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This draft is after the first round of edition, which is before the acceptance of 2015 1
TRR. 2
3
Agent-Based Microsimulation Approach for Design and Evaluation of Flexible 4
Work Schedule Policy 5
6
Zheng Zhu1, Chenfeng Xiong1, Xiqun Chen2, Xiang He1, Lei Zhang3 7
8
1. Graduate Research Assistant 9
2. Research Associate 10
3. Associate Professor 11
12
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
18
* Corresponding Author 19
20
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
38
Key words: flexible work schedule; agent-based model; DTA; positive model 39
2
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
57
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
71
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
3
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
88
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
116
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
4
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
130
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
142
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
156
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
5
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
194
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
203
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
6
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
219
Figure 1 PATI v.s. PAT 220
221
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
PATAT
AT
FixedSchedule
FlexibleSchedule
PATI
TT
TT SDE
7
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
238
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
269
8
270
Figure 2 Flowchart of the integrated model 271
272
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
285
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
9
286
Figure 3 A Real World Network: I-270/MD-355 Corridor 287
288
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
306
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
10
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
321
322
323
324
325
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11
326
327 Figure 4 Demand Pattern Change 328
329
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
346
5:00 6:00 7:00 8:00 9:00
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70% Agents with Flextime
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12
347
(a) Demand of agents with flextime 348
349
(b) Demand of agents without flextime 350
Figure 5 Demand Pattern Change for Both Agents 351
352
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
5:00 6:00 7:00 8:00 9:00
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13
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
381
382
(a) (b) 383
384
(c) (d) 385
Figure 6 Payoff Change Under 70% Scenario 386
387
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
Previous Departure Time
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7:00
8:00
9:00
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
Previous Departure Time
De
pa
rtu
re T
ime
Aft
er
Fle
xti
me
Po
lic
iy
Switching Log. Num. of Non-Flextime Agents (70%)
5:00 6:00 7:00 8:00 9:00
5:00
6:00
7:00
8:00
9:00
0
0.5
1
1.5
2
2.5
3
14
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
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