The control algorithm used for deciding on the speed limit in variable speed limit systems is crucial for the performance of the systems. The algorithm is designed to fulfil the purpose of the variable speed limit system, which can be one or several of the following aspects: increasing safety, increasing efficiency and decreasing environmental impacts. Today, many of the control algorithms used in practice are based on fixed thresholds in speed and/or flow. Therefore, they are not necessarily reflecting the current traffic conditions. Control algorithms with a greater level of complexity can be found in the literature. In this paper, four existing control algorithms are investigated to conclude on important characteristics affecting the performance of the variable speed limit system. The purpose of the variable speed limit system and, consequently, the design of the control algorithm differ. Requirements of the investigated control algorithms are that they should be easy to interpret and the execution time should be short. The algorithms are evaluated through microscopic traffic simulation. Performance indicators related to traffic safety, traffic efficiency and environmental impacts are presented. The results show that the characteristics of the variable speed limit system and the design of the control algorithm will have effect on the resulting traffic performance, given that the drivers comply with the variable speed limits. Moreover, the time needed to trigger the system, the duration and the size of speed limit reductions, and the location of the congestion are factors of importance for the performance of variable speed limit systems. Keywords: Variable speed limit systems, Control algorithms, Microscopic traffic simulation 1 Introduction conditions is collected using detectors often measuring Since its beginning, road traffic has increased tremen- local speed, flow or detector occupancy. A suitable vari- dously leading to congestion, safety problems and envi- able speed limit is calculated by the control algorithm ronmental issues [20, 21]. Today, urban motorways taking into account downstream and upstream traffic con- around the world are experiencing daily congestion during ditions. The purpose of a variable speed limit system can peak-hours. Hence, there is a need for traffic management be to increase safety, increase efficiency and/or decrease aiming at reducing the congestion and thereby increasing environmental impacts, and hence, the specific purpose is both efficiency and safety. One commonly applied traf- reflected in how the control algorithm is designed. fic management system for urban motorways is variable When implementing a VSL system the purpose of the speed limit (VSL) systems. VSL systems make use of a system but also the complexity and the level of detail of the control algorithm to adjust the speed limit based on the control algorithm are of importance. It is desirable to have prevailing road and traffic conditions. Coordinated vari- a control algorithm that is reflecting the specific purpose able speed limits are shown on a series of variable message of the system. However, at the same time it is desirable to signs along the managed road. Information about traffic have a control algorithm that is straightforward to imple- ment. For example, the required control input should be *Correspondence: email@example.com easy to measure, the current traffic conditions should be Swedish National Road and Transport Research Institute (VTI), SE-581 95 reflected in the speed limit change and the tuning param- Linköping, Sweden eters should be easy to interpret. Additionally, the control Linköping University, Department of Science and Technology, SE-601 74 Norrköping, Sweden algorithm should be able to run in real-time without com- Full list of author information is available at the end of the article putational delay. This results in a trade-off between the © The Author(s). 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Grumert et al. European Transport Research Review (2018) 10:21 Page 2 of 12 complexity of the algorithm and the degree of which the incident has occurred and thereby decreasing the algorithm is able to fulfil its defined purpose. VSL con- probability of further incidents and trol algorithms used in practice are often rule-based, only 2. Homogenization systems: preventing a traffic using a threshold of measured speed or flow as a basis breakdown by applying a slightly reduced speed limit for lowering the speed limit. More elaborate control algo- when the traffic flow is close to capacity to avoid rithms are proposed in the literature, but there are few unstable traffic conditions. studies comparing how the characteristics of these algo- rithms relates to each other and the final outcome of the In recently proposed systems, the goal has also been systems. to reduce environmental impacts and to relocate flow In this paper, we aim to investigate how the design of the to other parts of the network to reduce exhaust emis- control algorithm and the defined purpose of the VSL sys- sions, see e.g. (Gao, K: Multi-objective traffic management tem affect the performance of the traffic system. Further, for livability, Improve Near-motorway Livability in the the objective of the study is to summarize characteristics Netherlands. MS. Thesis, unpublished) . that should be considered when designing a VSL system. The first applications of VSL systems were incident Consequently, this study contributes to knowledge on the detection systems with the purpose to warn the drivers relationship between traffic conditions and variable speed of the incident and to decrease the risk of additional limits. incidents. Examples of implemented incident detection We investigate four existing VSL control algorithms; systems are the ones included in the Swedish and two of them proposed in the literature, one proposed in the Dutch  Motorway Control System (MCS). A com- the literature and implemented as a field trial and one bination of incident detection and homogenization are implemented in real traffic. The algorithms differ by their included in some VSL systems, such as in the VSL system objective and thereby also by the aspects included in in the UK . Studies from implemented systems show the control algorithm. Two of the control algorithms are benefits in traffic safety and flow homogenization (reduc- rule-based, but with different update rules [30, 52], one tion of the variance in speed between vehicles), while algorithm is control-theory based  and one algorithm improvements in traffic efficiency are limited. As a result is based on analytical expressions . The algorithms of increased costs of delays due to congestion, traffic effi- are evaluated, with respect to traffic efficiency, safety and ciency has also become an important aspect to consider environmental impact, by the use of microscopic traffic in the design of a VSL system. It is well-known that the simulation. This paper is the result of further analysis capacity at the onset of congestion tend to drop, leading and extension of a previous comparison of VSL control to an inefficient traffic system. The drop has been dis- algorithms . covered in many empirical studies, see e.g. [7, 48, 59]. In The remainder of the paper is organized as follows. First, and  the capacity drop is partly explained by an an introduction is given to variable speed limit systems increased number of lane-changes during unstable traf- and to the four VSL control algorithms. This is followed fic conditions. Another effect of lane-changing operations by a presentation of the evaluation method using micro- is stop-and-go traffic, as shown in and. For this scopic traffic simulation and a description of the simula- reason, homogenization VSL systems focusing on reduc- tion scenario. Then, simulation results are presented and ing differences in speed amongst the vehicles, and thereby discussed. Finally, conclusions from the study are given. also reduce the demand for lane-changes have been pro- posed in the literature. By reducing the speed limit at the onset of congestion, the capacity drop and flow break- 2 Variable speed limit systems down, can be delayed or even avoided. The systems are Variable Speed Limit (VSL) systems consist of a series of therefore not necessarily triggered when the mean speed VSL signs and associated detectors measuring the traffic on the road becomes low. Soriguera et. al. has con- conditions. The speed limits shown on the VSL signs are cluded that empirical studies, as early as 1972, indicate based on the observed traffic conditions close to the VSL that homogenization can be obtained with an appropriate sign, but usually also the traffic conditions at upstream speed limit when the flow is close to the capacity. Also, and downstream VSL signs. Independent variable speed many of the studies, including , show that a higher limits were first introduced in the 1960’s and as a critical density can be obtained without notably reducing system for motorway traffic control in the 1970’s . the traffic flow. Hence, by applying homogenization sys- Two main approaches exist [23, 36, 46]and have been tems, traffic throughput can be increased, which will lead differently defined in different studies. These two main to increased traffic efficiency. approaches are in this study defined as: Four different types of VSL control algorithms are com- 1. Incident detection systems: increasing safety by monly proposed in the literature: rule based, fuzzy-logic reducing the speed limit substantially when an based, analytical and control-theory based. The design Grumert et al. European Transport Research Review (2018) 10:21 Page 3 of 12 of the control algorithms are reflected in the purpose of shockwaves in order to increase throughput at the result- the VSL system and the required level of detail in the ing bottleneck. Hence, it can be seen as a combination implementation. The simplest VSL systems include rule- of an incident detection system and a homogenization based VSL control algorithms. The algorithms use thresh- system. By lowering the speed limit to a beforehand deter- olds for identifying incidents and situations with low mined value, the relationship between flow and speed will speeds. Most of the VSL systems used in practice are rule- change in accordance with traffic flow theory. As a result, based. Examples of implemented rule-based VSL control effects of shockwaves moving upstream can be reduced algorithms are included in the UK , the Swedish  and, hence, traffic efficiency can be improved. Finally, the and the Dutch  Motorway Control Systems (MCS) and fourth algorithm of the study is the Motorway Traffic Flow the Spanish dynamic speed limit system . Examples Control (MTFC) algorithm [4, 5, 38, 39]. The objective of in the literature are given in [2, 30, 32]. Another type of this algorithm is to maintain a stable traffic situation by VSL control algorithm is the fuzzy-logic based VSL con- keeping a detected occupancy as close to the capacity level trol algorithms, where the speed limit is decided based on as possible, and thereby avoiding a capacity drop. Since the how well the measured input matches a set of rules, see speed limit is lowered with the objective to avoid unsta- e.g. [6, 31, 34]. In analytical VSL control algorithms the ble traffic conditions it is categorized as a homogenization purpose is to analytically calculate the traffic states based algorithm. The algorithm is applied to known bottlenecks, on a measured reality, see e.g. [14, 18]. Finally, control where congested situations are frequently observed. theory based VSL control algorithms have been proposed The Swedish MCS has been evaluated through empiri- to find the optimal VSL strategy based on local feedback cal studies [41, 42]. These studies concluded that the main loops, such as the algorithms proposed in and or effect of the MCS is increased safety. This is in line with by using model predictive control, see e.g. [10, 15, 16, 58]. a study comparing the Swedish and the Dutch MCS . However, in the Netherlands accidents decreased by 20% 3 Variable speed limit algorithms in this study but in Sweden only homogenized speeds and lower speed Four existing VSL control algorithms are investigated; levels were found. This can be explained by the fact that two of them proposed in the literature, one proposed in the variable speed limits are not compulsory in Sweden. the literature and implemented as a field trial and one Further, the journey times was reduced by 10-15% in the implemented in real traffic. Requirements imposed on the Netherlands, compared to in Sweden where no such effect control algorithms are that they should be straightforward was observed. This is most probably the result of fewer to implement and easy to interpret. The execution time accidents that resulted in a reduction in travel time. The RCP algorithm has been evaluated through microscopic should be short and at the same time the applied variable speed limits should correspond to the purpose of the VSL traffic simulation [29, 30, 56]. The results presented in system. Two of the control algorithms have as objective [29, 30] show a trade-off between safety, measured as to increase safety, while two of them have as objective to decreased crash potential and traffic efficiency, measured increase traffic efficiency. as total time spent. Also, it is concluded in and  The first algorithm of this study is the rule-based inci- that there are threshold values for the crash potential for dent detection algorithm used in the Swedish Motorway which benefits in terms of both safety and efficiency can Control System (MCS) . From here on it is referred to be made. In a field trial of SPECIALIST itisshown as MCS. The second algorithm in the study, by us referred that the algorithm is able to resolve around 80% of the to as the Reducing Crash Potential (RCP) algorithm, is identified shockwaves with a gain in travel time as a result. proposed by Lee et. al. . The algorithm is a rule-based Hegyi et. al.  use macroscopic traffic simulation to incident detection algorithm but has a somewhat differ- conclude that SPECIALIST gives a decrease in total travel ent approach compared to the MCS since the main goal time spent and on average an increase in throughput of is to reduce the risk of incidents by considering a crash traffic flow. The MTFC has been evaluated using both potential instead of the measured mean speed. The objec- macroscopic traffic simulation [4, 5] and microscopic traf- tive is to avoid dangerous situations by detecting the crash fic simulation [38, 39]. The studies show improvements in potential at known problematic locations with a high risk efficiency, with reductions as high as 40% in total travel of an incident, and to reduce the crash potential by low- time. The details of the algorithms and the parameter ering the speed limit. The third algorithm of the study, settings used in this study are presented below. the SPEed ControlIng ALgorithm using Shockwave The- ory (SPECIALIST) presented by Hegyi et. al. , has as 3.1 The MCS algorithm objective to reduce the effects of shockwaves by lower- The VSL algorithm included in the MCS  uses thresh- ing the speed limit. The shockwaves are detected using olds for lowering and increasing the speed limit. One measurements from stationary detectors. An algorithm detector and one VSL sign is used for each lane but a com- including linear equations is applied to resolve identified mon speed limit is applied for all lanes. The algorithm Grumert et al. European Transport Research Review (2018) 10:21 Page 4 of 12 used for deciding on speed limit, v ,attime t and detector where v ˜ is the mean speed measured at detector station t,j j location j are based on the detector measurements, v ˜ , j. The intervention time, i.e. the time when the VSL sys- t,j and the use of the following speed limit updating scheme: tem is activated, is set to 10 min. The set of parameters used in the simulation are based on the near-optimal set –If v ˜ ≤ 45 km/h: t,j of parameters resulting from the calibration presented in and . – The speed limit at detector station j is set to v = 60 km/h. t,j 3.3 The SPECIALIST algorithm – Lead-in speed limits at two upstream detector The SPECIALIST algorithm  uses shockwave iden- stations are set to v = 80 km/h and t,j−1 tification to identify different states in speed and flow. v = 100 km/h, respectively. t,j−2 The algorithm is developed to detect and resolve mov- ing shockwaves. An extension also considering on-ramp –If v ˜ ≥ 45 km/h: t,j flows are proposed in . Linear equations are used to – The speed limit at detector station j, v ,and calculate the length and duration of the different states. t,j the associated lead in speed limits, v and Therefore, the length of the VSL activation area is depend- t,j−1 v , are reset to 120 km/h. ing on the level of congestion, the length of the congested t,j−2 area,etc.Also, thetimeofactivationisbased on thetraffic The thresholds are based on a study of the existing MCS conditions. Figure 1 gives an illustration of the algorithm. and the new speed limits that are recently implemented in The algorithm includes four phases related to the iden- Sweden . It is assumed that the most restrictive lane tified traffic states: is regulating the speed limit, i.e. the lane with the lowest – Phase 1: The thresholds for identification of a mean speed is considered when determining a common shockwave and activation of the system are based on speed limit for all lanes. The algorithm is repeated at all speed and flow. The system is activated when the detectors starting from the last downstream detector. mean speed and mean flow are below 50 km/h and 1500 veh/hour/lane, respectively. This results in a 3.2 The RCP algorithm start and end point of the congested state 2. In the RCP algorithm  VSLs are applied to a before- – Phase 2: A predefined lower speed limit is set to 60 hand known bottleneck and calculated based on the cur- km/h and applied to state 2 and an additional stretch rent value of the crash potential at the bottleneck. The upstream of the congested state, state 3. Additionally, crash potential, F , for detector station j at time t is cal- t,j state 4 becomes present as a result of vehicles starting culated by using a regression model estimated based on to slow down before entering to state 3. The tail of accident and traffic data. state 4 will propagate upstream or downstream +λ +λ +λ +λ +λ CVS Q COVV R P depending on the flow levels in the state. The t,j t,j t,j t,j t,j F = e , t,j predefined speed limits are applied along with the propagation of the tail. Lead-in speed limits at two where is a constant. The crash precursors used in the upstream detectors when the system is activated are model are the spatial and temporal variation in speed, 80 and 100 km/h, respectively. At the same time, λ and λ , the covariation in traffic volume between Q CVS t,j t,j speed limits are turned off downstream as the upstream and downstream locations, λ , and exter- COVV t,j congestion is dissolved and state 3 propagates nal factors, λ and λ . The calculations of crash pre- R P t,j t,j upstream. cursors are described in [28–30]. VSL activation is deter- – Phase 3: VSLs are applied to the tail of state 4 which mined based on threshold values of the crash potential. is propagating upstream. At the same time, VLSs are The risk of a crash is assumed to be highest just before the turned off at the head of state 4 which is also bottleneck. Therefore, the VSL is applied to a road stretch propagating upstream. Downstream of state 4 there is of 1000 meter just upstream of the bottleneck. Lead-in a discharging area, state 5, where the vehicles speed limit is applied on one section upstream of the high- accelerate from speed levels corresponding to the risk section. We use the threshold value for lowering the speed limit in state 4 towards free flow speed. speed limit given in . Both the VSL and the lead-in – Phase 4: Eventually only state 5 remains together with speed limit are based on measurements of speed to reflect the free flow states. No speed limit is applied. State 5 the conditions on the road, and are rounded to the nearest is propagating downstream until speeds 10 km/h. The variable speed limit and the lead-in speed corresponding to the maximum speed limit on the limit is calculated as road are obtained. The predetermined parameters, as well as the presented thresholds, are set according to v ˜ + v ˜ j−1 j+1 v = , parameter settings 2 in . 2 Grumert et al. European Transport Research Review (2018) 10:21 Page 5 of 12 Fig. 1 Illustration of the different states and phases in the SPECIALIST algorithm 3.4 The MTFC algorithm the purpose of the VSL system are affected by the type of In the MTFC algorithm  the speed limit is determined control algorithm. The base case and the algorithms are by controlling the occupancy at an identifiable bottleneck implemented and evaluated using the microscopic traffic towards a predefined estimate of the critical occupancy at simulator SUMO [8, 25]. Performance indicators related the specific bottleneck. The variable speed limit at time t to traffic efficiency, safety and environmental impact are is determined as a fraction, b (t), of the original speed limit considered. on the road. 4.1 Modeling VSL control algorithms in SUMO b (t) = b (t − 1) + K e (t) , For this study microscopic traffic simulation is a suitable method as it is necessary to keep track of individual vehi- where K is the integral gain and e (t) is the occupancy cles’ reactions toward changes in VSLs. SUMO is open error calculated as the difference between the critical source, multi-modal, space continuous and time discrete. occupancy, o ˆ , and the measured occupancy at the bot- out The car-following model used to model vehicle interac- tleneck, o ˜ (t).The occupancyatcapacityflowisin out this study set to 13% based on an investigation of tionsisdeveloped by Krauß and based on the calcu- the capacity level in the base case scenario in SUMO. lation of a safe speed, cf. the approach of Gipps . The The threshold is set to 1% below the critical level of the lane changing model is rule based. The core models in occupancy to limit the risk of exceeding the capacity. SUMO is further described by Krajzewicz . The VSL Algorithm specific parameters are taken from the study algorithms are implemented through python scripts . presented in . The VSLs varies between 20 and 100% SUMO’s Traffic Control Interface (TraCI) is used for com- of the original speed limit on the road and are rounded munication of the speed limits to be applied on each road to the nearest 10 km/h. Four detectors located around segment, and for accessing the mean values gathered by the bottleneck are included in the system. The occupancy the detectors in the simulation. measurement used in the algorithm is the maximum of When a speed limit is updated, the vehicles in the sim- the occupancy measurements of these four detectors. The ulation receive and adapt to this information according to speed limit is applied to an application area of 300 meter, the modeling of vehicle movements set out by SUMO. The located 275 meters upstream of the bottleneck. speed limit is adjusted based on the specific algorithm, and an updated speed limit is assigned to a road segment in the simulation when needed. 4 Evaluation method As a result, all vehicles on a road segment are assumed We analyze the traffic performance resulting from the use to get information about the new speed limit irrespec- of the four algorithms in a variable speed limit system tive of their location. An alternative would be to assume and a base case without VSLs. This is done in order to that the vehicles get information about a speed limit investigate how the level of detail of the algorithm and Grumert et al. European Transport Research Review (2018) 10:21 Page 6 of 12 change only when passing a variable speed limit sign. The we model an incident in the form of bottleneck activa- assumption made is a simplification and is the same for all tion. The reason for choosing this simulation scenario as the algorithms included in the comparison. As a result of a base case is that it has been shown to give representa- the simplification the vehicles in the simulation are adapt- tive characteristics of an incident in SUMO . Further, ing to a decrease, or an increase, in speed limit slightly the simple scenario makes it possible to isolate the effects earlier in time than what would be the case in reality. of the algorithms under identical traffic conditions. The As indicated in an earlier microscopic traffic simulation simulated road included in the evaluation is divided into based study , this will result in a more effective VSL fourteen 500-meter segments. Further, a start and end system and smoother transitions towards the new speed segment are included to avoid boundary effects, resulting limits compared to if information about a speed limit in a 9 km long simulated road. The bottleneck is located change only becomes available at specific points in space. 7.5 km downstream of the start segment. The maximum Further, the authors conclude that the smoother transi- allowed speed limit on the road is assumed to be 120 tions will result in that no temporary drop in capacity km/h. Figure 2 gives an illustration of the simulated road and flow will appear at the bottleneck at the activation stretch. of the VSL system. Also, for this reason, the difference The simulation is performed for a 55-min period, in speed between two segments becomes larger when the excluding a warm-up period of 5 min to prevent from VSL system is active. loading effects. First, the input flow is held constant at Thenumberofdetectors andVSL signsare varying 1500 veh/h for 10 min. Then, to activate the bottleneck depending on the applied algorithm. In MCS and SPE- and the algorithms, the flow is increased to 4500 veh/h CIALIST, the study includes fourteen equipped segments for 15 min, which is approximately 70% of the capacity of located 500 meters apart from each other, and with one three lanes. Finally, the flow is decreased to 1500 veh/h for detector and one VSL sign applied to each lane. For RCP, 30 min for the congestion to be resolved and the VSL signs the bottleneck location is assumed to be located where to become inactive. the number of lanes change from three lanes to two lanes. Mean values used in the algorithms for control of Hence, the detectors and the VSL signs are applied to theVSLsare basedonsmoothedmeanvaluesofmea- two 500-meter segments before the bottleneck. For MTFC surements over 30 s intervals. It is comparable to the the detectors are concentrated around the bottleneck and means used in the design of the MCS algorithm . the VSL signs are applied just upstream of the bottle- The smoothed mean values consist of the previous mean neck according to the description in Section 3. The time and the measured mean, weighted equally with a smooth- when new speed limits are updated and applied based on ingfactorof0.5.TheVSLs areassumedtobecom- prevailing traffic conditions are the same irrespective of pulsory for the vehicles in the simulations. For a more algorithm. Theupdatetimeisset to 30 s. detailed description of the implementation of the control algorithms see . 4.2 Base case - simulation scenario In order to make a consistent comparison, the same base 4.3 Vehicle parameters case is used as a starting point for the four algorithms. The Assumptions regarding the vehicle parameters are the base case consists of a three-lane road with a lane-drop same irrespectively of VSL system. The maximum accel- bottleneck at which the number of lanes is decreased to eration ability is set to 0.8 m/s and the reaction time is two. By increasing the flow to the capacity of two lanes set to 1.3 s based on an investigation of merging behavior Fig. 2 Illustration of the simulated road stretch Grumert et al. European Transport Research Review (2018) 10:21 Page 7 of 12 in SUMO . The desired speed factors are drawn from on the properties and the assumptions of the vehicles sim- a normal distribution with mean 1.0 and speed devia- ulated in SUMO. Consequently, the vehicles are assumed tion 0.1, based on a study by Varedian  in which a to be of the normal emitting catalyst equipped gasoline speed distribution was estimated for all vehicle types on fueled passenger car type in CMEM. Confidence inter- Swedish roads with a speed limit of 120 km/h. Thereby, vals taking into account the 20 simulation runs are used we implicitly assume a typical composition of vehicle to present the significance of the observed differences in types in the simulated traffic. Differences in vehicle length emissions. are, however, not considered. Remaining vehicle parame- ters used in the simulation are set to default values used 5 Computational results in SUMO version 0.19.0 .Vehicles are generated with In this section, results from the simulations are presented exponentially distributed headways. for all of the investigated algorithms and the base case. Results related to traffic efficiency, traffic safety and envi- 4.4 Performance indicators ronmental impacts are given. This is followed by a discus- The four algorithms included in the study are focused sion on how the different control algorithms manage to either on safety or efficiency. Hence, to evaluate how the fulfil the specific purpose of the variable speed limit sys- objectives of the algorithms affect the results both safety tem and how the characteristics of each control algorithm and efficiency indicators have been included. None of are reflected in the results. the algorithms have as objective to reduce environmen- tal impacts. Nonetheless, it is interesting to investigate 5.1 Traffic efficiency how the algorithms perform in that respect. Therefore, Figure 3 shows the mean speed over the whole stretch. a simple investigation of the environmental impacts is The base case without applying a VSL algorithm is plotted included. together with the four VSL systems. The standard error The effectiveness of the different algorithms is mea- of the means presented is less than or equal to 4.14 km/h. sured by the mean speed over the simulated road. The From the figure, we conclude that only one algorithm, the mean speed is calculated as a rolling average over 30 s MTFC, manages to increase the mean speed compared to intervals for the whole road stretch to get the overall the base case during congested conditions. Both the MCS impact on traffic efficiency. The smoothing factor is 0.5. and the RCP algorithms have mean speed levels that are A more detailed investigation of each of the algorithms slightly below the base case when the queue is building up is carried out by examining the mean speeds collected at and until the flow is decreasing again. The same holds for the individual detector stations. The means and standard the SPECIALIST algorithm, except for the most congested errors of the means are calculated based on 20 replications period where the algorithm manage to keep a mean speed of thesimulationfor thebasecaseand foreachofthe VSL that is somewhat higher than the base case. systems considered. A more detailed analysis of the different algorithms is The Coefficient of Variation of Speed (CVS) described done by investigating the mean speed for each detector in  is used as a measure of safety. The CVS is calculated station, and for each VSL algorithm, as shown in Fig. 4. for each lane i andaveragedoverasegment j as 1 σ CVS = , n s ¯ i=1 where σ and s ¯ is the standard deviation of speed and i i the mean speed, respectively. The CVS is presented as a mean over 20 simulation runs. Finally, the microscopic emission model CMEM is used for evaluation of environmental impacts. The model gives second by second tailpipe emissions, e ,asa tailpipe product of three parameters, fuel rate (r ), engine-out fuel emission index (i ) and catalyst pass fraction (C ), em/fuel pass that is e = r · i · C , tailpipe fuel em/fuel pass Fig. 3 Mean speed over the whole stretch for the base case and the In the evaluation, the vehicle specific parameters used in VSL algorithms CMEM have been adopted for emission estimation based Grumert et al. European Transport Research Review (2018) 10:21 Page 8 of 12 Basecase MCS MTFC 6 6 6 4 4 4 2 2 2 0 0 0 020 40 020 40 020 40 Time (minutes) Time (minutes) Time (minutes) SPECIALIST RCP 020 40 020 40 Time (minutes) Time (minutes) Fig. 4 Mean speed (km/h) at the detector stations for the base case and the VSL algorithms In the figure, the mean speed ranges from 20 (dark red) during congested condition. But also, the mean speeds to 120 (dark blue) km/h and the horizontal lines represent at detector stations close to the VSL controlled area are the location of the detector stations. The standard error of decreased compared to the base case. means presented are less than or equal to 7.02 km/h. As canbeseeninFig. 3 theMCS tendstohaveamean 5.2 Traffic safety speed slightly below the other algorithms under congested The CVS described in the Section Performance indica- conditions. This is consistent with Fig. 4, where it is con- tors is used as a measure of traffic safety. The CVS for cluded that the mean speeds at all detectors are lower each detector station is presented in Fig. 5.The CVS compared to the base case. Also, a larger area is influenced ranges from 0(dark blue)to0.3 (darkred). AhighCVS by lower mean speed compared to the base case. corresponds to a large variation in speed, and thereby a For the MTFC substantially higher mean speed over decrease in safety. The standard error of means presented the whole stretch, as well as for each detector station, are less than or equal to 0.06. are observed compared to the base case. In the congested The CVS around the bottleneck are lower for the MCS period, the mean speeds are around 90 km/h whereas in and RCP compared to the base case. SPECIALIST shows the base case the mean speeds ranges between 35 km/h a large area with high variation in speeds. Although for a and 70 km/h depending on detector station. small area at the bottleneck location, decreased levels of Traffic performance measured as mean speed over the CVS are detected. Just after the bottleneck location much whole stretch is lower for the SPECIALIST algorithm higher variations in speed are detected. Also at detec- compared to the base case, except in the most congested tor station 1 somewhat higher variations in speed are period. This is explained by the results in Fig. 4.The detected. The MTFC shows lower levels of CVS compared mean speed is lower for most detectors, as a result of to the base case, and the other algorithms. the lowering of speed limits upstream of the congestion. Nonetheless, close to the bottleneck, in the area between 5.3 Environmental impacts 4.5 and 6 km, the mean speed is higher during the con- In Table 1 emission levels calculated using CMEM are gested period. Further, the VSL application area is long. It presented. The environmental impacts measured with is only at detector station 1 that the original speed limit on CMEM shows small differences when comparing the the road is kept for the whole simulation period. base case with the algorithms. MTFC gives the biggest As canbeseeninFig. 4 the RCP shows lower mean improvements compared to the base case. Both the MCS speeds than the base case at detector stations 10 and 11 and the RCP are performing somewhat worse than the (between 5 to 6 km), where the speed limits are lowered base case. Length (km) Length (km) Length (km) Length (km) Length (km) Grumert et al. European Transport Research Review (2018) 10:21 Page 9 of 12 Fig. 5 The Coefficient of Variation of Speed (CVS) for the base case and the VSL algorithms 6 Discussions Netherlandsisobserved. This ismost probably duetothat The microscopic traffic simulation model has been cali- the VSLs in the Netherlands are compulsory, while the brated for the capacity and speed distributions observed VSLs in Sweden are only recommended. As a result, the on Swedish roads. Consequently, the results presented Dutch VSL system manages to reduce travel times due to indicate how the algorithms performs under typical that the system is more effective in decreasing the number Swedish conditions. However, the results should be valid of additional incidents. In the studied scenario no larger for motorways with similar conditions regardless of coun- incidents are simulated, and hence improvements due to try. By modeling congestion due to a lane drop, the effect avoidance of additional incidents cannot be observed. of merging, which is usually hard to calibrate in micro- The second rule-based control algorithm, RCP, does scopic traffic simulation, is limited. Thereby, the uncer- also show an increase in safety close to the bottleneck. tainty related to limitations in the simulation model is Even so, the objective of reducing the crash potential by reduced. smoothing of the traffic flow is not reflected in the results, The first rule-based control algorithm, MCS, show leading to that smaller effects on safety than expected are increased performance in safety close to the bottleneck observed. This is probably a result of the local control location due to the lowered speed limits and the lead- with lower speed limits only on two of the road segments. in speed limits. However, the algorithm uses the most As a result, the large differences in mean speed between simplistic rules compared to the other algorithms, with segments is counteracting the objective of the algorithm. a substantial lowering of the speed limit close to the Hence, the objective of improving safety at the bottleneck congested area, which limit the improvements in traffic is fulfilled but at the expense of decreased safety at other efficiency. The lead-in speed limits result in even larger reductions in efficiency by introducing additional delay in Table 1 Environmental impacts for the base case and the VSL the traffic system. Further, the algorithm become active algorithms only when low speeds are detected and when a breakdown VSL algorithm Mean CO2 (kg) Mean HC (g) Mean NOx (g) already occurred or is about to occur. The results from this Base case 1175±49 1767±101 3154±170 study is in line with the objective of the algorithm and the findings from the literature. In an empirical study of the RCP 1180±49 1825±97 3223±159 Swedish MCS no improvements were observed in traffic MCS 1183±51 1817±116 3219±187 efficiency, but the variance in speed between vehicles were MTFC 1172±45 1671±85 3023±143 reduced leading to increased traffic safety . Although, SPECIALIST 1165±47 1754±104 3124±169 in  a decrease in travel time in the similar MCS in the Grumert et al. European Transport Research Review (2018) 10:21 Page 10 of 12 locations along the road. In RCP, the focus is on safety, extensive detection equipment. Other explanations to the why a reduction in travel time is not necessarily observed. limited improvements in traffic efficiency are related to However, earlier studies of RCP [29, 30, 56]showeda the time of activation, the recovery rate, the lead-in speed reduction in both the crash potential and in travel time. limits and the size of the speed limit reduction. Except This is due to that the variable speed limits are reflect- from the size of the speed limit reduction, the factors are ing the mean speed on the road, rather than a predefined based on the estimated traffic states and the predefined much lower speed limit. In this study, based on manually parameters. Hence, one reason for the long VSL activa- adjusting the parameters, it was not possible to find a set tion time and slow recovery rate, and the long application of parameters which resulted in a reduction in both crash area, is the set of parameters applied in this study and, potential and an increase in mean speed and the resulting therefore, fine tuning of the parameters can improve the mean speeds are comparable to the base case. However, performance of the algorithm. more extensive tuning of the parameters can improve the As expected MTFC performs best of the studied algo- performance of the algorithm. Another explanation of the rithms when it comes to improving traffic efficiency. This limited improvements in traffic efficiency are related to is a result of that the algorithm is working to prevent a the recovery rate, i.e. the time when the algorithm is deac- potential breakdown before it actually occurs. Increased tivated and traffic conditions return to free flow. RCP traffic efficiency for MTFC have also been observed in has predefined fixed VSL activation times that sometimes [4, 5, 38, 39]. Additionally, traffic safety was increased as seem to be longer than necessary. a result of the increased traffic efficiency. This is in line SPECIALIST can be seen both as an incident detec- with a study where MTFC was compared to VSL algo- tion and a homogenization system. Since the system use rithms with the objective to improve safety . It should thresholds to identify incidents (moving jams) it becomes be noted that the algorithm works well at capacity levels active only when an incident has occurred. For SPECIAL- and for short time periods. However, longer time periods IST an increase in safety measured as CVS is in general and/or heavily congested conditions have not been inves- not observed, with exception of some improvements at tigated in this study. The system might give larger effects the bottleneck location. This can be explained by the long on traffic efficiency at higher flow levels, at least up to a stretch with lowered speed limits, which result in less con- certain level when the traffic becomes oversaturated. gestion and a higher mean speed around the bottleneck None of the studied algorithms were found to have compared to the base case. As a consequence, the varia- any substantial effect on emissions. Although, a more tions in speed are increasing in the area of the bottleneck. thorough investigation of the emissions might give more Even as farawayasatthe firstdetectorstation somewhat insight to how the algorithms may affect the environmen- higher variations in speed are detected as a result of the tal impact. starting point of the lowered speed limits being located Finally, note that the MCS and the SPECIALIST can be there. However, the goal of preventing further incidents applied for unknown bottleneck locations. Whilst, RCP and homogenizing the traffic flow by the use of lead-in and MTFC are applied at predefined bottleneck locations speed limits are reflected in the results. The longer areas and with bottleneck specific parameters. Identification of with lowered speed limit are resulting in less abrupt speed the bottleneck location and the bottleneck specific param- transitions in space compared to the base case. Hence, eters can be done based on offline calibration as in this safety is improved in the form of a more homogenous paper, or based on online calibration as described in , traffic flow. In earlier studies [17, 18], SPECIALIST gave and . decreased travel times. No overall improvements in travel time could be observed in this study. However, SPECIAL- 7Conclusions IST managed to improve the traffic efficiency close to the In this study, we have investigated how the performance bottleneck location. The lack of improvement in overall of VSL systems is affected by the design of the control traffic efficiency for SPECIALIST can be explained by the algorithm and the purpose of the system. Four algorithms, fact that the control algorithm is designed for backwards existing in the literature and implemented in real traffic, propagating shockwaves. So even though the conditions with different objectives are investigated. The results show for detecting a shockwave is fulfilled in the simulated that all of the algorithms are activated close to capacity scenario and an increase in speed is seen just at the bot- levels and the objective of all the algorithms are fulfilled tleneck, the algorithm would probably work better for close to the bottleneck. It is concluded that the design of moving shockwaves. On the other hand, this means that the control algorithm and the purpose of the VSL sys- the speed of the shockwave, and thereby the type of con- temwillhaveanimpactonwhichaspects of thetraffic gestion, needs to be identified in order to avoid activation conditions that are affected by the system. Desirable char- for other types of congestion such as accidents, inci- acteristics when implementing a control algorithm are dents, etc. This is usually not possible and would require fast reactions to changes in the traffic conditions, early Grumert et al. 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