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Practices in One-Lane Traffic Control on a Two-Lane Rural Highway (2018)

Chapter: Appendix A - Traffic Analysis for 1L2W Operations

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Suggested Citation:"Appendix A - Traffic Analysis for 1L2W Operations." National Academies of Sciences, Engineering, and Medicine. 2018. Practices in One-Lane Traffic Control on a Two-Lane Rural Highway. Washington, DC: The National Academies Press. doi: 10.17226/25174.
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Suggested Citation:"Appendix A - Traffic Analysis for 1L2W Operations." National Academies of Sciences, Engineering, and Medicine. 2018. Practices in One-Lane Traffic Control on a Two-Lane Rural Highway. Washington, DC: The National Academies Press. doi: 10.17226/25174.
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Suggested Citation:"Appendix A - Traffic Analysis for 1L2W Operations." National Academies of Sciences, Engineering, and Medicine. 2018. Practices in One-Lane Traffic Control on a Two-Lane Rural Highway. Washington, DC: The National Academies Press. doi: 10.17226/25174.
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Suggested Citation:"Appendix A - Traffic Analysis for 1L2W Operations." National Academies of Sciences, Engineering, and Medicine. 2018. Practices in One-Lane Traffic Control on a Two-Lane Rural Highway. Washington, DC: The National Academies Press. doi: 10.17226/25174.
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Suggested Citation:"Appendix A - Traffic Analysis for 1L2W Operations." National Academies of Sciences, Engineering, and Medicine. 2018. Practices in One-Lane Traffic Control on a Two-Lane Rural Highway. Washington, DC: The National Academies Press. doi: 10.17226/25174.
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Suggested Citation:"Appendix A - Traffic Analysis for 1L2W Operations." National Academies of Sciences, Engineering, and Medicine. 2018. Practices in One-Lane Traffic Control on a Two-Lane Rural Highway. Washington, DC: The National Academies Press. doi: 10.17226/25174.
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Suggested Citation:"Appendix A - Traffic Analysis for 1L2W Operations." National Academies of Sciences, Engineering, and Medicine. 2018. Practices in One-Lane Traffic Control on a Two-Lane Rural Highway. Washington, DC: The National Academies Press. doi: 10.17226/25174.
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Suggested Citation:"Appendix A - Traffic Analysis for 1L2W Operations." National Academies of Sciences, Engineering, and Medicine. 2018. Practices in One-Lane Traffic Control on a Two-Lane Rural Highway. Washington, DC: The National Academies Press. doi: 10.17226/25174.
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Suggested Citation:"Appendix A - Traffic Analysis for 1L2W Operations." National Academies of Sciences, Engineering, and Medicine. 2018. Practices in One-Lane Traffic Control on a Two-Lane Rural Highway. Washington, DC: The National Academies Press. doi: 10.17226/25174.
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Suggested Citation:"Appendix A - Traffic Analysis for 1L2W Operations." National Academies of Sciences, Engineering, and Medicine. 2018. Practices in One-Lane Traffic Control on a Two-Lane Rural Highway. Washington, DC: The National Academies Press. doi: 10.17226/25174.
×
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Suggested Citation:"Appendix A - Traffic Analysis for 1L2W Operations." National Academies of Sciences, Engineering, and Medicine. 2018. Practices in One-Lane Traffic Control on a Two-Lane Rural Highway. Washington, DC: The National Academies Press. doi: 10.17226/25174.
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104 This appendix provides a literature review of studies focused on 1L2W TTC zone traffic analysis, with a focus on delays and capacity and including the use of manual flagging or signal (TTCS) controls. Delay and Capacity Analysis Cassidy and Han developed a model to estimate vehicle delays and queue lengths at two-lane highway TTC zones that involve the closure of one lane and have flaggers stationed at the ends to guide traffic (Cassidy and Han 1993). The vehicle delays at 1L2W TTC zones consist of two parts: (1) queueing delay due to waiting in a queue at the TTC zone entrance and (2) travel-time delay due to slower than desired travel speeds as a result of work zone activity. The first part of the vehicle delay, queueing delay, was modeled using manual flagging TTC zone traffic control process and queueing theory. The second part of the vehicle delay, travel-time delay, was estimated using the difference between the actual average travel time through the TTC zone and the average travel time through the same road segment without the TTC zone. The length of a TTC zone was involved in the defined cycle length, effective green, effective red (see Table A-1), and travel time through the TTC zone. Start-up lost time, which was defined as the elapsed time between the last vehicle’s exit from the opposing direction and the entry of the first vehicle waiting in the queue in the subject direction, was incorporated into queueing delay. For manual flagging operations, the flaggers tend to extend green time beyond queue dissipation to accommodate arriving vehicles, thus this part of “ending lost time” was also incorporated into the estimation of queueing delay. Data were collected using the observation method at multiple 1L2W TTC zones in California. Time stamps of TTC zone traffic events were recorded using a laptop computer. Multiple parameters—such as average hourly demand, average saturation headway, and average saturation flow rate—were measured using the collected data. The proposed equations of cycle length, effective green, and effective red were evaluated by comparing the predicted values with the empirically measured values, and all predicted values agreed closely with measured values. Thus, the defined equations could be used in the TTC zone delay model, which is shown in Table A-2. Data from a single TTC zone were used to demonstrate the delay and queue length estima- tion procedure. The authors suggested that transportation organizations could use the proposed procedure to determine appropriate work zone lengths and operation hours according to their acceptable vehicle delays. However, this model is only applicable to undersaturated conditions, in which all queued vehicles are served during a single cycle without a significant increase in delays over those incurred in previous cycles. The model is also very sensitive to the prevailing traffic-flow variables such as vehicle travel speed, discharge rates, and lost times. These param- eters should be input with accordance to local conditions. A P P E N D I X A Traffic Analysis for 1L2W Operations

Traffic Analysis for 1L2W Operations 105 In a further study, a stochastic method to predict 1L2W TTC zone vehicle delay was proposed and validated by Cassidy et al., replacing their previously proposed deterministic queueing tech- niques (Cassidy et al. 1994). A Monte-Carlo simulation in combination with an approximate analysis of moments was used to develop a procedure for estimating percentile values of average directional delay per cycle. The equations serving as the basis for the stochastic delay estimation are the following: • The average queueing delay per vehicle: 1 2 1 1 (1) 2 d G C C q S i i i i = −    − selbairaV noitauqE sretemaraP (1) Cycle length (C) C = cycle length tt = time required for the last vehicle in platoon to traverse the TTC zone ti = effective green time for direction of travel i to = effective green time for opposing direction Ls = start-up lost time (2) Effective green time (ti) ti = effective green time for direction of travel i qi = traffic demand in direction i (per time interval) qo = traffic demand in the opposing direction s = saturation flow rate Lei= ending lost time for direction i Leo = Ending lost time for the opposing direction (3) Effective red time (ri) ri = effective red time C = cycle length ti = effective green time for direction of travel i Source: (Cassidy and Han 1993) Table A-1. Defined cycle length, effective green time, and effective red time for 1L2W TTC zone operations. selbairaVnoitauqEsretemaraP (4) Queueing delays (per vehicle) dq = average queueing delay per vehicle = vehicle arrival rate s = saturation flow rate r = effective red time f = flow per cycle (5) Travel-time delays (per vehicle) dt = average travel-time delay per vehicle tm = measured average travel time through TTC zone t0 = estimated average travel time through an open lane (with no TTC zone) with the same length of the TTC zone (6) Total delays (per vehicle) D = total TTC zone delay per vehicle Source: (Cassidy and Han 1993) Table A-2. TTC zone delay model.

106 Practices in One-Lane Traffic Control on a Two-Lane Rural Highway where di = average queueing delay per vehicle traveling in direction i, Gi = effective green time in direction i, C = cycle length, qi = traffic demand rate in direction i, and Si = saturation flow rate in direction i. • The total average TTC zone delay: (2)D d l V l V i i a n = + −   where Di = the total average TTC zone delay in direction i, l = TTC zone length, Va = average TTC zone travel speed in direction i, and Vn = average vehicle speed on the highway section in the absence of a TTC zone. Statistical distributions of parameters used in the delay estimation equations were determined based on empirical data. Monte-Carlo simulations were then used to select random values for those parameters. Eighteen scenarios were created to reflect different TTC zone length and traffic flow rate combinations, which did not extend far beyond the three observed test sites. The scenarios were evaluated through Monte-Carlo simulations, with 1,000 successive simulations for each scenario. Approximate moment analysis techniques were used to estimate percentile values of average cyclic delay. The results showed that the approximated mean and percentile average cyclic delays were within 15% of the values generated by Monte-Carlo simulation, with most within 5%. Although the Monte-Carlo–based method could capture the randomness of TTC zone operations better than the deterministic method, the Monte-Carlo–based method has some limitations. In their conclusion, Cassidy et al. (1994) suggested that the limitations of Monte-Carlo simulation could be overcome by formulating approximate expressions based on micro-simulation-generated delay distributions. Regarding the use of flaggers and TTCSs at 1L2W TTC zones, Al-Kaisy and Kerestes stated that manual flagging remained the usual practice for traffic control, but the efficiency of these methods was often questioned, as manual flagging uses common sense and intuitive rules to alter- nate the right-of-way (Al-Kaisy 2006 and Kerestes 2006). TTCSs could save the cost of labor, but TTCSs using pre-timed plans may not be as sensitive to traffic conditions as flaggers. Therefore, in their study, Al-Kaisy and Kerestes evaluated four different traffic control strategies: • A pre-timed or “periodic” right-of-way allocation that can be implemented by flaggers or a set of fixed-timed portable signals. • A fixed-queue rule that can be implemented by flaggers by visually examining the queue length and is also feasible for signals with advanced detection. • A saturation operation or “convoy” rule that keeps the open lane at the saturation flow rate may be approximated by well-trained flaggers or signals using an optimum timing plan designed for constant arrival rates. • An adaptive control similar to the convoy rule except that it extends the right-of-way in either direction when an approaching vehicle at the end of the discharged queue is detected. Adap- tive control is typically achieved by using signals collaborating with detectors installed at the two ends of the open lane. Average delay per vehicle was used as the performance measure. Variables that could poten- tially affect the efficiency of traffic control included length of closure, average vehicle speed, frequency of construction vehicle and (or) equipment access, start-up and clearance lost time, and traffic volume and directional split. Both deterministic and stochastic approaches were used

Traffic Analysis for 1L2W Operations 107 in the evaluation and were achieved using MS Excel spreadsheets and micro-simulation. Results showed that TTC zone closure length and average delay per vehicle were positively correlated for all four traffic control strategies, as shown in Figure A-1. Washburn et al. studied the impacts of lane closures on roadway capacity using a micro- simulation program named FlagSim (Washburn et al. 2008). Other than the capacity (or saturation flow rate) and green time proportion with limited range used in the study by Cassidy and Han (1993) and Cassidy et al. (1994), FlagSim uses a TTC zone capacity estimate based on measured saturation flow rates and green time proportions. Three flagging strategies (right-of-way change based on distance gap between approaching vehicles, maximum queue length in opposing direc- tion, or fixed green time) were used in FlagSim. Figure A-2 shows the relationships between TTC zone capacity and variables including TTC zone speed, green time, TTC zone length, and heavy vehicle percentage as the sensitivity analysis results for the simulation model. These variables were selected for the estimation of TTC zone delay and queue length. The models were validated through comparison with the procedure proposed by Cassidy et al. and the HCM uniform delay and queue length formulations for intersections. The TTC zone delay and queue length models were estimated using regression. The total delay estimated as 0.276980 % 0.242061 % 0.003387 0.148503 0.001376 (3) TotalDelay g C v s C g HV g i i i i i i ( ) ( )( ) ( )= − × + × + × + × − × × where TotalDelayi = total queue delay for a 1-hour time period for direction i (veh-hr), gi = effective green time for direction i, C = cycle length, Figure A-1. Impact of TTC zone closure length on average delay (Al-Kaisy and Kerestes 2006).

108 Practices in One-Lane Traffic Control on a Two-Lane Rural Highway v = traffic volume, s = saturation flow rate, and HVi = heavy vehicle percentage for direction i. The queue length was estimated as 0.616983 % 0.598965 % 0.0006855 0.299197 0.003199 (4) QueueLength g C v s C g HV g i i i i i i ( ) ( )( ) ( )= − × + × + × + × − × × where QueueLengthi = maximum queue length per cycle for direction i (veh/cycle). Zhu et al. developed an analytical procedure for estimating capacity and delay of 1L2W TTC zones considering both the use of flagging and TTCS controls (Zhu 2015, Zhu et al. 2016). The proposed capacity calculation procedure is similar to that used for intersection capacity calculation. For one of the two directions of travel for a 1L2W TTC zone, the capacity is calculated as (5)1 1 1 1 2 1 2 c s g l V l V g g L = + + + + (a) (b) (c) (d) Figure A-2. Relationship between TTC zone capacity and (a) TTC zone speed, (b) green time, (c) TTC zone length, and (d) heavy vehicle percentage (Washburn et al. 2008).

Traffic Analysis for 1L2W Operations 109 where c1 = the directional capacity of 1L2W TTC zone (passenger car unit/s); s1 = saturation flow rate in direction 1; g1, g2 = effective green time in direction 1, 2; l = TTC zone length; V1, V2 = vehicle speed within TTC zone in direction 1, 2; and L = total lost time (including start-up lost time and clearance lost time for both directions). Delay consists of two parts, deterministic queueing delay (which assumes the vehicle arrival rate is uniform) and stochastic delay (which captures the randomness of real-world vehicle arrival pattern). The mean deterministic queueing delay (for both undersaturated and over- saturated conditions) is predicted as 1 2 1 900 1 1 (6)1, , , 2d C g C X C g T X Xi x i i x i i i ( ) ( ) ( )= − −    + − + −   where d1,i = mean deterministic queueing delay in direction i (sec/veh); C = cycle length; gx,i = saturated green time in direction i, i.e., the portion of effective green time used for queue discharge; T = measured time (hr); and Xi = volume-to-capacity ratio or degree of saturation in direction i. The stochastic part of delay is calculated based on the HCM 2010 (TRB 2010) recommendation as 900 1 1 (7)2, 2d T X mkI cT X Xi i i i( ) ( )= − + − −    where d2,i = mean stochastic delay in direction i (sec/veh); m = vehicle arrival adjustment factor that accounts for the randomness in vehicle arrivals, modeled in micro-simulation; k = 0.5 for pre-timed control; I = 1.0 if signal is isolated; and c = capacity in vehicles per hour. Zhu et al. (2016) obtained data from both field observation and micro-simulation modeling, with different combinations of TTC zone length and traffic control methods covered, as shown in Table A-3. The 1L2W TTC zone delay and capacity analysis results from Zhu’s (2015) study are shown in Figure A-3 and Figure A-4. Optimal TTC Zone Length Ceder developed strategies to determine the optimal length of 1L2W TTC zones, with the objective function representing the trade-off between delay cost and operational cost (Ceder 2000). A TTCS control method was studied. The TTCS included three major parts: detectors

110 Practices in One-Lane Traffic Control on a Two-Lane Rural Highway Site No. TTC Zone Length Control Methods 1 Short (0.1–0.5 mi) Fixed phases 2 Short Maximum queue length 3 Short Time gap out 4 Long (0.5–1.0 mi) Fixed phases 5 Long Maximum queue length 6 Long Time gap out Source: (Zhu 2015) Table A-3. Site types for TTC zone capacity analysis. (a) (b) Figure A-3. Green time and average vehicle delay: (a) pre-timed signal versus flagger and (b) human flagger control with multiple traffic demand levels (Zhu 2015). (a) (b) Figure A-4. Capacity analysis: (a) impact of TTC zone length and (b) impact of average travel speed (Zhu 2015).

Traffic Analysis for 1L2W Operations 111 placed at the entrance and exit of the open single lane, a signal controller, and a portable set of traffic signals. The signal control algorithms maintained an optimal cycle time and splits, with the optimization objective being the minimization of total delay. To decide the optimal length of the TTC zone, the trade-off considering operation and traffic control cost and delay cost was estimated, with the objective of minimizing the total cost. Longer closure lengths increase the delay cost, but decrease the operational and traffic control cost and vice versa. However, the TTC zone length was still constrained by the space needed for main- tenance activity. Apart from that, there were also timing constraints involving the maximum/ minimum cycle time and degree of saturation. The objective function was (8)MINIMIZE Total Cost Delay Cost Operational Cost( )= + The delay cost was calculated as , 1, 2 (9)Delay Cost q d P ii i i i∑=    = where i = the direction of travel and constant P represents the average hourly cost (local average employee wage + fuel cost while waiting in a queue), q = hourly flow, and d = average delay per vehicle. The average vehicle delay was based on Webster’s (1958) model: 0.9 1 2 1 2 1 (10) 2 2 d c q i i i i i i i ( ) ( ) ( ) = − λ − λ χ + χ − χ    (11) g c i iλ = (12) q c sg i i i χ = where c = the signal cycle length, l = the effective green ratio with effective green (g) divided by cycle length (c), and c = the saturation flow rate with q representing the hourly traffic flow and s the saturation flow. The operation and control cost was estimated based on the actual operation arrangements and local economic characteristics. The results of Ceder’s (2000) paper suggested that the higher the number of vehicles passing through, the shorter the optimal closure length. Sensitivity analyses were also carried out for fuel price and wage as a function of closure length and traffic flow. Schonfeld and Chien also studied optimal TTC zone lengths in a 1L2W situation. A math- ematical model was built to optimize the TTC zone length, but control measures (manual flagging or portable signalization) were not mentioned (Schonfeld and Chien 1999). TTC zone mainte- nance activity cost and traffic delay cost were considered in the optimization model, with the objective of the model being to find the optimal TTC zone length (L) and discharge phase lengths (t1, t2 for two directions) that minimize the total cost. Results showed that the optimal TTC zone

112 Practices in One-Lane Traffic Control on a Two-Lane Rural Highway length decreases when the combined flow rate increases. The optimal clearance time decreases and the total discharge time increases as the combined flow rate increases. TTCS Operations To investigate the feasibility of using TTCSs in a TTC zone instead of manual flagging, Daniels et al. carried out a study on 1L2W TTC zones (Daniels et al. 2000b). Data were collected through three field tests on Texas highways. Four issues were addressed in the field study: • The feasibility of TTCSs for maintenance operations. Only pavement repair operations were conducted in the field test, and positive feedback was received from maintenance personnel. However, the cost-effectiveness needs to be studied further. The major affecting factors are the improvement of work efficiency and the frequency of use. • Driver comprehension and compliance. A signal-controlled TTC zone creates the appear- ance of, and driver expectancy of, operations similar to common signalized intersections; however, at signal-controlled TTC zones, the oncoming traffic may not be visible due to drivers’ inattention, roadway geometry, or terrain and thus a false sense of security may affect drivers’ reactions. However, feedback from drivers indicates that the portable signal control was less confusing than flagging. • TTC zone characteristics. There are several points to note regarding TTC zone characteristics when setting up portable signals. Characteristics such as whether the TTC zone is long term or short term, the visibility of traffic control devices, the presence of driveways or intersecting streets, and speed need to be considered based on field conditions. • Traffic signal operating characteristics within TTC zones. To replace flaggers, portable signals can be equipped with means of communication, carefully designed control logic, and conflict-monitoring facilities to ensure safety. Multiple operation modes exist to accommodate different needs. The relationship between TTC zone length and signal tim- ing needs to be considered carefully to avoid unreasonably long waiting times. Flashing red operation can only be used when there is a clear line of sight from one end of the TTC zone to the other. Serving as a proposal for revision of the TTCS sections of the Texas Manual on Uniform Traffic Control Devices, Daniels’ (2000b) study developed conservative guidelines that minimize the risk of state DOTs. As a basis for guidelines on TTCS operations, the study reported the following findings about signal timing parameters for TTCSs. Maximum wait time is approximately 4 minutes from experience. A wait time longer than that may lead to driver confusion and possible violations. Figure A-5 shows the maximum wait time threshold by delay time and length of TTC zone (by different speeds). Considering the elements that contribute to the maximum wait time, the following equation was proposed by the study: (13),Maximum Wait Time Y R B G Y R Bi i i o max o o o= + + + + + + where Yi, Yo = yellow clearance time in (subject, opposing) direction, RI, Ro = red clearance time in (subject, opposing) direction, Bi, Bo = buffer time in (subject, opposing) direction, and Goma = maximum green time in the opposing direction.

Traffic Analysis for 1L2W Operations 113 To determine the timing of TTCSs, these factors need to be considered: • Length of TTC zone (which may have to be separated into smaller jobs), • Number and variability of vehicles expected to approach each end of the TTC zone, • Speed of traffic approaching each end of the TTC zone, • Range of speeds within the TTC zone, and • The amount of buffer time used to separate exiting traffic from entering traffic. Then the following timing elements can be determined: • Maximum green time (actuated operation) or green time (pre-timed operation) based on Table A-4. • Minimum green time (actuated operation) uses a range of 7 to 10 seconds. Figure A-5. Impact of speed and length of TTC zone on maximum wait time (Daniels et al. 2000b). Queued Vehicles per Cycle Green Time (s)*,** 12 5 15 10 27 15 39 20 51 25 63 30 75 35 87 40 99 Source: (Daniels et al. 2000b) *Based on a total lost time of 3.3 s and a saturation flow rate of 1,500 passenger cars per hour green per lane. **Long green may cause wait times in the opposing direction to be greater than 240 seconds, depending on the length of the TTC zone. Table A-4. Green phase time setting per approach.

114 Practices in One-Lane Traffic Control on a Two-Lane Rural Highway • Extension interval (actuated operation) uses 2.4 seconds or 3 seconds if controller only accepts integer. • Yellow change interval is calculated with 2 2 (14)y t v a Gg = + + where y = length of yellow interval, t = driver perception/reaction time, v = velocity of approaching vehicle, a = deceleration rate, G = acceleration due to gravity (32 feet/s2), and g = grade of approach. Table A-5 gives some suggested yellow change interval values regarding various speed and grade combinations. • Red clearance interval = TTC zone travel time + buffer time. Summary This Appendix reviewed literature on delay and capacity analysis of 1L2W TTC zones. The analysis methods have developed from a deterministic, queueing-based one to a combination of deterministic and stochastic models. By applying delay and capacity analysis, optimal lengths of 1L2W TTC zones can be estimated and used in practice. Compared with traditional manual flagging for 1L2W TTC zone traffic control, TTCSs provide more alternative control strategies to better utilize the TTC zone section capacity and reduce traffic delays. Some states, like Texas, have started to develop guidelines specifically for TTCS operations in 1L2W TTC zones. 85th Percentile Speed (mph) Grade of Approach Uphill Level Downhill +4% +3% +2% +1% 0 −1% −2% −3% −4% 25 2.7 2.7 2.8 2.8 2.9 2.9 3.0 3.1 3.2 35 3.3 3.4 3.5 3.5 3.6 3.6 3.8 3.9 4.0 45 4.0 4.1 4.2 4.2 4.4 4.5 4.6 4.7 4.8 Source: (Daniels et al. 2000b) Table A-5. Yellow change intervals (in seconds) for various speed and grade combinations.

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TRB's National Cooperative Highway Research Program (NCHRP) Synthesis 525: Practices in One-Lane Traffic Control on a Two-Lane Rural Highway identifies innovative practices and devices for establishing one-lane traffic control on rural two-lane highways. Temporary traffic control, also known as maintenance of traffic, is critical to minimizing congestion and maintaining mobility during planned and unplanned activities as well as providing a safe work zone for both road users and workers. Innovative examples of one-lane two-way traffic control operations at roundabouts and applications of temporary portable rumble strips and driveway assistance devices are also discussed in this synthesis, providing additional insights on the state of the practice.

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