Research Article Development of Degree-of-Priority...

Hindawi Publishing CorporationDiscrete Dynamics in Nature and SocietyVolume 2013 Article ID 283207 10 pageshttpdxdoiorg1011552013283207

Research ArticleDevelopment of Degree-of-Priority Based Control Strategy forEmergency Vehicle Preemption Operation

Jiawen Wang Wanjing Ma and Xiaoguang Yang

Key Laboratory of Road and Traffic Engineering of the Ministry of Education Tongji University 4800 Caorsquoan RoadShanghai 201804 China

Correspondence should be addressed to Wanjing Ma mawanjingtongjieducn

Received 22 August 2013 Accepted 5 November 2013

Academic Editor Huimin Niu

Copyright copy 2013 Jiawen Wang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This paper proposes a degree-of-priority based control strategy for emergency vehicle preemption operation to decrease the impactsof emergency vehicles on normal trafficThe proposedmodel features its effectiveness to the following three aspects (1) amultilayerfuzzy model was established to determine the degree-of-priority based on emergency vehicle preemption demand intensity andpreemption influence intensity (2) for emergency vehicles with proper classification a travel time estimationmodel for emergencytraffic was formulated an optimal emergency route determines model based on the level of priority of emergency events and theemergency vehicle travel time was developed to minimize evacuation time as well as minimize the adverse impacts of preemptionon normal traffic and (3) a conditional traffic signals priority control method at each intersection of the evacuation route wasbuilt so that traffic queue at each intersection can be cleared before the arrival of emergency vehicles A simulation model basedon field data was developed and the performance of the proposed strategy was compared with the conventional local detectionbased method under the microscopic simulation model The results validated the efficiency of the proposed strategy in terms ofminimizing the delay of emergency vehicles and reducing adverse impacts on normal traffic

1 Introduction

Providing safe and fast driving environment for emergencyvehicles to reduce travel time and delay is a critical issuein traffic evacuation Under effective preemption ones canreach their destinations at the earliest possible time whichis one of most critical factors in saving lives and reducingproperty loss At the same time reducing the adverse impactsof emergency vehicles on normal traffic so that they cancause the least disturbance to network traffic flow is thekey to avoid the grid-lock caused by emergency accidents[1 2] While substantial progress has been made in theareas of vehicle detection and communication technologiesto increase the efficiency of emergency vehicles current state-of-the-art in signal preemption in China has not reached thepoint where signal clearance strategy considering the adverseimpact or normal traffic can be automatically generated andimplemented in real time

To date most preemption systems developed operate ona single-intersection basis and require local detection of an

emergency vehicle to activate a signal preemption sequence ateach intersection [3 4] Existing signal preemption methodscan be classified into several categories such as opticalinfrared light acoustic special types of loop detection andGPS-based systems [5 6] The optical systems that aredeveloped in the 1960rsquos use a strobe-lamp on the vehicle andan optical sensor per approach to an intersection requir-ing a clear line-of-sight path between the vehicle and theintersection [7]The sound-based systems use the directionalmicrophones installed at an intersection to detect the sirenof vehicles approaching a given intersection therefore nospecial equipment is required for the emergency vehicles [8]In a GPS-based system being operated in Taicang Chinaboth an emergency vehicle and an intersection are equippedwith a GPS receiver and a radio transceiver for two-waycommunication In recent studies a route-based dynamicstrategy was developed for efficient preemption of trafficsignals for emergency vehicles in real time by Kwon et al [9]And Louisell and Collura [10] proposed a simple algorithmto estimate emergency vehicle travel time savings based on

2 Discrete Dynamics in Nature and Society

Network geometrydata

Network trafficparameters

Emergency demandparameters

Exist

Emergency vehicle preemptioncontrol request detection module

Degree-of-prioritycalculation module

Travel time estimationmodule

Route selection parameterscalculation

Emergency route selectionmodule

Select a appropriatepreemption control method

Affected arearestore

Control methodoptimization

Emergency vehicle controlscheme

Input

Output

Yes No

Figure 1 Structure of degree-of-priority based signal preemption strategies

a field operational Mussa and Selekwa [11] reported on thedevelopment of a transition procedure based on the quadraticoptimization method that aimed at reducing disutility mea-sures to motorists during the transition period Haghani etal [12] concentrated on developing an optimization modelfor developing flexible dispatching strategies that take theadvantage of available real-time travel time information Inrecent years Yun et al [13 14] have optimized the exit phasecontrols for emergency vehicle preemption and compared theemergency vehicle preemption methods with a hardware-in-the-loop simulation He et al [15] presented a heuristic algo-rithm for traffic signal control with simultaneous multiplepriority requests at isolated intersections in the context ofvehicle-to-infrastructure communications being available onpriority vehicles and the method could reduce average busdelay in congested conditions by about 50 Savolainen etal [16] developed a dynamically activated emergency vehiclealert system to provide an additional visual cue tomotorists ofan impending emergency vehiclersquos approach Route selectionis one of the fundamental problems in emergency logisticsmanagement [17ndash20] In order to send the commodities asquickly as possible the path which costs least should beselected A vast amount of the literature [21ndash25] has beenproduced up until now

As indicated above while there has been substantialprogress in developing local preemption technologies andmuch research has focused on the impact of transit priority[26ndash28] the impact of EV preemption has not been wellstudied a few research studies on decreasing the adverseimpacts of preemption on normal traffic have been foundin the literature Qin and Khan [29] report two new control

strategies for emergency vehicle signal preemption whichreduce the response time and minimize the impact of EVoperation on general traffic Developing degree-of-prioritybased control strategy that can provide an efficient and safetraveling environment for emergency vehicleswithminimumdisruption on network traffic is of critical importance inmanaging urban traffic

Based on the above achievements this paper presentsa dynamic preemption approach that combines a degree ofcontrol priority classification procedure and a route-basedpreemption method to provide the most appropriate routeand control strategy for an emergency vehicle under a givennetwork traffic conditions and emergency issue conditionsThe proposed method was evaluated in part of the roadsnetwork in Beijing China using a microscopic networksimulation model and its effectiveness was compared withthe existing local-detection based method

This paper is organized as follows the first part is theintroduction of emergency vehicle preemption methodsThesecond part is the model of degree of priority classificationand travel time prediction The third part is developmentof emergency vehicle preemption strategy and performanceevaluation Last part is conclusion

2 Degree-of-Priority Based Signal Preemption

Figure 1 shows the structure of the degree-of-priority basedsignal preemption strategy developed in this study Inputdata include emergency demand parameters network traf-fic parameters and network data Emergency demandparameters are obtained when emergency issue happens

Discrete Dynamics in Nature and Society 3

Preemption controldemand intensity fuzzy

calculation

Estimated lossTarget traveltime

Road sectionssaturation Road grade

Priority demandintensity

Preemption controlimpact intensity

Degree of preemption control priorityclassification

Input

Main process

Output

Preemption controlimpact intensity fuzzy

calculation

Degree of preemption control priority

Figure 2 Emergency vehicle preemption signal control priority classification process

Network traffic parameters are continuously collected by fielddetectors Network geometry data are static data provided bygovernment Control strategy for emergency vehicle preemp-tion will be started as soon as emergency issue happens andthe first step is classifying degree-of-priority of emergencyvehicles in each road section which corresponds to intensityneeds of emergency vehicle preemption Then travel time ofemergency flow in each road section is predicted based onthe input data and degree of priority Next two-objectiveoptimization model is established to calculate route selectionparameters and select the optimal route for emergency flowIn this research the well-known Dijkstra algorithm [30] isadopted to find the optimal route that has the minimumroute selection parameter for a given origin-destination pairAt last signal control method is developed to optimize theemergency vehicle preemption plan and affected area restorecontrol plan is proposed

3 Degree of Priority Classification Model

Degree of priority is an important parameter of emergencyvehicle in this research which corresponds to the importantlevel and degree of influence of emergency vehicle in eachroad section Because both importance level of emergencyvehicle and degree of influence to normal network traffic floware difficult to measure accurately degree of priority couldbe calculated by the genetic algorithm or fuzzy algorithmIn this study researchers developed a three-step multilayerfuzzy algorithm to calculate the degree of priority in threesteps

To calculate preemption demand intensity the serious-ness and urgency of the emergency issue should be estimatedbased on desired travel time of emergency vehicle andestimated loss of the emergency issue In the fuzzy reasoningof preemption demand intensity calculation fuzzy inputsare the estimated loss parameter 119875119897119896 of emergency issue 119896and the urgency parameter 119880119896 Fuzzy output is preemptiondemand intensity 119868pd For the convenience of computing inthis research the ranges of estimated loss parameter 119875119897119896 andthe urgency parameter119880119896 are defined as 0 to 1 (see Figure 2)

The estimated loss parameter 119875119897119896 can be calculated asfollows

119875119897119896 =

Log (119871119896 +119899119871(119875)

119896)

10 (1)

In (1) 119875119897119896 is the estimated loss parameter of emergencyissue 119896 119871119896 is the estimated economic loss of emergency issue119896 with 10000 CNY as its unit 119871(119875)

119896is the conversion coeffi-

cient of casualties 119899 is the estimated number of casualtiesAccording to this formula emergency events anticipated tohave a higher estimated loss would result in a higher intensityof response

The urgency parameter 119880119896 can be calculated as follows

119880119896 = 1 minussum119895

119899=1(119871119896119899V119898119899)

119879119905

(2)

In (2) 119880119896 is the urgency parameter of emergency issue 119896119879119905 is the desired travel time of emergency vehicle appointedby decision makers 119871119896119899 is the length of road section 119899 inthe shortest route 119895 V119898119899 is the top speed of the emergencyvehicle in road section 119899 From the formula we can find withthe decrease of the urgency parameter 119880119896 the emergencyvehicle is more urgent It makes these two parameters fuzzyby membership function as shown in Figures 3(a) and 3(b)to calculate the preemption demand intensity

Fuzzy rules of preemption demand intensity classificationare shown in Table 1(a) In Table 1 VH HM L VL is shortfor Very High High Medium Low Very Low

The membership function of preemption demand inten-sity is triangular and the range is [0 1] Then the exact valuefunction of preemption demand intensity is obtained throughthe center-of-gravity defuzzification

To consider the impact of emergency vehicle preemptionon normal network traffic flow preemption impact intensityis proposed to reflect the degree of this impact Fuzzy inputsof preemption impact intensity fuzzy calculation are city roadgrade V119889119895 of road section 119895 and saturation 119909119895 of road section 119895The city road grade is divided into expressway arterial road


1Estimated loss parameter

108060402

0

Deg

ree o

f mem

bers

hip

0908070605040302010

VLLM

HVH

(a) Membership function of estimated loss parameter Plk

108060402

0

Deg

ree o

f mem

bers

hip

Urgency parameter10908070605040302010

VLLM

HVH

(b) Membership function of road grade vdj

108060402

00 20 40 60 80 100 120

Road grade

Deg

ree o

f mem

bers

hip

VLLM

HVH

(c) Membership function of urgency parameter Uk

08060402

0

Saturation of road sectionD

egre

e of m

embe

rshi

p10908070605040302010

VLLM

HVH

(d) Membership function of saturation xj

Figure 3 Membership function in degree of priority classification model

secondary trunk road and branch road which are indicatedby value of V119889119895 80 60 40 30 indicates Expressway ArterialRoad Secondary Trunk Road Branch Road respectivelySaturation of road section is calculated by volumes andcapacity of the road section It makes these two parametersfuzzy by membership function that is shown in Figures 3(c)and 3(d) to calculate preemption impact intensity Fuzzyrules of preemption impact intensity calculation are shownin Table 1(b)

Themembership function of preemption impact intensityis triangular and the range is [0 1] Then the exact valuefunction of preemption impact intensity is obtained throughthe center-of-gravity defuzzification

To calculate degree of priority of emergency vehicleon each road section fuzzy rules of emergency vehiclepreemption priority classification are used The fuzzy rule isshow in Table 1(c)

In Table 1(c) when preemption impact intensity is veryhigh the degree of priority is classified as a low value toavoid the impact on normal network traffic flow And whenpreemption impact intensity is very low normal networktraffic flow volume is low So the road impedance to emer-gency vehicle is low enough to classify degree of priority asa low value Therefore when Preemption Impact Intensity ismedium a high value is given according to these rules

Themembership function of emergency vehicle degree ofpriority is triangular and the range is [0 1] Then the exactvalue function of emergency vehicle preemption priority is

obtained through the center-of-gravity defuzzification Theemergency vehicle degree of priority119863119901 is an important inputin selecting control method

4 Travel Time Prediction Model forEmergency Vehicle

Road section clearance time Δ119905 is an important parameterthat affects total travel time and delay of emergency vehiclesIt stands for the time difference between the moment 119905119890when the sections are changed into emergency state and themoment 119905119894119899 when the emergency vehicles enter the sectionsThe road section clearance time of different control methodsis not the same and it is related to emergency vehicledegree of priority of the road section The higher degreeof priority the longer road section clearance time In theurban road system the difference of traffic characteristicsvehicles will become discrete The traffic flow setup fromthe upper intersection will become discrete and the lengthof platoon will become long before the platoon arrives atthe lower intersection This phenomenon is called platoondispersion Previous studies have demonstrated that thespeeds of vehicles follow Gaussian distributions

In the multilane sections lane-clear speed varies directlywith mean time-headway Lane-clear speed has the dimen-sions of pcukmsdots

The lane-change behavior is very fast then the distanceof platoon moving in the lane-change period is short


Table 1 Fuzzy rules in degree of priority classification model

(a) Fuzzy rules of preemption demand intensity calculation

119880119896

119868pd

119875119897119896 VH H M L VLVH VH VH H H MH VH H H M LM H H M L VLL H M L VL VLVL M L VL VL VL

(b) Fuzzy rules of preemption impact intensity calculation

119909119895119868pi

V119889119895 VH H M L VLVH VH VH H M MH VH H M L LM H M M L VLL M L L VL VLVL L VL VL VL VL

(c) Fuzzy rules of emergency vehicle preemption priority classification

119868pd119863119901

119868pi VH H M L VLVH VH VH VH VH VHH H H VH VH HM M H VH H ML L L M L VLVL VL VL L L VL

so the distance is negligible Total quantity of vehicles on roadsection 119896 can be calculated as follows

119899119896 =119881119896119871119896

119873119896V119896 (3)

In (3) 119899119896 is total quantity of vehicles on road section 119896Parameter 119881119896 is the current volume of section 119896 Parameter119871119896 is length of section 119896 Parameter119873119896 is the number of lanesin section 119896 Parameter V119896 is mean travel speed of normalvehicles in section 119896 And quantity of vehicles that leave thelane in unit time 1198991015840

119896is calculated as follows

1198991015840

119896= 120573120583119871119896

119873119896

119881119896

(4)

In (4) Parameter 120573 is lane clear influence coefficient thatrepresents the influence of different lane-clear methods onlane clear speed Its value is defined as 1 when the lane-clearmethod is changing the lane from inside lane to outside lanein the two-lane sectionsThe value is demarcated by followingsimulation experience And parameter 120583 is the ratio of lane-clear speed to mean time-headway The value is demarcatedby following simulation experience

Then we can find quantity of vehicles on the emergencylane after normal vehicle avoiding emergency vehicle 119899119890119896 iscalculated as follows

119899119890119896 = max (119899119896 minus 1199051198961198991015840

119896 0) = max(

119881119896119871119896

119873119896V119896minus 119905119896120573120583119871119896

119873119896

119881119896

0)

(5)

In (5) 119905119896 is road section clearance time It is a functionof emergency vehicle degree of priority 119863119901119896 The formula isshown in (4)This formula should be calibrated based on fielddata in application Consider the following

119905119896 = 119891 (119863119901119896) (6)

The applications and studies of road section travel func-tion are themost popularmethods to estimate the emergencyvehicle travel time by free flow speed traffic volume orcapacity of the section This study proposed an emergencyvehicle travel time estimation model for the emergencyvehicle control method based on bureau of public roadsfunction (BPR function) [31] BPR function was proposedby FHWA in 1964 in the US [32] It is the most widelyused impedance function in the traffic-planning field In thisfunction travel time is the nonlinear function using the ratioof traffic volume to capacity as the parameter

The definition of the public roads function is defined asfollows

119879119896 = 1198790 [1 + 119886(119881119896 (119905)

119862119896 (119905))

119887

] (7)

In (7) 119879119896(119905) is emergency vehicle estimated travel time inroad section 119896 at 119905 Parameter 1198790 is the travel time when thevolume of section 119896 is zero Parameter 119881119896(119905) is the volume ofsection 119896 at 119905 Parameter 119862119896(119905) is the capacity of section 119896 at 119905Parameters 119886 and 119887 are coefficients whose advised values are119886 = 015 and 119887 = 4

Based on above BPR function this study built the emer-gency vehicle travel time estimation model for the sectionsthat are applied to different kinds of control methods asfollows

119879119896 =119871119896

V119890[1 + 119886(

119899119890119896119873119896119881119896

119871119896119862119896

)

119887

] (8)

In (8) 119899119890119896 can be calculated by (5) then one can get thefollowing

119879119896 =119871119896

V119890[

[

1 + 119886(max(1198812

119896119871119896 minus Δ119905119896120573120583119873

2

119896V119896 0)

119881119896119871119896119862119896

)

119887

]

]

(9)

In the formulation (8) and (9) 119879119896 is emergency vehicleestimated travel time in section 119896 Parameter 119881119896 is currentvolume of section 119896 Parameter 119871119896 is length of section119896 Parameter 119873119896 is the number of lanes in section 119896Parameter V119896 is mean travel speed of normal vehicles insection 119896 Parameter V119890 is mean travel speed of emergencyvehicles Parameter 120573 is lane clear influence coefficient


Parameter 120583 is the ratio of lane-clear speed to mean time-headway Parameter Δ119905119896 is road section clearance time ofsection 119896 Parameters 119886 and 119887 are coefficients demarcated byfollowing simulation experience

If road section clearance timeΔ119905119896 takes zero that is to saythe emergency vehicle control method is disabled 119879119896 can becalculated by the following equation

119879119896 =119871119896

V119890[1 + 119886(

119881119896

119862119896

)

119887

] (10)

5 Development of Emergency VehiclePreemption Strategies

51 Route Selection Parameter Calculation and Optimal RouteSelection In order to select the optimal route for emergencyvehicle route selection parameter should be calculated Theroute selection method should provide an efficient andsafe traveling route for emergency vehicle with minimumdisruption on network traffic And the disruption on net-work traffic of emergency vehicle declines with decliningdegree of priorityTherefore the model has two optimizationobjectives including reducing route travel time to minimumand controlling the sum of degree of priority in the routeto minimum In this study route selection parameter 119875119896 isdefined as follows

119875119896 = 119879119896 + 120578119863119901119896 (11)

In (9) 119879119896 is emergency vehicle estimated travel time inroad section 119896 119863119901119896 is emergency vehicle degree of priorityin road section 119896 Parameter 120578 is degree of priority adjustingcoefficients which will be determined in specific case

Once the location of an emergency issue and emergencyfacilities (police stations aid stations etc) is determinedthe route-selection algorithm determines the best route thathas the minimum route selection parameter for a givenorigindestination pair In the proposed strategy a networkis represented as a set of linksnodes and the well-knownshortest-path algorithmdeveloped byDijkstra [30] is adoptedto find the optimal route Dijkstrarsquos algorithm has beenproven to result in the shortest-path from a single source ona weighted directed graph where all edge weights have non-negative values [33] In the proposed strategy a given networkismodeled as a set of directional links with nonnegative routeselection parameter 119875119896 and Dijkstrarsquos algorithm is applied tofind the minimum 119875119896 route

52 Control Method Selection and Optimization As soon asthe emergency route is determined this study proposes astrategy to select the control method based on degree ofpriority Experience-based control method choice suggestionis shown in Table 2

When degree of priority of the emergency vehicle iswithin 00 to 04 no control method will be implementedto minimize negative effects of emergency vehicle on normalnetwork traffic flow And if degree of priority is within 04 to07 green-wave signal control method will be implementedto reduce travel time of emergency vehicle Further when

Table 2 Emergency vehicle control method choice suggestion

Degree of priority Control method00ndash04 None04ndash07 Green-wave signal preemption07ndash09 Lane clearance preemption09-10 Road clearance preemption

degree of priority is within 07 to 09 the degree of priorityis high enough to implement lane clearance control methodadditionally based on green-wave signal control method Atlast if degree of priority is within 09 to 10 related roadsections will be temporarily closed to reduce travel time ofemergency vehicle

Determining the right offset times to activate the greensignal for the intersections along the emergency route is ofcritical importance in reducing travel time of emergencyvehicles andminimizing negative effects of signal preemptionon normal traffic flow As soon as the road sections thatimplement green-wave signal controlmethod are determinedfor a given emergency vehicle the signal offset time of relatedintersections is adjusted to ensure unidirectional green wavepreemptionWe record the target offset between downstreamintersection 119862119889119896 and upstream intersection 119862119906119896 of roadsection 119896 as 119874119896 Then offset 119874119896 can be calculated as follows

119874119896 = 119879119896 mod 119862119889119896 (12)

Record the original offset between downstream intersec-tion 119862119889119896 and upstream intersection 119862119906119896 as 119874

1015840

119896 So the offset

adjustment recorded as Δ119874119896 is calculated as follows

Δ119874119896 = 119874119896 minus 1198741015840

119896 (13)

If 119862119889119896 lt sum119896

119894=0119879119894 offset should be adjusted per cycle

Δ119874adj119896 is calculated as follows

Δ119874adj119896 =Δ119874119896

lfloorsum119896

119894=0119879119894119862119889119896rfloor

(14)

Else offset should be adjusted per cycle Δ119874adj119896 = 0When the emergency vehicle departs change the cycle of

each downstream intersection to 119862119889119896 minusΔ119874adj119896 until the offsetis equal to target offset

Lane clearance controlmethod is an importantmethod toreduce travel time of emergency vehicle further Emergencylane is enabled by traffic police or variable lane control systemwhen the emergency vehicle reache last road section Startuptime of emergency lane is determined by road section traveltime of emergency vehicle

6 Performance Evaluation

Finally the proposed degree-of-priority based control strat-egy is evaluated in a part of road network in Xicheng districtBeijing China Figure 4 is the diagram of the road network

This area adopted SCOOT signalized intersections con-trol system Network traffic parameters and network data areshown in Table 3


C1

C4 C5 C6

C3EV

S1

S2 S3

S7

S5 S6

S4

Star

t

Endi

ng

C2

Location ofemergency

issue

Figure 4 The simulation model of road network in beijing

Table 3 Network parameters and data

Section name Section number Length (m) Road grade Traffic volume (PCUh) 312 730ndash312 800 Capacity (PCUh)Direction of arrow Reversed direction

Naoshikou Rd S1 517 Arterial road 1087 896 3200West Xuanwumen Rd S2 445 Arterial road 684 768 2400West Xuanwumen Rd S3 480 Arterial road 589 656 1600Tonglinge Rd S4 485 Branch road 102 140 600Xinwenhua Rd S5 442 Secondary trunk road 348 268 800Xinwenhua Rd S6 477 Secondary trunk road 248 375 800Xuanwumen Rd S7 463 Arterial road 1395 1674 3200

In this case fire occurs in a restaurant near intersectionC6 Emergency vehicle that is composed of three fire trucksstarts from fire station near intersection C1 To reduce lossthe desired travel time of emergency vehicle is set at 180 sThe estimated loss is 2000000 CNY and two of the injuredare waiting to be rescued A microsimulation model basedon VISSIM is set up to calibrate some parameters in thestrategies The main processes of simulation are shown inFigure 5

At a random time the section in the simulator enteredinto emergency state which is shown in Figure 5(1) Whenthe section was under emergency state the vehicles onemergency lane changed to outside lane to clear a lane forthe emergency vehicle Then the emergency vehicle passedthe intersection quickly under intersection signal controlstrategy The former process is shown in Figures 5(2) 5(3)5(4) and 5(5) According to the simulation parameters ofcontrol strategy in this case are shown in Table 4

Based on the degree-of-priority based control strategyand the data in Table 4 degree of priority and emergencyvehicle travel time in each road section are calculated byBeijing Special Control System which is developed by J+traffic Tech Co The results are shown in Table 5

By using shortest-path algorithm developed by Dijkstrathe emergency routes based on different 120578 are shown inFigures 6(b) and 6(c)

In Figures 6(b) and 6(c) the red line indicates the roadsections that adopt none of the control method and thegreen line indicates the road sections that adopt green-wavesignal control method In this study these two plans areevaluated in simulation software based on cellular automatadeveloped by authors The degree-of-priority based controlstrategy is compared with the local-detection based methodin the software based on the same set of vehicle inputs In themicrosimulation traffic network emergency vehicle detectorsare set at 100m from the intersection stop line For a faircomparison a common set of 15 different random seeds wasused for the simulation of each preemption route and theirresults were averaged The simulation results are shown inTable 6

As shown in Table 6 the emergency vehicle travel timeunder degree-of-priority based control strategy exhibits anindistinctive degraded performance However a clear patternof the degraded performance in terms of average delay isexhibited under the degree-of-priority based control strategyAlong with degree of priority adjusting coefficient 120578 increasethus the selected route is different the average delay isdeclining in evidence This indicates the efficiency of theproposed strategy by reducing unnecessary preemption ina given network thus minimizing the delay because ofpreemption without decreasing much efficiency


Section enters intoemergency state

Section clearance time t0Start at random

timeEmergency vehicleenter the section

Intersection signalpreemption control

Emergency vehiclepass the intersection

Travel time of emergency vehicle t

(1) (2) (3) (4) (5)

1

2

3

4

5

1

2

3

4

5

1

2

3

4

5

1

2

3

4

5

1

2

34

5

6

67

7

Figure 5 Main processes of simulation based on VISSIM

Table 4 Parameters of control strategy in evaluation

Parameters Symbol ValueConversion coefficient of casualties 119871

(119875)

119896 70

Road section clearance time Δ119905119896

When119863119901 lt 04 Δ119905119896 = 3When 04 lt 119863119901 lt 07 Δ119905119896 = 6

Else Δ119905119896 = 20Lane clear influence coefficient 120573 1Ratio of lane-clear speed 120583 1357Coefficients of BPR function 119886 196Coefficients of BPR function 119887 159Degree-of-priority adjusting coefficients 120578 [10 50 100 200]

Table 5 Calculation results of degree-of-priority and emergency vehicle travel time

Section number 119909119895 119868pi 119868pd 119863119901 Δ119905119896 119879119896

120578

1 50 100 200S1 034 048 017 041 60 310 351 516 722 1134S2 029 039 017 039 30 267 306 461 654 1041S3 037 054 017 041 60 288 329 492 695 1102S4 017 021 017 025 30 582 607 705 828 1074S5 044 037 017 037 30 402 440 588 773 1144S6 031 025 017 025 30 431 456 556 681 931S7 044 062 017 036 30 280 317 462 643 1006

Table 6 Simulation results from different preemption strategies

Routes Item Local-detection based method Degree-of-priority based preemption

Route 1EV travel time (sec) 103 106Total vehicle hours 113 108Average delay (sec) 196 152


Route 3EV travel time (sec) 159 mdashTotal vehicle hours 111 mdashAverage delay (sec) 191 mdash


EV

Route 1Route 2Route 3

(a) Sample network

T7 = 280 sDp7 = 036

Dp2 = 039 Dp3 = 041

T2 = 267 s T3 = 288 sEV

120578 = 1 50 100

(b) Route 1

Dp4 = 025

Dp2 = 039

Dp2 = 025

T2 = 267 s

T2 = 431 s

EV

T4 = 582 s

120578 = 200

(c) Route 2

Figure 6 Sample network and selected emergency routes based on different 120578

7 Conclusions

The primary objective of this paper is developing a degree-of-priority based control strategy for emergency vehicleoperation to decrease the adverse impacts of emergencyvehicles on normal traffic aswell as avoid the grid-lock causedby emergency issues A uniform optimization structure isdesigned which is consisted by a fuzzy logic based modelthat was proposed to determine the degree-of-priority ofan emergency event Then an optimal emergency routeselection model was built based on degree-of-priority andthe estimated travel time of emergency vehicle Four types ofsignal control methods were proposed to minimize the delayof emergency vehicles as well as adverse impacts on normaltraffic Therefore the traffic signals at the intersections alongthe emergency route can be adjusted effectively in advanceand traffic queue at each intersection can be cleared for theapproaching emergency vehicles This strategy is evaluatedin simulation software based on the data of a part of roadnetwork in Xicheng district Beijing China The resultsindicate that the proposed approach is a viable additionto local-detection based method in urban area and can

minimize the delay of emergency vehicles without muchadverse effects on normal traffic Future research includesthe development of an efficient calibration method for thedegree of priority with parameters which can be measuredand the enhancement of the simulationmodel to evaluate theperformance of the strategy in large road network

Conflict of Interests

The authors declare that they have no conflict of interestsregarding the publication of this paper

Acknowledgments

This research was made possible through funding from theMinistry of Science and Technology of China under Grantno 2011AA110305 The authors wish to acknowledge the vastand helpful assistance from Intelligent Transportation SystemResearch Center Transportation System Engineering andITS Research Group School of Transportation EngineeringTongji University The Beijing Special Control System wasestablished with the great help of J+ traffic Tech Co Ltd


References

[1] Transportation Research Board (TRB) Proceedings of NationalConference on Traffic Incident Management 2002

[2] U S Department of Transportation (DOT) Fatality AnalysisReporting System NHTSA Washington DC USA 2002

[3] Federal Highway Administration (FHWA) Traffic Signal Pre-emption for Emergency Vehicles A Cross-Cutting Study 2006

[4] D Deeter H M Zarean and D Register ldquoRural ITS ToolboxSection 3 Emergency Services Subsection 3 1 EmergencyVehicle Traffic Signal Preemptionrdquo 2001

[5] D Bullock J Morales and B Sanderson ldquoEvaluation ofemergency vehicle signal preemption on the Route 7 Virginiacorridorrdquo FHWA-RD-99-70 Federal Highway AdministrationRichmond Va USA 1999

[6] D Bullock and E Nelson ldquoImpact evaluation of emergencyvehicle preemption on signalized corridor operationrdquo in Pro-ceedings of the TRB Annual Meeting Transportation ResearchBoard Washington DC USA January 2000

[7] K Hunter-Zaworski and A Danaher ldquoNE Multnomah streetOpticom bus signal priority pilot studyrdquo Final Report TNW97-03 Seattle Wash USA 1995

[8] Traffic Technologies LLC ldquoSonem 2000 digital siren detectorrdquoTechnicalDocument for Installation TrafficTechnologies LLC2001

[9] E Kwon K Sangho and B Rober ldquoRoute-based dynamicpreemption of traffic signals for emergency vehicles operationsrdquoin Transportation Research Record Transportation ResearchBoard of the National AcademiesWashington DC USA 2003

[10] C Louisell and J Collura ldquoA simple algorithm to estimateemergency vehicle travel time savings on preemption equippedcorridors a method based on a field operational testrdquo inTransportationResearchRecord TransportationResearchBoardof the National Academies Washington DC USA 2005

[11] R Mussa and M F Selekwa ldquoDevelopment of an optimaltransition procedure for coordinated traffic signalsrdquo Journal ofAdvances in Transportation Studies vol 3 pp 57ndash70 2004

[12] A Haghani H J Hu and Q Tian ldquoAn optimization modelfor real-time emergency vehicle dispatching and routingrdquo inTransportationResearchRecord TransportationResearchBoardof the National Academies Washington DC USA 2003

[13] I Yun B B Park C K Lee and Y T Oh ldquoComparison ofemergency vehicle preemption methods using a hardware-in-the-loop simulationrdquo KSCE Journal of Civil Engineering vol 16no 6 pp 1057ndash1063 2012

[14] I Yun B B Park C K Lee and Y T Oh ldquoInvestigation on theexit phase controls for emergency vehicle preemptionrdquo KSCEJournal of Civil Engineering vol 15 no 8 pp 1419ndash1426 2011

[15] Q He K L Head and J Ding ldquoHeuristic algorithm for prioritytraffic signal controlrdquoTransportation Research Record vol 2259pp 1ndash7 2011

[16] P T Savolainen T K Datta I Ghosh and T J Gates ldquoEffectsof dynamically activated emergency vehicle warning sign ondriver behavior at urban intersectionsrdquo Transportation ResearchRecord vol 2149 pp 77ndash83 2010

[17] T S Glickman and E Erkut ldquoAssessment of hazardous materialrisks for rail yard safetyrdquo Safety Science vol 45 no 7 pp 813ndash822 2007

[18] M Davidich and G Koster ldquoTowards automatic and robustadjustment of human behavioral parameters in a pedestrianstream model to measured datardquo Safety Science vol 50 no 5pp 1253ndash1260 2012

[19] F Ozel ldquoTime pressure and stress as a factor during emergencyegressrdquo Safety Science vol 38 no 2 pp 95ndash107 2001

[20] S Heliovaara J-M Kuusinen T Rinne T Korhonen and HEhtamo ldquoPedestrian behavior and exit selection in evacuationof a corridormdashan experimental studyrdquo Safety Science vol 50 no2 pp 221ndash227 2012

[21] J-B Sheu ldquoAn emergency logistics distribution approach forquick response to urgent relief demand in disastersrdquo Trans-portation Research E vol 43 no 6 pp 687ndash709 2007

[22] Y Deng and F T S Chan ldquoA new fuzzy dempster MCDMmethod and its application in supplier selectionrdquoExpert Systemswith Applications vol 38 no 8 pp 9854ndash9861 2011

[23] Y Deng R Sadiq W Jiang and S Tesfamariam ldquoRisk analysisin a linguistic environment a fuzzy evidential reasoning-basedapproachrdquo Expert Systems with Applications vol 38 no 12 pp15438ndash15446 2011

[24] A Hatami-Marbini M Tavana M Moradi and F Kangi ldquoAfuzzy group electre method for safety and health assessment inhazardous waste recycling facilitiesrdquo Safety Science vol 51 no1 pp 414ndash426 2013

[25] L Ozdamar and C S Pedamallu ldquoA comparison of two math-ematical models for earthquake relief logisticsrdquo InternationalJournal of Logistics Systems and Management vol 10 no 3 pp361ndash373 2011

[26] H Rakha and Y Zhang ldquoSensitivity analysis of transit signalpriority impacts on operation of a signalized intersectionrdquoJournal of Transportation Engineering vol 130 no 6 pp 796ndash804 2004

[27] F DionH Rakha andY Zhang ldquoEvaluation of potential transitsignal priority benefits along a fixed-time signalized arterialrdquoJournal of Transportation Engineering vol 130 no 3 pp 294ndash303 2004

[28] R J Baker J Collura J J Dale et al An Overview of TransitSignal Priority-Revised andUpdated ITSAmericaWashingtonDC USA 2004

[29] X Qin and A M Khan ldquoControl strategies of traffic signaltiming transition for emergency vehicle preemptionrdquo Trans-portation Research C vol 25 pp 1ndash17 2012

[30] E W Dijkstra ldquoA note on two problems in connexion withgraphsrdquo Numerische Mathematik vol 1 pp 269ndash271 1959

[31] H Spiess ldquoConical volume-delay functionsrdquo TransportationScience vol 24 no 2 pp 153ndash158 1990

[32] US Department of Transportation Federal Highway Adminis-tration Highway History 2011 httpwwwfhwadotgovhigh-wayhistorynepa01cfm

[33] T H Cormen C E Leiserson R L Rivest and C SteinIntroduction to Algorithms MIT Press Cambridge Mass USA2nd edition 2001

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


Network geometrydata

Network trafficparameters

Emergency demandparameters

Exist

Emergency vehicle preemptioncontrol request detection module

Degree-of-prioritycalculation module

Travel time estimationmodule

Route selection parameterscalculation

Emergency route selectionmodule

Select a appropriatepreemption control method

Affected arearestore

Control methodoptimization

Emergency vehicle controlscheme

Input

Output

Yes No

Figure 1 Structure of degree-of-priority based signal preemption strategies

a field operational Mussa and Selekwa [11] reported on thedevelopment of a transition procedure based on the quadraticoptimization method that aimed at reducing disutility mea-sures to motorists during the transition period Haghani etal [12] concentrated on developing an optimization modelfor developing flexible dispatching strategies that take theadvantage of available real-time travel time information Inrecent years Yun et al [13 14] have optimized the exit phasecontrols for emergency vehicle preemption and compared theemergency vehicle preemption methods with a hardware-in-the-loop simulation He et al [15] presented a heuristic algo-rithm for traffic signal control with simultaneous multiplepriority requests at isolated intersections in the context ofvehicle-to-infrastructure communications being available onpriority vehicles and the method could reduce average busdelay in congested conditions by about 50 Savolainen etal [16] developed a dynamically activated emergency vehiclealert system to provide an additional visual cue tomotorists ofan impending emergency vehiclersquos approach Route selectionis one of the fundamental problems in emergency logisticsmanagement [17ndash20] In order to send the commodities asquickly as possible the path which costs least should beselected A vast amount of the literature [21ndash25] has beenproduced up until now

As indicated above while there has been substantialprogress in developing local preemption technologies andmuch research has focused on the impact of transit priority[26ndash28] the impact of EV preemption has not been wellstudied a few research studies on decreasing the adverseimpacts of preemption on normal traffic have been foundin the literature Qin and Khan [29] report two new control

strategies for emergency vehicle signal preemption whichreduce the response time and minimize the impact of EVoperation on general traffic Developing degree-of-prioritybased control strategy that can provide an efficient and safetraveling environment for emergency vehicleswithminimumdisruption on network traffic is of critical importance inmanaging urban traffic

Based on the above achievements this paper presentsa dynamic preemption approach that combines a degree ofcontrol priority classification procedure and a route-basedpreemption method to provide the most appropriate routeand control strategy for an emergency vehicle under a givennetwork traffic conditions and emergency issue conditionsThe proposed method was evaluated in part of the roadsnetwork in Beijing China using a microscopic networksimulation model and its effectiveness was compared withthe existing local-detection based method

This paper is organized as follows the first part is theintroduction of emergency vehicle preemption methodsThesecond part is the model of degree of priority classificationand travel time prediction The third part is developmentof emergency vehicle preemption strategy and performanceevaluation Last part is conclusion

2 Degree-of-Priority Based Signal Preemption

Figure 1 shows the structure of the degree-of-priority basedsignal preemption strategy developed in this study Inputdata include emergency demand parameters network traf-fic parameters and network data Emergency demandparameters are obtained when emergency issue happens



calculation






Input

Main process

Output


calculation








119875119897119896 =

Log (119871119896 +119899119871(119875)

119896)

10 (1)





119880119896 = 1 minussum119895

119899=1(119871119896119899V119898119899)

119879119905

(2)







108060402

0

Deg

ree o

f mem

bers

hip

0908070605040302010

VLLM

HVH


108060402

0

Deg

ree o

f mem

bers

hip


VLLM

HVH


108060402

00 20 40 60 80 100 120

Road grade

Deg

ree o

f mem

bers

hip

VLLM

HVH


08060402

0


egre

e of m

embe

rshi

p10908070605040302010

VLLM

HVH
















119880119896

119868pd



119909119895119868pi



119868pd119863119901



119899119896 =119881119896119871119896

119873119896V119896 (3)



1198991015840

119896= 120573120583119871119896

119873119896

119881119896

(4)



119899119890119896 = max (119899119896 minus 1199051198961198991015840

119896 0) = max(

119881119896119871119896

119873119896V119896minus 119905119896120573120583119871119896

119873119896

119881119896

0)

(5)


119905119896 = 119891 (119863119901119896) (6)



119879119896 = 1198790 [1 + 119886(119881119896 (119905)

119862119896 (119905))

119887

] (7)



119879119896 =119871119896

V119890[1 + 119886(

119899119890119896119873119896119881119896

119871119896119862119896

)

119887

] (8)


119879119896 =119871119896

V119890[

[

1 + 119886(max(1198812

119896119871119896 minus Δ119905119896120573120583119873

2

119896V119896 0)

119881119896119871119896119862119896

)

119887

]

]

(9)





119879119896 =119871119896

V119890[1 + 119886(

119881119896

119862119896

)

119887

] (10)



119875119896 = 119879119896 + 120578119863119901119896 (11)









119874119896 = 119879119896 mod 119862119889119896 (12)


1015840



Δ119874119896 = 119874119896 minus 1198741015840

119896 (13)

If 119862119889119896 lt sum119896



Δ119874adj119896 =Δ119874119896

lfloorsum119896

119894=0119879119894119862119889119896rfloor

(14)








C1

C4 C5 C6

C3EV

S1

S2 S3

S7

S5 S6

S4

Star

t

Endi

ng

C2


issue


















(1) (2) (3) (4) (5)

1

2

3

4

5

1

2

3

4

5

1

2

3

4

5

1

2

3

4

5

1

2

34

5

6

67

7




(119875)

119896 70






120578

1 50 100 200S1 034 048 017 041 60 310 351 516 722 1134S2 029 039 017 039 30 267 306 461 654 1041S3 037 054 017 041 60 288 329 492 695 1102S4 017 021 017 025 30 582 607 705 828 1074S5 044 037 017 037 30 402 440 588 773 1144S6 031 025 017 025 30 431 456 556 681 931S7 044 062 017 036 30 280 317 462 643 1006







EV


(a) Sample network

T7 = 280 sDp7 = 036

Dp2 = 039 Dp3 = 041

T2 = 267 s T3 = 288 sEV

120578 = 1 50 100

(b) Route 1

Dp4 = 025

Dp2 = 039

Dp2 = 025

T2 = 267 s

T2 = 431 s

EV

T4 = 582 s

120578 = 200

(c) Route 2


7 Conclusions





Acknowledgments



References









































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











calculation






Input

Main process

Output


calculation








119875119897119896 =

Log (119871119896 +119899119871(119875)

119896)

10 (1)





119880119896 = 1 minussum119895

119899=1(119871119896119899V119898119899)

119879119905

(2)







108060402

0

Deg

ree o

f mem

bers

hip

0908070605040302010

VLLM

HVH


108060402

0

Deg

ree o

f mem

bers

hip


VLLM

HVH


108060402

00 20 40 60 80 100 120

Road grade

Deg

ree o

f mem

bers

hip

VLLM

HVH


08060402

0


egre

e of m

embe

rshi

p10908070605040302010

VLLM

HVH
















119880119896

119868pd



119909119895119868pi



119868pd119863119901



119899119896 =119881119896119871119896

119873119896V119896 (3)



1198991015840

119896= 120573120583119871119896

119873119896

119881119896

(4)



119899119890119896 = max (119899119896 minus 1199051198961198991015840

119896 0) = max(

119881119896119871119896

119873119896V119896minus 119905119896120573120583119871119896

119873119896

119881119896

0)

(5)


119905119896 = 119891 (119863119901119896) (6)



119879119896 = 1198790 [1 + 119886(119881119896 (119905)

119862119896 (119905))

119887

] (7)



119879119896 =119871119896

V119890[1 + 119886(

119899119890119896119873119896119881119896

119871119896119862119896

)

119887

] (8)


119879119896 =119871119896

V119890[

[

1 + 119886(max(1198812

119896119871119896 minus Δ119905119896120573120583119873

2

119896V119896 0)

119881119896119871119896119862119896

)

119887

]

]

(9)





119879119896 =119871119896

V119890[1 + 119886(

119881119896

119862119896

)

119887

] (10)



119875119896 = 119879119896 + 120578119863119901119896 (11)









119874119896 = 119879119896 mod 119862119889119896 (12)


1015840



Δ119874119896 = 119874119896 minus 1198741015840

119896 (13)

If 119862119889119896 lt sum119896



Δ119874adj119896 =Δ119874119896

lfloorsum119896

119894=0119879119894119862119889119896rfloor

(14)








C1

C4 C5 C6

C3EV

S1

S2 S3

S7

S5 S6

S4

Star

t

Endi

ng

C2


issue


















(1) (2) (3) (4) (5)

1

2

3

4

5

1

2

3

4

5

1

2

3

4

5

1

2

3

4

5

1

2

34

5

6

67

7




(119875)

119896 70






120578

1 50 100 200S1 034 048 017 041 60 310 351 516 722 1134S2 029 039 017 039 30 267 306 461 654 1041S3 037 054 017 041 60 288 329 492 695 1102S4 017 021 017 025 30 582 607 705 828 1074S5 044 037 017 037 30 402 440 588 773 1144S6 031 025 017 025 30 431 456 556 681 931S7 044 062 017 036 30 280 317 462 643 1006







EV


(a) Sample network

T7 = 280 sDp7 = 036

Dp2 = 039 Dp3 = 041

T2 = 267 s T3 = 288 sEV

120578 = 1 50 100

(b) Route 1

Dp4 = 025

Dp2 = 039

Dp2 = 025

T2 = 267 s

T2 = 431 s

EV

T4 = 582 s

120578 = 200

(c) Route 2


7 Conclusions





Acknowledgments



References









































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











108060402

0

Deg

ree o

f mem

bers

hip

0908070605040302010

VLLM

HVH


108060402

0

Deg

ree o

f mem

bers

hip


VLLM

HVH


108060402

00 20 40 60 80 100 120

Road grade

Deg

ree o

f mem

bers

hip

VLLM

HVH


08060402

0


egre

e of m

embe

rshi

p10908070605040302010

VLLM

HVH
















119880119896

119868pd



119909119895119868pi



119868pd119863119901



119899119896 =119881119896119871119896

119873119896V119896 (3)



1198991015840

119896= 120573120583119871119896

119873119896

119881119896

(4)



119899119890119896 = max (119899119896 minus 1199051198961198991015840

119896 0) = max(

119881119896119871119896

119873119896V119896minus 119905119896120573120583119871119896

119873119896

119881119896

0)

(5)


119905119896 = 119891 (119863119901119896) (6)



119879119896 = 1198790 [1 + 119886(119881119896 (119905)

119862119896 (119905))

119887

] (7)



119879119896 =119871119896

V119890[1 + 119886(

119899119890119896119873119896119881119896

119871119896119862119896

)

119887

] (8)


119879119896 =119871119896

V119890[

[

1 + 119886(max(1198812

119896119871119896 minus Δ119905119896120573120583119873

2

119896V119896 0)

119881119896119871119896119862119896

)

119887

]

]

(9)





119879119896 =119871119896

V119890[1 + 119886(

119881119896

119862119896

)

119887

] (10)



119875119896 = 119879119896 + 120578119863119901119896 (11)









119874119896 = 119879119896 mod 119862119889119896 (12)


1015840



Δ119874119896 = 119874119896 minus 1198741015840

119896 (13)

If 119862119889119896 lt sum119896



Δ119874adj119896 =Δ119874119896

lfloorsum119896

119894=0119879119894119862119889119896rfloor

(14)








C1

C4 C5 C6

C3EV

S1

S2 S3

S7

S5 S6

S4

Star

t

Endi

ng

C2


issue


















(1) (2) (3) (4) (5)

1

2

3

4

5

1

2

3

4

5

1

2

3

4

5

1

2

3

4

5

1

2

34

5

6

67

7




(119875)

119896 70






120578

1 50 100 200S1 034 048 017 041 60 310 351 516 722 1134S2 029 039 017 039 30 267 306 461 654 1041S3 037 054 017 041 60 288 329 492 695 1102S4 017 021 017 025 30 582 607 705 828 1074S5 044 037 017 037 30 402 440 588 773 1144S6 031 025 017 025 30 431 456 556 681 931S7 044 062 017 036 30 280 317 462 643 1006







EV


(a) Sample network

T7 = 280 sDp7 = 036

Dp2 = 039 Dp3 = 041

T2 = 267 s T3 = 288 sEV

120578 = 1 50 100

(b) Route 1

Dp4 = 025

Dp2 = 039

Dp2 = 025

T2 = 267 s

T2 = 431 s

EV

T4 = 582 s

120578 = 200

(c) Route 2


7 Conclusions





Acknowledgments



References









































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












119880119896

119868pd



119909119895119868pi



119868pd119863119901



119899119896 =119881119896119871119896

119873119896V119896 (3)



1198991015840

119896= 120573120583119871119896

119873119896

119881119896

(4)



119899119890119896 = max (119899119896 minus 1199051198961198991015840

119896 0) = max(

119881119896119871119896

119873119896V119896minus 119905119896120573120583119871119896

119873119896

119881119896

0)

(5)


119905119896 = 119891 (119863119901119896) (6)



119879119896 = 1198790 [1 + 119886(119881119896 (119905)

119862119896 (119905))

119887

] (7)



119879119896 =119871119896

V119890[1 + 119886(

119899119890119896119873119896119881119896

119871119896119862119896

)

119887

] (8)


119879119896 =119871119896

V119890[

[

1 + 119886(max(1198812

119896119871119896 minus Δ119905119896120573120583119873

2

119896V119896 0)

119881119896119871119896119862119896

)

119887

]

]

(9)





119879119896 =119871119896

V119890[1 + 119886(

119881119896

119862119896

)

119887

] (10)



119875119896 = 119879119896 + 120578119863119901119896 (11)









119874119896 = 119879119896 mod 119862119889119896 (12)


1015840



Δ119874119896 = 119874119896 minus 1198741015840

119896 (13)

If 119862119889119896 lt sum119896



Δ119874adj119896 =Δ119874119896

lfloorsum119896

119894=0119879119894119862119889119896rfloor

(14)








C1

C4 C5 C6

C3EV

S1

S2 S3

S7

S5 S6

S4

Star

t

Endi

ng

C2


issue


















(1) (2) (3) (4) (5)

1

2

3

4

5

1

2

3

4

5

1

2

3

4

5

1

2

3

4

5

1

2

34

5

6

67

7




(119875)

119896 70






120578

1 50 100 200S1 034 048 017 041 60 310 351 516 722 1134S2 029 039 017 039 30 267 306 461 654 1041S3 037 054 017 041 60 288 329 492 695 1102S4 017 021 017 025 30 582 607 705 828 1074S5 044 037 017 037 30 402 440 588 773 1144S6 031 025 017 025 30 431 456 556 681 931S7 044 062 017 036 30 280 317 462 643 1006







EV


(a) Sample network

T7 = 280 sDp7 = 036

Dp2 = 039 Dp3 = 041

T2 = 267 s T3 = 288 sEV

120578 = 1 50 100

(b) Route 1

Dp4 = 025

Dp2 = 039

Dp2 = 025

T2 = 267 s

T2 = 431 s

EV

T4 = 582 s

120578 = 200

(c) Route 2


7 Conclusions





Acknowledgments



References









































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












119879119896 =119871119896

V119890[1 + 119886(

119881119896

119862119896

)

119887

] (10)



119875119896 = 119879119896 + 120578119863119901119896 (11)









119874119896 = 119879119896 mod 119862119889119896 (12)


1015840



Δ119874119896 = 119874119896 minus 1198741015840

119896 (13)

If 119862119889119896 lt sum119896



Δ119874adj119896 =Δ119874119896

lfloorsum119896

119894=0119879119894119862119889119896rfloor

(14)








C1

C4 C5 C6

C3EV

S1

S2 S3

S7

S5 S6

S4

Star

t

Endi

ng

C2


issue


















(1) (2) (3) (4) (5)

1

2

3

4

5

1

2

3

4

5

1

2

3

4

5

1

2

3

4

5

1

2

34

5

6

67

7




(119875)

119896 70






120578

1 50 100 200S1 034 048 017 041 60 310 351 516 722 1134S2 029 039 017 039 30 267 306 461 654 1041S3 037 054 017 041 60 288 329 492 695 1102S4 017 021 017 025 30 582 607 705 828 1074S5 044 037 017 037 30 402 440 588 773 1144S6 031 025 017 025 30 431 456 556 681 931S7 044 062 017 036 30 280 317 462 643 1006







EV


(a) Sample network

T7 = 280 sDp7 = 036

Dp2 = 039 Dp3 = 041

T2 = 267 s T3 = 288 sEV

120578 = 1 50 100

(b) Route 1

Dp4 = 025

Dp2 = 039

Dp2 = 025

T2 = 267 s

T2 = 431 s

EV

T4 = 582 s

120578 = 200

(c) Route 2


7 Conclusions





Acknowledgments



References









































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










C1

C4 C5 C6

C3EV

S1

S2 S3

S7

S5 S6

S4

Star

t

Endi

ng

C2


issue


















(1) (2) (3) (4) (5)

1

2

3

4

5

1

2

3

4

5

1

2

3

4

5

1

2

3

4

5

1

2

34

5

6

67

7




(119875)

119896 70






120578

1 50 100 200S1 034 048 017 041 60 310 351 516 722 1134S2 029 039 017 039 30 267 306 461 654 1041S3 037 054 017 041 60 288 329 492 695 1102S4 017 021 017 025 30 582 607 705 828 1074S5 044 037 017 037 30 402 440 588 773 1144S6 031 025 017 025 30 431 456 556 681 931S7 044 062 017 036 30 280 317 462 643 1006







EV


(a) Sample network

T7 = 280 sDp7 = 036

Dp2 = 039 Dp3 = 041

T2 = 267 s T3 = 288 sEV

120578 = 1 50 100

(b) Route 1

Dp4 = 025

Dp2 = 039

Dp2 = 025

T2 = 267 s

T2 = 431 s

EV

T4 = 582 s

120578 = 200

(c) Route 2


7 Conclusions





Acknowledgments



References









































Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















(1) (2) (3) (4) (5)

1

2

3

4

5

1

2

3

4

5

1

2

3

4

5

1

2

3

4

5

1

2

34

5

6

67

7




(119875)

119896 70






120578

1 50 100 200S1 034 048 017 041 60 310 351 516 722 1134S2 029 039 017 039 30 267 306 461 654 1041S3 037 054 017 041 60 288 329 492 695 1102S4 017 021 017 025 30 582 607 705 828 1074S5 044 037 017 037 30 402 440 588 773 1144S6 031 025 017 025 30 431 456 556 681 931S7 044 062 017 036 30 280 317 462 643 1006







EV


(a) Sample network

T7 = 280 sDp7 = 036

Dp2 = 039 Dp3 = 041

T2 = 267 s T3 = 288 sEV

120578 = 1 50 100

(b) Route 1

Dp4 = 025

Dp2 = 039

Dp2 = 025

T2 = 267 s

T2 = 431 s

EV

T4 = 582 s

120578 = 200

(c) Route 2


7 Conclusions





Acknowledgments



References









































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










EV


(a) Sample network

T7 = 280 sDp7 = 036

Dp2 = 039 Dp3 = 041

T2 = 267 s T3 = 288 sEV

120578 = 1 50 100

(b) Route 1

Dp4 = 025

Dp2 = 039

Dp2 = 025

T2 = 267 s

T2 = 431 s

EV

T4 = 582 s

120578 = 200

(c) Route 2


7 Conclusions





Acknowledgments



References









































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










References









































Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









Research Article Development of Degree-of-Priority...

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