35.80 31352 34210 36.6 30297 36474 33.38 30479 32693 35.27 36.57 29679 23716 35.6 29168 25541 34.42 29220 23228 35.53 35.18 41196 30000 37.77 40388 32556 31.80 40037 28676 34.92 33.73 31273 34071 39.63 30714 37157 37.42 30895 33601 36.93 43.18 29605 23640 38.06 29450 25894 34.45 29134 23167 38.56 36.77 41257 30043 35.05 40344 32622 36.53 40589 29598 36.11 35.97 31231 34184 34.90 30237 36516 34.08 30843 33617 34.98 36.35 29226 23373 36.01 29694 26095 36.63 29122 23162 36.33

Buses 43253 41293 44271 48738 46754 49949 60617 60680 61451 42973 41526 44212 48876 46652 49663 60938 58360 61736 43269 41311 45455 48713 47510 51111 60878 59575 61831 43088 41349 45561 48933 46412 49790 61030 58939 61977 42982 41318 44097 48864 47523 49812 61683 58488 62000

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Table 12. Comparisons of different ratios of the EATW of ingress trips. Alternatives of Ratios of the EATW of Ingress Trips Average Speed Traffic Control (KMH) TW1 TW2 TW3 TW4 TW5 0.2 0.3 0.2 0.2 0.1 17.18 0.2 0.2 0.3 0.2 0.1 16.42 TCP 1-1 0.2 0.2 0.2 0.2 0.2 15.85 Average 16.48 0.2 0.3 0.2 0.2 0.1 15.86 0.2 0.2 0.3 0.2 0.1 17.19 TCP 1-2 0.2 0.2 0.2 0.2 0.2 15.3 16.12 Average 0.2 0.3 0.2 0.2 0.1 17.43 0.2 0.2 0.3 0.2 0.1 18.30 TCP 1-3 0.2 0.2 0.2 0.2 0.2 16.15 Average 17.29 TCP 2-1 0.2 0.3 0.2 0.2 0.1 15.62 0.2 0.2 0.3 0.2 0.1 16.11 0.2 0.2 0.2 0.2 0.2 15.77 15.83 Average TCP 2-2 0.2 0.3 0.2 0.2 0.1 15.86 0.2 0.2 0.3 0.2 0.1 17.77 0.2 0.2 0.2 0.2 0.2 16.26 16.63 Average TCP 2-3 0.2 0.3 0.2 0.2 0.1 16.08 0.2 0.2 0.3 0.2 0.1 16.56 0.2 0.2 0.2 0.2 0.2 19.41 Average 17.35 TCP 3-1 0.2 0.3 0.2 0.2 0.1 16.42 0.2 0.2 0.3 0.2 0.1 16.65 0.2 0.2 0.2 0.2 0.2 17.24 Average 16.77 TCP 3-2 0.2 0.3 0.2 0.2 0.1 16.60 0.2 0.2 0.3 0.2 0.1 16.83 0.2 0.2 0.2 0.2 0.2 16.16 Average 16.53 TCP 3-3 0.2 0.3 0.2 0.2 0.1 17.71 0.2 0.2 0.3 0.2 0.1 16.22 0.2 0.2 0.2 0.2 0.2 17.24 Average 17.06 TCP 4-1 0.2 0.3 0.2 0.2 0.1 16.80 0.2 0.2 0.3 0.2 0.1 15.33 0.2 0.2 0.2 0.2 0.2 16.54 16.22 Average TCP 4-2 0.2 0.3 0.2 0.2 0.1 18.70 0.2 0.2 0.3 0.2 0.1 17.02 0.2 0.2 0.2 0.2 0.2 16.28 Average 17.33 TCP 4-3 0.2 0.3 0.2 0.2 0.1 14.23 0.2 0.2 0.3 0.2 0.1 16.50 0.2 0.2 0.2 0.2 0.2 17.11 Average 15.95 TCP 5-1 0.2 0.3 0.2 0.2 0.1 17.56 0.2 0.2 0.3 0.2 0.1 16.57 0.2 0.2 0.2 0.2 0.2 14.94 Average 16.36 TCP 5-2 0.2 0.3 0.2 0.2 0.1 16.52 0.2 0.2 0.3 0.2 0.1 16.81 0.2 0.2 0.2 0.2 0.2 17.16 Average 16.83 TCP 5-3 0.2 0.3 0.2 0.2 0.1 16.69 0.2 0.2 0.3 0.2 0.1 16.07 0.2 0.2 0.2 0.2 0.2 18.17 16.98 Average

Total Arrival Vehicles (Vehicle) 250772 246100 245491 247454 245584 246625 232042 241417 240826 203108 224552 222828 239969 244375 235479 239941 233022 248701 240001 240575 215617 235720 198752 216697 248361 244867 228899 240709 241405 246181 242233 243273 196243 235037 243731 225004 243567 235109 238493 239056 206569 241563 245764 231299 218058 231423 212422 220634 197316 250266 228376 225319 238310 246028 216987 233775 235501 236351 206237 226029

Average Travel Time (Minutes) 34.39 35.93 37.04 35.79 37.58 34.09 39.07 36.91 33.83 35.27 38.78 35.96 38.23 36.49 37.44 37.39 37.99 33.40 36.66 36.02 39.38 36.78 33.77 36.64 35.74 35.40 35.69 35.61 35.80 34.87 36.56 35.74 36.57 36.70 34.72 36.00 35.18 39.27 36.10 36.85 33.73 34.95 36.09 34.92 43.18 36.75 37.70 39.21 36.77 35.15 40.54 37.49 35.97 35.23 36.36 35.85 36.35 37.67 35.76 36.59

Trips (Persons) Motorcycles 41151 40730 43533

Cars 29876 29619 28190

Buses 43253 43925 42551

31331 31425 33679

34210 34298 32099

48738 48560 48495

29929 30318 32288

23725 24100 22458

60617 59865 59527

41350 40635 43560

29957 29490 28216

42973 44147 42499

31331 30784 33582

34073 33379 32164

48876 50110 48526

29725 29376 32220 30440 41111 40585 43392

23610 23148 22415 23058 29899 29454 28136

60938 61748 59638 60775 43269 44234 42745

31352 29996 32974

34210 32429 31290

48713 51846 50002

29679 29265 32233

23716 23135 22419

60878 61871 59621

41196 40657 43446

30000 29573 28091

43088 44044 42738

31273 30905 33576

34071 33652 32111

48933 49720 48587

29605 29287 32359

23640 23150 22491

61030 61831 59425

41257 40601 43465

30043 29606 28234

42982 44069 42571

31231 30853 33693

34184 33600 32225

48864 49821 48357

29226 29267 32259

23373 23137 22419

61683 61867 59598

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Besides the issue of computational efficiency, the major difficulty in applying this simulation-based PSE travel choice model for planning applications is how to realistically estimate the time-dependent OD demands for PSEs. These event-generated travel demands can vary due to the nature of individual events. More research is recommended to explore the travel demands of other types of special events and their participation. Especially for those PSEs without tickets, the travel associated with such special events can produce significant site-specific or even regional impacts, including severe traffic congestion or transit overcrowding. Acknowledgements The authors wish to thank Lihung Luke Cheng from CitiLabs Incorporated Company for his appreciated assistance during the project. References Balakrishna, R., 2006. Off-line calibration of dynamic traffic assignment models. Ph.D. Dissertation, Massachusetts Institute of Technology, Cambridge, UK. 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