PREDICTION OF TOOL WEAR USING ARTIFICIAL NEURAL NETWORK IN TURNING OF MILD STEEL
Minor Transport
1. 4/28/2015
Transportation Engineering | Jamie Arnold, Mustafa Cakalci, Luke
Dujmovic
UNIVERSITY
OF SOUTH
AUSTRALIA
COLLECTION AND ANALYSIS OF DETAILED
TRAFFIC DATA
2. Introduction
In trafficmanagementanddesign,the mostessentialinformationinatrafficstreamis the
knowledge anddistributionof arrival patternsandheadways.Thisisparticularlynecessaryfor
roundabouts,uncontrolledintersections suchasSTOPand GIVE WAY, T junctions,parkinglot
entrancesandexitsetc.
The aim of thisanalysisisto collectdataon a low-mediumvolume road,thisdatawill include
informationonthe headwaysandarrival timesof vehiclestravellinginaone-waytrafficstreamin
the same direction.Thenusingtheoretical modellingsuchasPoissondistributionandthe negative
exponential model,fitthatdata intoa theoretical model.
Once the data has beenmodelled,we canthenuse the datato estimate delaysandthe road
absorptioncapacity.
The experimentprocedure will involve atthe same time,recordingtimesatwhich121 consecutive
vehiclespassafixedpointbythe roadand countingthe numberof vehiclespassingafixedpoint
using10 secondintervals.
The site locationwill needtobe 300m away fromany intersectionthatcanaffectthe flow of traffic;
thusthe areathat has beendecidedisChandlersHill roadinHappyValley(refertoFigure 1).Forthe
modellingmethodstowork,anacceptable optimumvolume between200-400veh/hrisnecessary.
Figure 1: Chandlers Hill Road Street View (GoogleMaps)
3. Suburb: Happy Valley Tuesday 14/4/2014 14:00 Road: Chandlers Hill road
AnalysisLocation
Figure 2: Focus Area for Traffic Analysis (GoogleMaps)
4. 1) Headways
Headwaycan be definedasthe time betweenthe same points(typicallythe frontof the vehicle) of a
vehicle thatpassesagivenlocationonthe road.
For thisanalysisthe vehicleheadwaysare basedonrandom arrivals,where the distributionof
headwaysina trafficstreakismodelledaccordingto apatternof vehicle arrivals.Inotherwords,
there will be atrendwhere the numberof vehicleswill decrease exponentiallyasthe headway
increases;thisisknown asthe negative exponentialfunction.
To theoreticallycalculate the probabilitythatthe headwaywillexceedatime t,the following
formulawill be usedwhere q istrafficvolume inveh/s(Figure2).
The negative exponential headwaydistributionisderivedfromthe assumptionof randomarrivalsof
vehicles,itsapplicabilityisrestrictedtolightertrafficflows ( maximumof 600 veh/hr),where there
are fewvehicle interactionstoinfluencethe travel behaviourof anyindividualvehicle.Further,it
appliesonlytouninterrupted flow;thisanalysiswasconductedata minimumof 300m away from
any intersectionthatwouldinterrupttrafficflow. Finally,the negative exponential distribution
allowsheadwaysrightdowntozerodurationandtherefore cannotcorrectlyrepresentanysituation
inwhichthe minimumfeasible headwayisgreaterthanzero,suchas trafficflow ina single lane.
(Erceg,John,pg17)
Where vehicle arrivalsare essentiallyrandombutthe minimumpossibleheadwayisgreaterthan
zero(whichwouldapplytothissectionof chandlershill road),the displacednegative exponential
distribution isanappropriate representationof headways.Asillustratedby Figure 6,the trendhas
the same shape as the negative exponential butisdisplacedtothe rightby an interval β, equal to
the minimumpossible headway.(Erceg,John,pg18) Asthe negative exponential formuladoesnot
include thisinterval,we will notuse forourtheoretical values.
Figure 3: Random Traffic Formula for Probability of Headways (Erceg, John, pg 16)
Figure 4: Displaced Negative Exponential Function trend
7. (b) Findthe proportionofheadwaysexceeding 4 secondsand the proportionexceeding 8 seconds.
Table 3: Proportion of Headways according to traffic data
c) Comparethese proportionswiththe theoretical proportionspredictedby the Random Traffic
Model1 with the same trafficvolume,(i.e. volumeq givenby q = 120/(t121 - t1) where ti is the
arrival time for the ith vehicle).
If q = 120/ (t121 - t1)
T121-T1 = 1209 seconds= 0.34 hours
q = 120/0.34 = 357veh/hr = 0.099veh/s
Therefore usingthe formulafrom Figure 2:
Table 4: Probability of Headways (Random Traffic Model)
Tables3 and 4 highlightthe percentagesof whichthe headwaysexceed4and 8 seconds,when
comparingthemtheyhave the same trend,which istheybothdecrease asthe headwaytime
increases. Howeverthe probabilitiesforTable 4,basedonthe random trafficmodel,are notas
precise as the actual proportioninTable 3.
It shouldbe importanttonote that there are more functionsforanalysingheadwaysthanjustthe
negative exponentialmodel.The shifting negativeandthe bunched exponential modelsare usedfor
headwayinvestigations;currentlythe mostcommonlyusedrandomtrafficmodelisthe negative
exponential function(Akçelik & Chung , pg3).
Thismodel forrandomtrafficignoresthe minimumarrival headway(∆) andproportionof free
vehiclesinatrafficstream(φ),the negative exponential functionisasimple functionasitignores
these parameters,thiscouldtherefore explainthe difference whencomparingthe proportionsin
Table 3 and4.
Proportion of Headways Number of Cars Proportion
Exceeding 4 secs 101 83.50%
Exceeding 8 secs 64 52.90%
Random Traffic Model Probability Number of Cars
Exceeding 4 secs 67.30% 82
Exceeding 8 secs 45.30% 55
8. The displacednegativeexponentialfunctioncouldhave beenusedforthe bunchedmodel to
determine the displacement/the minimumarrival headwaytime.
It wouldhave beeninterestingtosee if the proportionsfromTable 3matchedthe probabilitiesfrom
the bunchedmodel. If forexample we introducedavalue for∆ and φ to be 1.5 secondsand0.9
respectively,we wouldobtainanewvalue basedonthe bunched model (Figure 5),usingthe values
basedon the data fromTable 4, we wouldhave animprovementonthe probabilitybyaround5-7%.
The bunched methodisnotas common,howeveritisconsideredtobe more accurate than the
othertwo exponentialmodels.(Akçelik & Chung , pg23). Considerthe bunchedexponential
functionforan analysismethodasitisfoundto be more accurate but it still needstobe introduced
withinthe lowflowrate proportions(Maximum600veh/h).
As the analysiswasconductedonsite withonlyatimer,itis possible thatsome headwaytimesare
not accurate inregardsto the pointof the vehicle passingthe same location;itisbasedonhuman
observationthough itwouldhave onlyinfluencedthe resultbyaminorpercentage.
In the future toget a precise result,itcouldbe possibletointroduce some technologythatmeasures
headwaysaccurately.
10. Poisson Distribution
To findthe expectedfrequenciesof the vehiclecountsbasedonthe trafficvolumes,we needto
determine the probabilitiesof x vehiclesarrivinginagiventime interval t. Consideringourcase
where ourtrafficisin a one-waystream, the probabilityof numberof vehiclesarrive inatime
interval canbe predictedusingthe followingformula.
Justlike ourtrafficdata we will use a time interval of 10 secondsand a trafficvolume of 357veh/hr,
the numberof vehiclesarrivingwill be measureduptoa maximumof 5.
Probability of Vehicles Occurring in Time Interval (%)
Number of Vehicles Occurring
Time Interval 0 1 2 3 4 5
10 37.16 36.79 18.21 6.01 1.49 0.29
Table 6: Theoretical Probabilities of Vehicles
As we have a probabilityof vehiclesarrivalsinaninterval we cannow multiplythisby the traffic
volume overthe 30 minsto obtainan expectedfrequencyof vehicles.
Range (Vehicle Number) Frequency (Number of Vehicles)
0 66
1 66
2 33
3 11
4 3
5 1
Table 7: Expected Frequencies of Arrivals based on Traffic Volume over 30mins
Table 8: Observed Frequencies of Arrivals based on traffic volume over 30 mins
Range (Vehicle Number) Frequency (Number of Vehicles)
0 70
1 64
2 23
3 16
4 4
5 3
Figure 6: Probability formula of vehicle arrivals in a time interval
13. X² Goodness of fit comparison
Whenwe attemptto fita statistical model toobserveddata,we shouldconsiderhow wellthe model
fitsthe data. One statistical testthataddressesthisissue isthe chi-square goodnessof fittest.The
chi- square testis of the form (http://www.stat.yale.edu)
We musthypothesisethatthe expectedtrafficnumbersbasedonthe probabilitiesdetermined from
Poisson’sdistributionare correctandconformto the observedvalues.
Number of Vehicles Expected Number Observed Number Difference
0 66 70 4
1 66 64 -2
2 33 23 -10
3 11 16 5
4 3 4 1
5 1 3 2
Table 9: Expected vs. Observed Frequencies
Chi SquaresValue = X²= ∑
16
66
+
4
66
+
100
33
+
25
11
+
1
3
+
4
1
= 9.93
We will use analphafactor or significance level of 5% / ɑ=0.05.
The degreesof freedomare equal tothe numberof vehicles, k, minus1;inthiscase the numberof
vehicle numberisequal to6, therefore the degree of freedomisequal to5.
Usingfigure 8 below,the correspondingcritical chi squared value for5degreesof freedomanda
significance level of 0.05 isequal to 11.07. As the critical value ismore extreme thanthe chi squared
value (11.07>9.93), we can accept the hypothesisthatthe observeddatafitsthe expectedmodel.
Figure 10: Chi-Square test formula
Figure 11: Chi Square distribution table
15. Table 11- Proportion of all Pedestrians times (Delay or No Delay)
Pedestrian Number Pedestrian Arrival Times Delay or No Delay
1 32 Delay
2 62 No Delay
3 93 No Delay
4 123 No Delay
5 153 No Delay
6 183 Delay
7 214 No Delay
8 244 Delay
9 274 No Delay
10 304 No Delay
11 334 No Delay
12 365 No Delay
13 395 No Delay
14 425 Delay
15 455 No Delay
16 486 Delay
17 516 Delay
18 546 Delay
19 576 Delay
20 606 No Delay
21 637 No Delay
22 667 Delay
23 697 Delay
24 727 Delay
25 758 No Delay
26 788 No Delay
27 818 No Delay
28 848 No Delay
29 879 Delay
30 909 No Delay
31 939 No Delay
32 969 No Delay
33 999 Delay
34 1030 No Delay
35 1060 No Delay
36 1090 No Delay
37 1120 Delay
38 1151 Delay
39 1181 No Delay
40 1211 Delay
16. To findthe proportionof pedestrianswhowouldnothave towaitto cross the road, we needto
determine the numberof pedestrianswhichhave experienced nodelays,refertoTable 10 and 11,
we compare the pedestrianarrival time withthatof the arrival timesinthe majortraffic stream.If
the pedestrianhasa suitable gaptocross (5 secondsbetweenvehiclesinthe majortrafficstream),
thentheysuffernodelay;theywill be delayedif the time betweenvehiclesinthe majortraffic
streamis lessthan5.
There are 24 pedestriansthatexperience nodelay,the total numberof pedestrian’s amountto40.
The proportions of pedestriansthatsuffernodelayare:
𝑃𝑟𝑜𝑝𝑜𝑟𝑡𝑖𝑜𝑛 (𝑁𝑜𝑡 𝐷𝑒𝑙𝑎𝑦𝑒𝑑) =
24
40
= 0.60%
At the pointonthe road,if 40 pedestrianswishedtocrossthe road, 60% of themwill sufferno
waitingtime betweenvehiclesinthe majortrafficstream.
Pedestrian Number Pedestrian Arrival Times Delay or No Delay Waiting Time (seconds)
1 32 Delay 7
6 183 Delay 1
8 244 Delay 4
14 425 Delay 1
16 486 Delay 4
17 516 Delay 20
18 546 Delay 4
19 576 Delay 1
22 667 Delay 1
23 697 Delay 1
24 727 Delay 9
29 879 Delay 2
33 999 Delay 3
37 1120 Delay 3
38 1151 Delay 1
40 1211 Delay 1
Cumulative Waiting time = 63 seconds
Table 12- The mean waiting time for Pedestrians that are experiencing delays
The mean waitingtime forthe pedestrians, whohave experienceddelays,iscalculatedbydividing
the cumulative waitingtime bythe numberof pedestriansdelayed.
The total waitingtime (Refertotable 12) = 63 Seconds,
the numberof pedestrianswhohas experienceddelays=16
𝑀𝑒𝑎𝑛 𝑊𝑎𝑖𝑡𝑖𝑛𝑔 𝑇𝑖𝑚𝑒 (𝐷𝑒𝑙𝑎𝑦𝑒𝑑 𝑃𝑒𝑑𝑒𝑠𝑡𝑟𝑖𝑎𝑛𝑠) =
63
16
= 3.9 𝑠𝑒𝑐𝑜𝑛𝑑𝑠
For 40 pedestriansof whom16 are delayed,the meanwaitingtime is3.9seconds.
18. The mean waitingtime forall pedestrians includingthose whohave andhave notexperienced
delays,iscalculatedbythe total waitingtime overthe numberof pedestrians. The total waitingtime
(Refertotable 13) = 63 Seconds,andthere are 40 pedestrians.
𝑀𝑒𝑎𝑛 𝑊𝑎𝑖𝑡𝑖𝑛𝑔 𝑡𝑖𝑚𝑒 𝑓𝑜𝑟 𝑎𝑙𝑙 𝑝𝑒𝑑𝑒𝑠𝑡𝑟𝑖𝑎𝑛𝑠 =
63
40
= 1.58 𝑠𝑒𝑐𝑜𝑛𝑑𝑠
Theoretical Methods
Proportion Delayed
= 1 − 𝑒−𝑞𝑇
Where:
q = the volume of the conflictingmajortrafficstream, inveh/s,and
T = the size of the critical gap(or critical lag),ins/veh
𝑞 =
120
(𝑡121 − 𝑡1)
We know that ( 𝑡121 − 𝑡1) = 1209 𝑠𝑒𝑐𝑜𝑛𝑑𝑠 𝑤ℎ𝑖𝑐ℎ 𝑖𝑠
1209
3600
= 0.34 ℎ𝑜𝑢𝑟𝑠
𝑞 =
120
0.34
=
357𝑣𝑒ℎ
ℎ𝑟
= 0.099 𝑣𝑒ℎ/𝑠
Where:
q = 0.099 veh/s
Tc= 5 seconds
Therefore, Proportion Delayed = 1 − 𝑒(−0.099∗5)
= 0.39%
Therefore = 39% 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑒𝑑𝑒𝑠𝑡𝑟𝑖𝑎𝑛𝑠 𝑎𝑟𝑒 𝑑𝑒𝑙𝑎𝑦𝑒𝑑
Which means proportion that is not delayed = 1 − 0.39 = 0.61%
The proportion of pedestriansthatare notdelayed usingthe formulaabove equatesto61%. The
observedproportionthatwasnotdelayed were 60%,comparingthiswiththe theoretical value of
61% showshighaccuracy withour results.Howeveritis importanttonote that there wasan
assumptionmade withsome of the pedestriantimes.Forexample,referringtoTables10 and11, we
can observe thatvehicle 40arrivesat the same time aspedestrian14,is thispedestriandelayed?
Well if a pedestriancrossingisnotpresentthenwe canassume thatthe vehicle hasthe rightof way;
therefore the pedestrianwill have towaitforthatvehicle topassthem.To be conservative aone
19. seconddelaywasthenappliedtoall pedestriansthatarrivedatthe same time as a vehicle,this
happenedinmultiple cases,e.g.pedestrians6,19, 22 and 38.
Alternativelyif these pedestrianstookthe chance tocross at the same time,apart fromgettinghit
by a car, theywouldsuffernodelay,thisinturnwouldmake ourproportionof passengersthatare
not delayedincrease.
Average Waiting time Delayed
As minorroadvehiclesorpedestriansarrivedrandomly,some mayexperience delayandsome not.
The average delayforthose actuallydelayedvehiclesorpedestrianscanbe predictedby relationship
below.
𝑊𝑑 =
1
𝑞𝑒(−𝑞𝑇𝑐) −
𝑇𝑐
1 − 𝑒(−𝑞𝑇𝑐)
Where:
Wh – The average delayforall
q- Trafficflowrate of the majorroad
Tc- Critical gaprequiredbyminorroad vehicle orpedestrians
q = 0.099 veh/s
Tc= 5 seconds
∴ 𝑊𝑑 =
1
0.099∗ 𝑒(−0.099∗5) −
5
1 − 𝑒(−0.099∗5) = 3.8 𝑠𝑒𝑐𝑜𝑛𝑑𝑠
From the above equation ourtheoretical result forthe meantime of delayedvehiclesis3.8 seconds.
Our observedresultforthe delayedvehicleswas 3.9 seconds, thispotentiallyshowsthatthe
formulaabove whichisbasedonAdam’sdelayequationcomplywithourobservedresults.This
randomtrafficmodel equationhasbeenrefinedtoavalue thatis precise toalmostthe 100th
value.
Againrelatingbackto the pedestrianarrivalsatthe same time asthe vehicles,the meanwaiting
time forthe delayedpedestrianscouldhave differedbysome margin.
20. Isolated Minor Road Delay (Adams’ delay equation)
The average delayat stopline (forall vehiclesfromminorroador all pedestrians) isgivenbythe
equationbelow.
𝑊ℎ =
1
𝑞𝑒(−𝑞𝑇𝑐) −
1
𝑞
− 𝑇𝑐
Where:
q = 0.099 veh/s
Tc= 5 seconds
𝑊ℎ =
1
0.099 ∗ 𝑒(−0.099∗5) −
1
0.099
− 5 = 1.47 𝑠𝑒𝑐𝑜𝑛𝑑𝑠
Basedon Adam’s Delayequation the average minorroaddelayhasa resultof 1.47 seconds. The
observed resultwas 1.58 seconds.AgainAdam’sdelayequationshowshighaccuracybasedon our
observeddata.Asthese resultswere compiledon onlyone dayforone hour, itwouldbe interesting
to see howaccurate thisequationisbasedondifferentdaysanddifferenthours,thisisassuming
that the volume still remainswithinthe optimumrange of 200-400 veh/hr.
the highprecisionof ourresultscouldalsobe explainedbyourtrafficvolume.Aspreviously
mentionedthe randomtrafficmodelisusedbestwhenthe maximumvehicle countdoesnotexceed
600veh/hr,also the optimumrange forthe random trafficmodel is200-400 veh/hr,asour volume
on ChandlersHill roadis357 veh/hr,itcouldbe safe to say our volume fitsinthe optimumrange.
21. 4) AbsorptionCapacity
Vehicle Number Vehicle Arrival Times Delay or No Delay
1 32 Delay
2 62 No Delay
3 93 No Delay
4 123 No Delay
5 153 No Delay
6 183 Delay
7 214 No Delay
8 244 Delay
9 274 No Delay
10 304 No Delay
11 334 No Delay
12 365 No Delay
13 395 No Delay
14 425 Delay
15 455 No Delay
16 486 Delay
17 516 Delay
18 546 Delay
19 576 Delay
20 606 No Delay
21 637 No Delay
22 667 Delay
23 697 Delay
24 727 Delay
25 758 No Delay
26 788 No Delay
27 818 No Delay
28 848 No Delay
29 879 Delay
30 909 No Delay
31 939 No Delay
32 969 No Delay
33 999 Delay
34 1030 No Delay
35 1060 No Delay
36 1090 No Delay
37 1120 Delay
38 1151 Delay
39 1181 No Delay
40 1211 Delay
Table 14: Vehicle arrival times for a limited arrival situation
22. Limited Arrivals
The table above illustratesthe arrival timesforall vehiclesinaminortrafficstream, like the
pedestrianarrivalsinTable 11theyarrive at the same time andwish to performa LEFT turn in5
seconds.Asthere isonlylimitedarrivalsthere will be no follow uptime forthe vehicles.
For the situationof limitedarrivals,the numberof vehiclesexperiencingnodelayfor5secondgaps,
N,is 24 vehicles.The value forTisfoundas,T = (t121-t1) whichisto 1209 seconds.
Therefore the total absorptioncapacityof the roadis;
𝑁
𝑇
=
24
1209
= 0.020 Vehicles per second.
Therefore toconvertabsorptioncapacitytovehiclesperhour,absorptioncapacityismultipliedby
3600. For a situationinwhichthere are limitedvehicles, the roadhasan absorptioncapacityof
0.020 ∗ 3600 = 72 Vehiclesperhour.
24. Infinite Arrivals
If we consideredaninfinitenumberof arrivals,thenthe numberof vehicleswishingtoturnwouldbe
the amountof time necessarytocomplete thatturnvs.the gap acceptance in the majortraffic
stream.Whenthere isan unlimitedamountof vehiclesinaqueue thenitwill be necessaryto
considera followuptime,whichisthe amountof time betweenavehicleturningandthe nextcarin
the queue beingable tocomplete the turn.Forthiswe will consideracritical gap time of 5 seconds
and a followuptime of 2 seconds.
Table 15 highlightsthe numberof vehiclesthatcan turnwithinaninfinite numberof arrivals.If there
islessthan a 7 secondgapin the majortrafficstreamthenno vehiclesfromthe minortrafficstream
will completethe turn.Underan infinitenumberof arrivals, the numberof vehiclesthatcanturn is
foundto be 127.
Therefore the observed absorption capacity under the infinite arrivals conditions is found to be;
𝑁
𝑇
=
127
1209
= 0.105 Vehicles per second.
To convertthe observedabsorptioncapacitytovehiclesperhour,absorptioncapacityismultiplied
by 3600.
Therefore forinfinite arrivals, the roadhasan observedabsorptioncapacityof 0.105 ∗ 3600 = 378
vehiclesperhour.
Theoretical Absorption Capacity
The theoretical absorptioncapacityisfoundbyusingthe followingformula;
𝐶 =
𝑞 ∗ 𝑒−𝑞∗𝑇
1 − 𝑒−𝑞∗𝑇0
Where,q= volume of the conflictingmajortrafficstream(veh/s)
T = the size of the critical gap (s/veh)
𝑇0 = the follow-upheadway(s/veh)
C = the theoretical absorptioncapacity(veh/s)
Therefore, q= 0.099 veh/s,T= 5 s/veh, 𝑇0 = 2 s/veh
𝐶 =
0.099∗𝑒−0.099∗5
1−𝑒−0.099∗2
= 0.334 Vehicles per second.
Therefore theoretical absorptioncapacityforthe infinite arrival situationis 0.334 ∗ 3600 =
1209 vehiclesperhour.
The practical absorptioncapacityis 𝐶 𝑝 = 0.8𝐶 = 0.8 ∗ 1209 = 968 Vehiclesperhour.
There appearsto be a high difference betweenthe resultsof the observedandthe theoretical data.
An explanationforthiscanbe providedbyhighlightingthatthe absorption capacityformulaappears
to have a lineartrend,the followuptime andcritical gaptime remainthe same.
25. If we putthisintoa realisticsituationthe critical gaptime andfollow uptime willnotbe the same
for the everydeparture.Forexampleanoldwomanmaybe at a T-junction,she hasa gap time of 9
secondsinthe major trafficstreambetweenthe carthatjust passedandthe nextcar, howevershe
decidednottotake the turn as she doesn’tbelieve she hasenoughtime.Suchsituationslike thiscan
occur whenthere isinfinitearrivals.The theoretical model assumesthatinaninfinite arrival
situationthatthe queue of cars will departina repeatingmanner.
Conclusion
The aim of thisanalysiswasto collecttrafficdataand use the data to estimate delaysandmajor
road absorptioncapacity.Usingthe randomtrafficmodel,the datawas comparedwithwhatwere
predictedusingtheoretical methods.
ChandlersHill roadwasconsideredasuitable roadforthisanalysisasthe volume waswithinan
optimumrange of the random trafficmodel.Usingseveral formulasbasedonthe randomtraffic
model suchas the negative exponentialfunction,Adam’sformulaandabsorptioncapacity,the data
that wascollectedfromthe roadwas comparedwiththese theoretical values.
The theoretical valuesthatwere obtainedfromthe modelsandfunctionsalignedwiththe observed
valuesquite well.Animportantnote totake awayfromthisanalysisisthatthe currentmethodsfor
calculatingtrafficmovementandengineeringconceptsthatare inplace complywithobserveddata
can model several trafficconditions.
Some methodssuchas the negative exponentialmethodcanbe refinedtoobtainvaluesthatsuite a
certaintrafficsituation.Byincludingadditional valuesorfactorswithinthe formulathe datacan be
predictedmore accurately.
There can be some small errorsthat can occur withintrafficmanagementmethods,forexample
comparingthe vehicles/pedestriansthatsufferdelayandnondelaycanbe quite complicatedif they
arrive at the same time as a vehicle passingfromthe majortrafficstream. Observational datacan
alsobe inaccurate andtechnologyisa muchmore viable meansof verifyingtrafficdata.
The predicteddatafrom the randomtrafficmodel canbe quite useful indeterminingthe necessary
trafficmanagementsolutionforaspecificsituation, forexample,stop/give waysignsandT-
junctions.If we candetermine the trafficvolume,gapacceptance androadabsorptionwe can
introduce anappropriate solution foraroad before itisintroduced.
Ultimatelythe modellingmethodsare notalwaysaccurate,howeverastransportengineering
involvesalotof planningthese methodsare suitableformodellingwhatobservational methods
cannot.
26. References
AKÇELIK,R. andCHUNG, E. (1994). Calibrationof the bunchedexponential distributionof arrival
headways. RoadandTransport Research 3 (1),pp 42-59.
Erceg, John. Guideto trafficmanagement.Sydney:Austroads, 2007, pg 14-19
Chi-Square Goodnessof FitTest.2015. Chi-Square Goodnessof FitTest.[ONLINE] Available
at: http://www.stat.yale.edu/Courses/1997-98/101/chigf.htm.[Accessed20 April 2015].
