Download pdf - Flexible Work Schedule Draft TRB - Zheng 20141110

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This draft is after the first round of edition, which is before the acceptance of 2015 1

TRR. 2

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Agent-Based Microsimulation Approach for Design and Evaluation of Flexible 4

Work Schedule Policy 5

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Zheng Zhu1, Chenfeng Xiong1, Xiqun Chen2, Xiang He1, Lei Zhang3 7

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1. Graduate Research Assistant 9

2. Research Associate 10

3. Associate Professor 11

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Department of Civil and Environmental Engineering 13

University of Maryland 14

1173 Glenn Martin Hall, College Park, MD 20742 15

Tel.: 301-405-2881 16

Email: [email protected] 17

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* Corresponding Author 19

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Date: August 1, 2014; November 15, 2014 21

Word Count: 4,519 words + 8 Figures = 6,519 words 22

Abstract 23

The policy of flexible work schedule has been proposed for years in order to stimulate 24

the redistribution of departure time among commuters. However, its potential 25

influence on travelers’ day-to-day traffic dynamics is infrequently seen in existing 26

studies. This paper extends an agent-based positive departure time model to gain 27

perspective on travelers’ dynamic reaction towards the flexible work schedule policy. 28

Unlike most rational behavior models, the positive model emphasizes the bounded 29

rationality in people’s actual behavior, and allows for heterogeneity among travelers. 30

Dynamic traffic assignment (DTA) is integrated with this proposed model to build up 31

the feedback loop between individual choice (demand side) and network performance 32

(supply side). Scenarios of different percentages of population with flexible work 33

schedule are analyzed. It is found that travelers with flexibility in work schedule tend 34

to depart later to avoid peak periods in the morning. The average travel time in the 35

network will decrease by at most 22%, when the policy of flexible work schedule is 36

implemented. 37

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Key words: flexible work schedule; agent-based model; DTA; positive model 39

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1. Introduction 40

The acceleration of urbanization is witnessed all around the world. Both population 41

and vehicle ownership are rapidly growing, and the induced traffic congestion 42

becomes an increasingly pervasive problem in people’s daily life. In 2011, 43

transportation congestion caused $121 billion economic loss in 498 U.S. urban areas, 44

which was 5 times as that in 1982 (in 2011 dollars) (1). Approximately 63% of total 45

delay occurred during peak periods when the commuting demand was high (1). 46

Working trips play an essential role in the “transportation life of the nation” (2). 47

Therefore, mitigating peak congestions can be a feasible solution to meet the 48

challenge of the urban growth. Various planning policies have been implemented to 49

mitigate urban congestion, e.g., encouraging the use of public transit, and imposing 50

restriction to auto ownership or usage. Although these policies have effectively 51

relieved the pressure of high travel demand, they were not designed specifically to 52

tackle severe congestions during peak periods. The objective of managing commuting 53

demand is very challenging because people should commute to work anyway. As 54

Anthony mentioned (2), traffic congestion would not eventually ameliorate until 55

people changed their daily behaviors. 56

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Rather than these transportation policies, there is an alternative way to gradually 58

inspire redistribution of trips: flexible work schedule. Traditionally, employees should 59

be present at work places during a specific time period (usually from 9 a.m. to 6 p.m.). 60

These traditional work schedules come from several reasons (e.g., human’s common 61

habit of sleeping at night). A consequence of this fixed work schedule is that 62

commuting trips are centralized during peak hours. Compared with the traditional 9 63

a.m. to 6 p.m. (or 8 a.m. to 5 p.m.) office hours, flexible work schedules (referred as 64

flextime policies hereafter) are becoming increasingly popular, which allow 65

employees to choose their preferred arrival/departure times. For example, employees 66

can arrive at their offices anytime between 8 a.m. to 10 a.m. and leave for home 67

anytime between 4 p.m. to 6 p.m. This policy is believed to be family friendly and 68

productive. However, its impact on urban traffic congestion is rarely seen in existing 69

studies. 70

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The motivation and objective of this paper is to explore potential impacts of this 72

policy on the network performance. In order to capture and characterize how people 73

shift their departure times under different levels of flextime policies, an agent-based 74

positive departure time model (21) is employed in this paper, which simulates 75

travelers’ departure time changes based on their travel experience. The dynamic traffic 76

assignment (DTA) simulator DynusT (3) is integrated with the positive model to 77

obtain traffic condition. Unlike rational behavior models, this study emphasizes the 78

bounded rationality in people’s actual behavior. A real-world application based on an 79

extracted network from the previous Inter County Connector (ICC) model (4) in the 80

State of Maryland is illustrated. Different levels of this flextime policy are tested for 81

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morning commuting trips in the study area. The purpose of this study is to illustrate 82

the capability of integrated agent-based behavior models and DTA for real-world 83

applications; and to investigate empirically the impact of flexible work schedules on 84

network performance. Since this paper only adopts traveler behavior model and traffic 85

assignment model, the direct impact on urban traffic conditions is the only focus, 86

leaving social benefits of this policy for future research. 87

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The article is organized as follows: Section 2 presents a comprehensive literature 89

review on current congestion mitigation policies and the models employed to analyze 90

the effect of those policies. Section 3 briefly introduces the framework of the positive 91

model, as well as the integration of the positive model with a mesoscopic 92

simulation-based DTA simulator. Section 4 presents a real-world case study with 93

scenarios assuming different levels of flextime policies. The discussions and 94

conclusions are drawn in Section 5. 95

2. Literature Review 96

Various planning approaches have been proposed to relieve urban traffic congestion. 97

They mitigate traffic congestions by expanding roadway capacity, encouraging public 98

transit, or limiting auto-ownership (i.e., vehicle registrations fees (5)) and auto-usage 99

i.e., congestion pricing (6)). It is undeniable that these policies have been repeatedly 100

used for congestion management. Although there have been plenty of explorations on 101

these policies, research gap still exists for the analysis of transportation impacts of 102

flexible work schedule policies. Flexible work schedule, as known as flextime policy, 103

is a promising measure that should be effective in mitigating congestion. There are 104

numerous studies underlining potential benefits of this policy. Common conclusions 105

have been drawn: 1) flexible work schedules are expected to “increase employees’ job 106

satisfaction, organizational commitment, productivity, and decrease absenteeism and 107

turnover” (7); and 2) flexible schedules tend to reduce time and role conflicts between 108

work and family non-work responsibilities (such as social activities and children care). 109

Due to these benefits, the implementation of the flextime policy has been increasing 110

rapidly (from 15% of employees with flexible work schedule in 1991 to 27% in 1999) 111

(8). In addition, work schedules in the U.S. seem to be more and more differentiated 112

and flexible (8). Flextime policy receives a high evaluation as a work/life balancing 113

policy. However, there are few studies illustrating its potential value for transportation 114

demand management and peak-hour traffic congestion mitigation. 115

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While flextime related questions are often considered in travel surveys, (e.g., 2009 117

National Household Travel Survey (9), and Chicago’s Travel Tracker Survey (10)), 118

the questions were simplistic in nature (i.e., simple yes-no questions about whether 119

the survey participant had flexibility in work scheduling). This simplicity makes it 120

difficult to fully understand behavioral changes due to flextime policies. Saleh and 121

Farrell defined the individual’s “level of flexibility” to investigate departure time 122

choice (11). The level of flexibility is determined by traveler’s work schedule 123

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flexibility, personal constraints such as home-responsible activities before work, and 124

socio-economic characteristics. They found that departure time choice could be 125

affected by work/non-work flexibilities and individuals’ socio-economic types. A 126

multinomial Logit model was adapted to investigate the departure time preference for 127

people with flextime. Results showed that flextime increased the probability of 128

post-peak travel and reduced the probability of pre-peak travel (12). 129

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Brewer (13-14) tried to link travel behavior and the flexible work design, and made an 131

assumption of impacts on traffic conditions. A game theoretical method was adopted 132

to model the choice between flexible schedule and non-flexible schedule. No traffic 133

models were used in these studies. Later on, bottleneck models and network 134

equilibrium had been adopted to analyze the economic impact of flextime policy 135

(15-18). The embedded equilibrium condition where no travelers could find better 136

departure time with less cost increased models’ computational burden, especially 137

when user heterogeneity, capacity uncertainty, and behavioral-changing process 138

needed to be captured. This hinders bottleneck models’ application potential in 139

real-world analysis wherein an urban region can easily include thousands of links and 140

tens of millions of heterogeneous commuters. 141

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Considering flexible work schedule policy as a potential attainable alternative to 143

improve traffic condition, this study applies an agent-based departure time choice 144

model to investigate both demand pattern changes and traffic improvement under this 145

policy. Unlike previous models, an agent-based model focuses on actions and 146

interactions of autonomous agents. One of the earliest agent-based models was for 147

segregation (19). With the development of scientific computer, this concept has been 148

widespread to various areas. In transportation research, agent-based studies have 149

already been conducted for studies of demand patterns, such as departure time choice, 150

route choice, traffic diversion, and policy-makers’ investment decisions (20-27). 151

Agent-based models are capable to capture individual-level behavior changes. 152

Individual’s decision and behavior are then aggregated for the traffic demand analysis. 153

This makes agent-based models more powerful over traditional four-step models that 154

ignore the heterogeneity of individuals (28-29). 155

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In terms of the departure time analysis, there used to be extensive research applying 157

rational behavior theory, such as the bottleneck model (16, 30-31), discrete departure 158

time choice models (32-35). Under rational behavior theory, travelers have access to 159

the information of all feasible alternatives and maximize their utility (36). The 160

agent-based departure time choice model in this study is known as a positive model 161

(20). Unlike rational approaches, positive theory assumes that individuals no longer 162

have perfect knowledge to maximize their utilities. The proposed agent-based positive 163

departure time model explicitly simulates the goal, knowledge, learning, and search 164

ability of the travelers in the simulation network (22, 37). The framework of the 165

positive departure time choice model was first developed by Zhang and Xiong (20) 166

under the Search, Information, Learning, and Knowledge (SILK) theory (37). The 167

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model was applied to a large-scale peak spreading study (4) and a numerical study on 168

demand/supply uncertainty (21). This paper would expand Zhang and Xiong’s model 169

in three aspects: 1) improve the calculation of payoff for flextime policy study; 2) 170

consider demand/supply uncertainty to enhance the reality; and 3) adopt a multi-day 171

knowledge updating to obtain traveling agent’s information on travel time reliability. 172

Here “multi-day” means running several rounds of simulation for one demand type, 173

which will be introduced in Section 3.1. 174

3. Agent-Based Modeling Framework for Flextime Policy 175

Analysis 176

3.1 Behavior Model 177

Based on previous studies (20-22), the positive departure time model provides a 178

framework for the flextime policy modeling. For each traveler (agent) in the model, 179

he/she is able to acquire traffic information from his/her prior travel experience or 180

other sources (e.g., traveler information systems). Travelers’ knowledge and 181

subjective beliefs about traffic conditions are formed through a perception and 182

learning process. With the explicitly measured knowledge and subjective beliefs, the 183

model can determine personal attitude towards his/her current traffic conditions. That 184

is, how much the person expects to benefit from additional days of searches. 185

Subjective search gain is defined to measure this benefit. It is theorized as the gap 186

between the experienced best situation (the simulation day with best payoff) and the 187

ideal situation (travel on free flow speed, arrive at destination at preferred arrival time 188

(PAT)). Correspondingly, search cost is defined to quantify a person’s perceived loss 189

in each round of search. This may result from a traveler’s searching efforts (e.g., time, 190

monetary, mental efforts, and the risk for worse travel experience). The trade-off 191

between the subjective search gain and the perceived search cost determines the start 192

and the termination of an agent’s searching process. 193

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Once a traveler stops searching, he/she would repeat his/her current departure time for 195

the rest of the simulation days. Otherwise, the traveler would find a new departure 196

time based on current knowledge and a set of search rules. The traveler needs to map 197

his/her spatial knowledge to the traffic conditions of the alternative departure time. 198

Then a binary decision is made based on a set of decision rules about whether or not 199

to switch to the new departure time. After all the agents have made decisions, the 200

individual-level behaviors are aggregated for the traffic modeling of a new day. Refer 201

to (20) for a full-scale view about the search rules and decision rules. 202

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In this research, three major improvements are considered to enhance the robustness 204

of the flexible work schedule modeling. Firstly, as individual-level decisions are made 205

based on current travel experience, it is necessary to build a linkage between work 206

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flexibility and the quantitative attitude towards travel experience. In previous studies, 207

this attitude was modeled following the rational behavior theory: 208

( ) ( ) ( ) ( )V t T t SDE t SDL t 209

( ) max(0,( ( )))SDE t PAT t T t (1) 210

( ) max(0,( ( ) ))SDL t t T t PAT 211

where t is the departure time, V(t) is the payoff at t, T(t) is the travel time associated 212

with t; PAT is the preferred arrival time to destination, SDE/SDL represent schedule 213

delay early/late, and , and are coefficients. In this paper, PAT is replaced 214

by the preferred arrival time interval (PATI). As illustrated in Figure 1, a traveler 215

arrives earlier than PAT would gain negative utility due to SDE; however, after he/she 216

has gained flexibility in schedule, the traveler will no longer has SDE with the same 217

departure time and travel experience (30). 218

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Figure 1 PATI v.s. PAT 220

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Secondly, uncertainty of both supply and demand sides is simulated in this paper to 222

enhance the authenticity of the scenarios. Due to physical and operational factors, 223

such as the road constructions and maintenance, incidents, and weather, some 224

roadways may lose capacity or be blocked during certain time periods. In order to 225

model supply side uncertainty, the whole 2013 incident data of the study area is 226

obtained from Regional Integrated Transportation Information System (RITIS) (38). 227

Based on RITIS data, we assume the incident frequency follows Poisson distribution 228

with rate 1.74 (times/day). The duration of incidents is assumed to follow Exponential 229

distribution with rate 1/37 (minute-1). The location of an incident is determined by a 230

link’s failure probability in direct proportion with its volume. Demand, also varies 231

DepartureTime

DepartureTime

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AT

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TT SDE

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from day to day following the variation of social activities and events. The demand 232

side uncertainty is introduced by randomness of the total travel demand from day to 233

day. The coefficient of variation (CV, defined as the demand standard deviation 234

divided by the mean travel demand) can be used to measure the demand-side 235

fluctuation. In this study, the day-to-day CV was assumed to have a Uniform 236

distribution from 0 to 0.15. 237

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Thirdly, a multi-day knowledge updating is adopted instead of single-day learning and 239

decision making. It is assumed that travelers will not change their departure times 240

within one week. Before every new week of searching and switching, one week’s (5 241

simulation work days) travel experience will be simulated. The departure time of each 242

individual remains the same during the week. After the multi-day simulation, the 243

average and standard deviation of travel time for every agent are calculated as a 244

statistical travel experience. There are two purposes for this modification: to avoid 245

simulation noise that may lead to unreasonable behavior change; to capture the impact 246

of travel reliability on departure time choice. 247

3.2 Integration of Behavior Model with Dynamic Traffic 248

Assignment 249

In this study, the mesoscopic traffic simulator DynusT (3) is integrated with the 250

positive model to simulate travel experience and model dynamic departure time 251

choice. The integration flowchart is shown in Figure 2. The modeling of departure 252

time shift begins from the static OD estimated via planning models. Multimodal static 253

OD estimation and dynamic OD calibration are then conducted to obtain 254

time-dependent OD tables for study area. Details of these OD estimation approaches 255

can be found in (4). In order to calculate travelers’ current experience, DTA is initially 256

applied to pursue dynamic user equilibrium (DUE), after which travelers’ travel time 257

are collected. Meanwhile, their paths are extracted to calculate free flow travel time 258

(FFTT) as their ideal travel condition. Here FFTT and current travel time are used to 259

initialize their search gain. Heterogeneity is embedded when synthesizing these 260

travelers with socio-demographic variables including: income, gender, flexibility of 261

arrival times, search cost, etc. Under such initialization, dynamic assignment is 262

adopted to simulate weekly traffic knowledge learning process. Travelers’ weekly 263

average and standard deviation of travel time are updated as new information. Then 264

positive model is employed to simulate agents’ travel experience learning, departure 265

time searching, and decision making process. The iterative loops of the departure time 266

modeling would not terminate until only a small percentage of individuals (5%) are 267

still searching for alternative departure times. 268

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Figure 2 Flowchart of the integrated model 271

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4. Flextime Policy Scenario Analysis 273

In order to demonstrate the capability of the model in analyzing the impact of flextime 274

policies, a real world application is illustrated in this section. The selected study area 275

is shown in Figure 3, which includes Rockville, North Bethesda, and Gaithersburg in 276

Montgomery County of Maryland. Based on Metropolitan Washington Council of 277

Governments (MWCOG) planning model version 2.3 the population in this area is 278

306,590; and the number of employment is 206,529. Three major roadways (I-495, 279

I-270 and MD355) and other minor/local roadways are coded via DynusT in this 280

study. There are 61 traffic analysis zones, 201 nodes and 1,077 links in total. Already 281

containing AM peak period, the simulation horizon is from 5:00 a.m. to 10:00 a.m. 282

237,903 vehicles are extracted from the ICC model for the corresponding time period. 283

The demand has already been calibrated and validated in the previous work (4). 284

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DTA ModelStatic OD from Planning Model

Time-Dependent OD

Estimation & Calibration

Initial Situation

DUE Assignment

FFTT Calculating

PopulationSynthesizing

DTA ModelProposed Positive

Model

No Convergence

Convergence

End

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Figure 3 A Real World Network: I-270/MD-355 Corridor 287

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There are 11 scenarios designed in this paper, with 0%, 10%, 20% to 100% of the 289

agents randomly assigned with flexible work schedules. Although the flexible 290

schedule percentage in the study area is around 29.1% according to 2007-2008 291

Transportation Planning Board (TPB) and Baltimore Metropolitan Council (BMC) 292

Household Travel Survey, this paper tries to explore different flextime levels to 293

further understand the impact of this policy. Socio-demographic variables such as 294

gender and income level are generated by the sample distribution in 2007-2008 295

TPB/BMC Household Travel Survey. In order to reduce the impact of simulation 296

noise, 5 rounds of simulations are performed for each scenario. The 0% scenario is 297

considered as a base case. This base case is assumed to be the original traffic situation, 298

in which everyone has habitual departure time and arrival time provided by dynamic 299

user equilibrium. In these scenarios, people assigned with flexible schedule can arrive 300

any time within their PATI. PATI is assumed to be a two-hour time interval with the 301

current PAT positioned in the center. For example, if a traveler’s PAT is 9:00 a.m., 302

his/her PATI should be from 8:00 a.m. to 10:00 a.m. It takes around 10 weeks (50 303

simulation days) for each simulation to reach convergence, so there are around 2,750 304

iterations in total. 305

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After the interaction between departure time change and traffic system performance, 307

only a fraction of travelers (around 5%) are still looking for new departure times. This 308

stable situation among travelers is regarded as behavioral user equilibrium (BUE) (37). 309

The impacts of flextime policy on the demand pattern are displayed in Figure 4. The 310

curves without dots denote the base case situation, which means no agents have 311

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flexible schedule; the curves with dots denote the scenarios with different percentages 312

of flextime agents. As the percentages of agents with flexible schedules increase, the 313

demand during the peak period (6:00 a.m. to 8:00 a.m.) shifts to later time periods 314

(8:30 a.m. to 10:00 a.m.). A peak spreading is found that the peak period in base case 315

(6:00 a.m. to 9:00 a.m.) has been expanded to a broader time interval. After the 316

percentage of flextime agents increases to 60%, there is no obvious peak period 317

(compared with the base case demand). The demand distributes smoothly from 6:00 318

a.m. to 10:00 a.m., which is consistent with previous studies (12, 18). The scenario of 319

100% flextime agents represents the case of most significant peak spreading. 320

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327 Figure 4 Demand Pattern Change 328

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To better understand the demand pattern changes due to the implementation of 330

flexible work schedule policies, Figure 5 illustrates the demand patterns for flextime 331

agents and non-flextime agents separately. Figure 5(a) summarizes the demand 332

pattern change for agents with flextime. The 11 curves from bottom to top correspond 333

to the scenarios with increasing ratios of flex-time agents from 0% to 100%; while in 334

Figure 5(b), the 11 curves from bottom to top correspond to the scenarios with 335

decreasing ratios (100% to 0%). For travelers who have flexible work schedules, even 336

if this ratio is relatively low, there is no significant peak in the demand pattern; while, 337

for travelers without the flextime policy, an obvious peak can be observed between 338

6:00 a.m. and 9:00 a.m. almost in every scenario. This phenomenon implies that 339

travelers with flexible work schedules tend to depart later to avoid the peak hours. As 340

the percentage of agents with flextime increases, the absolute number of travelers who 341

switch their departure time out of peak hours is also growing. It is found that travelers 342

with flextime have a major contribution to the peak spreading and the demand shifting 343

phenomena as discussed above. On the other hand, this policy has very little impact 344

on the demand pattern of the travelers without flexible work schedules. 345

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(a) Demand of agents with flextime 348

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(b) Demand of agents without flextime 350

Figure 5 Demand Pattern Change for Both Agents 351

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Figure 6 indicates the interesting finding that flextime travelers choose to depart later 353

while there is almost no change on the demand pattern of travelers without flexible 354

work schedules. The 70% scenario is selected for analysis because: 1) the total 355

demand is evenly distributed from 7:00 a.m. to 10:00 a.m. (Figure 4); and 2) two 356

groups of agents obtain different changes in their payoff. Figure 6(a) illustrates the 357

payoff changes for the agents with flexible schedules. The horizontal axis represents 358

the original departure time, the vertical axis represents the departure time that agents 359

shift to, and the grey scale represents the payoff change ratio. Obviously, people who 360

used to depart during peak hours benefit the most from the peak spreading effort. That 361

is, the payoff for these travelers increases nearly 50%. There is little change of payoff 362

for travelers who used to depart around 5:00 a.m., because they used to enjoy the 363

FFTT before flextime policy. Figure 6(b) shows how many agents have shifted 364

departure time from/to different time periods (presented as the logarithm of the 365

switching population in grey scale). According to the dark points along the diagonal 366

line, the majority of these travelers still depart at their original time. Travelers who 367

used to depart during AM peak (6:00 a.m. to 9:00 a.m.) period have a much higher 368

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rate to switch their departure time. For those who change behavior, a later departure 369

time is much more preferred than an earlier one. When some portion of travelers 370

departs later, traffic congestion is eased and there is less incentive for the rest of 371

people to change their behavior. This “later-preferred” demand trend also leads to the 372

peak spreading phenomenon discussed above. Different results are analyzed for 373

non-flextime agents, as illustrated in Figure 6(c) and 6(d). Before 9:00 a.m., 374

non-flextime agents may have minor increase in their payoff (Figure 6c), which is 375

resulted from the mitigated traffic congestion. Travelers departing after 9:00 a.m. will 376

suffer a loss of payoff due to the demand increase. Similar to flextime agents, the 377

majority of non-flextime agents stay unchanged (Figure 6d). What is different is that 378

the number of agents switching earlier/later is almost identical, which leads to a stable 379

demand pattern for these agents. 380

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Figure 6 Payoff Change Under 70% Scenario 386

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The average travel time diagram (Figure 7) shows the impact of individual behavior 388

changes on the aggregate network performance. The horizontal axis represents the 389

departure time, the vertical axis represents the percentage of flextime travelers, and 390

the grey scale represents the average travel time in minutes. The traffic condition 391

during the AM peak is improved as the flextime agent percentage increases. For 392

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example, in the base case, there is a “congested departure interval” occurring between 393

6:40 and 9:00 a.m., which means the average travel time for travelers departing within 394

this time period is over 12 minutes. This “congested interval” gradually disappears 395

after the flextime ratio increases to 50%. However, the relationship between travel 396

time and flextime ratio is not monotonic. Travelers departing after 9:30 a.m. will 397

suffer a small bottleneck when this ratio surpasses 70%. Unlike the traffic congestion 398

during the AM peak in the base case, this bottleneck is resulted from the payoff gain 399

for the agents with flexible work schedule. For the entire simulation horizon, Figure 8 400

shows the overall average travel time of different policy scenarios. In this case study, 401

scenarios with flextime policy all perform better than the base case; the traffic system 402

with 60% flextime agents reaches the best results in terms of travel time delay, 403

leading to a total travel time saving of 10,785 hours (22.3%). 404

405

0 406

Figure 7 Travel Time Change for the Whole Population 407

408

Time

% o

f F

lex

tim

e A

ge

nts

Avg. Travel Time for All Agents (min)

5:00 6:00 7:00 8:00 9:00

0

10

20

30

40

50

60

70

80

90

100

4

6

8

10

12

14

16

18

15

409

Figure 8 Network Average Travel Time 410

5. Discussions and Conclusions 411

This paper attempts to gain perception about travelers’ reaction towards flexible work 412

schedule policy. Unlike previous flextime studies, the research goal in this paper is 413

achieved through further developing the modeling framework of an agent-based 414

positive departure time choice model. Individual knowledge learning and decision 415

making process is specified and empirically modeled to understand the potential 416

influence of this policy on day-to-day traffic dynamics. DTA is integrated with this 417

agent-based positive departure time choice model. One remarkable advantage of this 418

integrated model is its ability to build a feedback between demand-side individual 419

choice and supply-side network performance. The disadvantage (we may also call it 420

our future research opportunity) is that the agent behavior (search rules and decision 421

rules) already built in this study area may be inapplicable for other study areas. Thus, 422

the model requires further calibration before applying to other study areas or scenarios. 423

One alternative calibration method is to apply simulation based optimization to adjust 424

the probability distribution of the new departure time searching (39), which will be 425

explored in future research. 426

427

Different scenarios of various percentages of flextime agents are tested in a real world 428

network in Montgomery County, Maryland. It has been found that travelers with 429

schedule flexibility tend to make their travel later, which is the same as (12). This 430

result is in accordance with the purpose of flextime policy, which aims at balancing 431

the conflict between work and family. Travelers’ individual level behavior change 432

may lead to significant improvement on traffic system. As these flextime travelers 433

switch from AM peak to post-peak periods, the congestion during peak hours is 434

alleviated. However, the improvement of traffic condition has few influences on the 435

0 10 20 30 40 50 60 70 80 90 100

8

9

10

11

12

13

14

12.51

10.7110.9

10.43

10.810.55

9.7210

9.63

10.23

9.85

Average Travel Time (min)

% of Agents with Flextime

Tra

ve

l T

ime

(m

in)

16

demand pattern of agents without flexible schedules. The network with 60% flextime 436

travelers performs the best. Under such condition, original AM peak in the base case 437

will spread between 6:00 a.m. and 10:00 a.m.. Compared to the base case, 10,785 438

hours (22.3%) of traffic delay would be saved. Since the current flextime ratio is 439

around 30%, the 60% or upper flextime ratio seems unpractical. In addition, results 440

may not be the same for other areas or networks. This paper holds a theoretical 441

analysis for prospect of future demand management policies. 442

443

In this research, the assumption in terms of flextime policy is strong: the PATI is a 444

two-hour time window based on travelers’ PAT. This is a shallow attempt to 445

demonstrate the capability of this integrated agent-based model to capture departure 446

time change under behavior related policies. Departure time flexibility modeling can 447

be a complex problem because travelers’ flexibility is determined by a variety of 448

factors, i.e. travelers’ ability to start work later/earlier, traveler’s house responsibility, 449

and social-economic characteristics. All these features can be taken into account for 450

future research. In addition, it will be more interesting and meaningful if monetary 451

stimulus is considered in flextime policy study. That is, a traveler can get some 452

monetary reward if he/she switches from peak period to off-peak period. Thus, it 453

allows us to have perspective view on the monetary cost and welfare gain due to the 454

introduction of flextime policy. Furthermore, comparisons can be conducted between 455

traffic demand management and other congestion mitigation methods, such as 456

roadway capacity extension. 457

458

Furthermore, this integrated model is also applicable for studying the impact of other 459

management policies, demand increase, and even roadway incidents on travel 460

behavior. Since departure time is the only dependent variable in its current framework, 461

the model still requests further development to capture travelers’ behavior change in 462

route choice, mode choice, lane choice, etc. The authors expect to empirically 463

estimate and embed other behavior rules into this framework for more comprehensive 464

analysis. 465

Acknowledgement 466

This research is financially supported by a National Science Foundation CAREER 467

Award, “Reliability as an Emergent Property of Transportation Networks”, and the 468

U.S. Federal Highway Administration Exploratory Advanced Research Program. The 469

opinions in this paper do not necessarily reflect the official views of NSF or FHWA. 470

They assume no liability for the content or use of this paper. The authors are 471

responsible for all statements in this paper. 472

473

17

References 474

1. Schrank, D., Eisele, B., Lomax, T., (2012). The Urban Mobility Report. Texas 475

Transportation Institute, College Station, TX. 476

2. Anthony, D. (2004). Still Stuck in Traffic: Coping with Peak-Hour Traffic 477

Congestion. Brookings Institution Press. 478

3. Chiu, Y. C., Nava, E., Zheng, H., Bustillos, B. (2011). DynusT User's Manual. 479

4. Zhang, L., Chang, G. L., Zhu, S., Xiong, C., Du, L., Mollanejad, M., Mahapatra, S. 480

(2012). Integrating an Agent-Based Travel Behavior Model with Large-Scale 481

Microscopic Traffic Simulation for Corridor-Level and Subarea Transportation 482

Operations and Planning Applications. Journal of Urban Planning and Development, 483

139(2), 94-103. 484

5. Goh, M. (2002). Congestion Management and Electronic Road Pricing in 485

Singapore. Journal of Transport Geography, 10(1), 29-38. 486

6. De Palma, A., Lindsey, R. (2011). Traffic congestion pricing methodologies and 487

technologies. Transportation Research Part C, 19(6), 1377-1399. 488

7. Rogier, S.A., Padgett, M.Y. (2004). The Impact of Utilizing a Flexible Work 489

Schedule on the Perceived Career Advancement Potential of Women. Human 490

Resource Development Quarterly, 15(1), 89-106. 491

8. Golden, L. (2001). Flexible Work Schedules Which Workers Get Them? American 492

Behavioral Scientist, 44(7), 1157-1178. 493

9. Santos, A., McGuckin, N., Nakamoto, H., Gray, D., Liss, S. (2011). Summary of 494

Travel Trends: 2009 National Household Travel Survey (No. FHWA-PL-II-022). 495

10. Chicago Metropolitan Agency for Planning (CMAP). (2008). Travel Tracker 496

Survey. https://www.cmap.illinois.gov/data/transportation/travel-tracker-survey 497

11. Saleh, W., Farrell, S. (2005). Implications of Congestion Charging for Departure 498

Time Choice: Work and Non-work Schedule Flexibility. Transportation Research Part 499

A, 39(7), 773-791. 500

12. He, S.Y. (2013). Does Flexitime affect Choice of Departure Time for Morning 501

Home-based Commuting Trips? Evidence from Two Regions in California. Transport 502

Policy, 25, 210-221. 503

13. Brewer, A.M. (1998). Work Design, Flexible Work Arrangements and Travel 504

Behaviour: Policy Implications. Transport Policy, 5(2), 93-101. 505

14. Brewer, A.M., Hensher, D.A. (2000). Distributed Work and Travel Behaviour: The 506

Dynamics of Interactive Agency Choices Between Employers and Employees. 507

Transportation, 27(1), 117-148. 508

15. Mun, S.I., Yonekawa, M. (2006). Flextime, Traffic Congestion and Urban 509

Productivity. Journal of Transport Economics and Policy, 40(3), 329-358. 510

16. Vickrey, W. S. (1969). Congestion Theory and Transport Investment. American 511

Economic Review, 59, 251-261. 512

17. Yoshimura, M., Okumura, M. (2001). Optimal Commuting and Work Start Time 513

Distribution under Flexible Work Hours System on Motor Commuting. In 514

Proceedings of the Eastern Asia Society for Transportation Studies, 10(3), 455-69. 515

https://www.cmap.illinois.gov/data/transportation/travel-tracker-survey

18

18. Xiao, L., Liu, R., Huang, H. (2014). Congestion Behavior under Uncertainty on 516

Morning Commute with Preferred Arrival Time Interval. Discrete Dynamics in Nature 517

and Society, 767851. 518

19. Schelling, T.C. (1971). Dynamic Models of Segregation. Journal of Mathematical 519

Sociology, 1(2), 143-186. 520

20. Zhang, L., Xiong, C. (2012). A Positive Model of Departure Time Choice. In the 521

4th Transportation Research Board Conference on Innovations in Travel Modeling 522

(ITM). Tampa, FL. 523

21. Xiong, C., Zhang, L. (2013). Positive Model of Departure Time Choice under 524

Road Pricing and Uncertainty. Transportation Research Record: Journal of the 525

Transportation Research Board, 2345(1), 117-125. 526

22. Zhang, L., Levinson, D. (2004). An Agent-Based Approach to Travel Demand 527

Forecasting: Exploratory Analysis. In Transportation Research Record: Journal of the 528

Transportation Research Board, No. 1898, Transportation Research Board of the 529

National Academies, Washington, D.C., 28-36. 530

23. Bazzan, A.L.C., Wahle, J., Klügl, F. (1999). Agents in Traffic Modelling—from 531

Reactive to Social Behaviour. In KI-99: Advances in Artificial Intelligence, pp. 532

303-306. Springer Berlin Heidelberg. 533

24. Rossetti, R.J., Bordini, R.H., Bazzan, A.L., Bampi, S., Liu, R., Vliet, D.V. (2002). 534

Using BDI Agents to Improve Driver Modelling in a Commuter Scenario. 535

Transportation Research Part C, 10(5), 373-398. 536

25. Chen, B., Cheng, H.H. (2010). A Review of the Applications of Agent Technology 537

in Traffic and Transportation Systems. IEEE Transactions on Intelligent 538

Transportation Systems, 11(2), 485-497. 539

26. Adler, J.L., Blue, V.J. (2002). A Cooperative Multi-agent Transportation 540

Management and Route Guidance System. Transportation Research Part C, 10(5) 541

433-454. 542

27. Xiong, C., Zhang, L. (2013). A Descriptive Bayesian Approach to Modeling and 543

Calibrating Drivers' En Route Diversion Behavior. IEEE Transactions on Intelligent 544

Transportation Systems, 14(4), 1817-1824. 545

28. Zhang, L., Levinson, D. (2004). Agent-Based Approach to Travel Demand 546

Modeling: Exploratory Analysis. Transportation Research Record: Journal of the 547

Transportation Research Board, 1898, 28-36. 548

29. Balmer, M., Axhausen, K.W., Nagel, K. (2006). Agent-Based Demand-Modeling 549

Framework for Large-Scale Microsimulations. Transportation Research Record: 550

Journal of the Transportation Research Board, 1985, 125-134. 551

30. Ramadurai, G., Ukkusuri, S.V., Zhao, J., Pang, J.-S. (2010). Linear 552

Complementarity Formulation for Single Bottleneck Model with Heterogeneous 553

Commuters. Transportation Research Part B, 44(2), 193-214. 554

31. Arnott, R., de Palma, A., Lindsey, R. (1990). Economics of a Bottleneck. Journal 555

of Urban Economics, 27(1), 111-130. 556

32. Small, K.A. (1982). The Scheduling of Consumer Activities: Work Trips. 557

American Economic Review, 72, 467-479. 558

33. Small, K.A. (1987). A Discrete Choice Model for Ordered Alternatives. 559

19

Econometrica, 55, 409-424 560

34. Vovsha, P. (1997). Application of Cross-Nested Logit Model to Mode Choice in 561

Tel Aviv, Israel, Metropolitan Area. Transportation Research Record: Journal of the 562

Transportation Research Board, 1607, 6-15. 563

35. Lemp, J. D., Kockelman, K. M. Damien, P. (2010). The Continuous Cross-Nested 564

Logit Model: Formulation and Application for Departure Time Choice. 565

Transportation Research Part B, 44, 646-661. 566

36. Samuelson, P. 1947. Foundations of Economic Analysis. Harvard University Press, 567

Cambridge, Massachusetts. 568

37. Zhang, L. (2007). Developing a Positive Approach to Travel Demand Forecasting: 569

Theory and Model. Traffic and Transportation Theory, 17, 136-150. 570

38. Regional Integrated Transportation Information System (RITIS). (2009). 571

<https://www.ritis.org/> 572

39. Chen, X., Zhang, L., He, X., Xiong, C., Li, Z. (2014). Surrogate-Based 573

Optimization of Expensive-to-Evaluate Objective for Optimal Highway Toll Charges 574

in Transportation Network. Computer-Aided Civil and Infrastructure Engineering, 575

29(5), 359-381. 576