STATISTIC METHOD IN TRAFFIC ENGINEERING

1
STATISTIC METHOD IN TRAFFIC ENGINEERING
2
INTRODUCTION

• This chapter introduces commonly-used statistical
  analysis techniques in traffic engineering.
  Because traffic engineering and traffic
  engineering studies involve collection and
  analysis of large amounts of data, it is
  important to understand some of the statistical
  theory that underlies the handling and analysis
  of such information.

3
SPOT SPEED STUDY

• Spot speed studies are conducted to estimate the
  distribution of speeds of vehicles in a stream of
  traffic at a particular location on a highway.
• A spot speed study is carried out by recording
  the speeds of a sample of vehicles at a specified
  location

4
AIM OF SPOT SPEED STUDY

• Establish parameters for traffic operation and
  control, such as speed zones, speed limits (85th
  percentile speed is commonly used as the speed
  limit on a road), and passing restrictions.
• Evaluate the effectiveness of traffic control
  devices, such as variable message signs at work
  zones.
• Monitor the effect of speed enforcement programs
  such as the use of drone radar and the use of
  differential speed limits for passenger cars and
  trucks.

5
AIM OF SPOT SPEED STUDY

• Evaluate and or determine the adequacy of highway
  geometric characteristics such as radii of
  horizontal curves and lengths of vertical curves.
• Evaluate the effect of speed on highway safety
  through the analysis of crash data for different
  speed characteristics.
• Determine speed trends.
• Determine whether complaints about speeding are
  valid.

6
DATA OF SPOT SPEED STUDY

• UNGROUPED DATA
• GROUPED DATA

7
UNGROUPED DATA

• EXAMPLE ( All Units in km/h)
• 63, 63, 55, 58, 68, 61, 68, 63, 55, 62, 72,
  57, 61, 68, 78, 64, 63, 51, 59, 75, 70, 74, 58,
  69, 65, 66, 58, 72, 74, 75, 60, 73, 69, 57, 63,
  65, 72, 59
• DETERMINE
• MEAN,MODE,MEDIAN,STANDARD DEVIATION SPEED?

8
NUMERICAL REPRESENTATION

• MEAN
• MODE
• MEDIAN
• STANDARD DEVIATION
• COEFFICIENT OF VARIATION
• P85 (ROAD SPEED LIMIT)
• P95 (ROAD DESIGN SPEED)
• P15

9
MEAN SPEED

• Average speed of all the observed vehicles
• a ? a / n
• a speed of vehicle
• n number of observation
• a 2463 / 38
• 64.816 km/h

10
MODE SPEED

• The speed that occurs most frequent
• Unimodal, distribution with one mode,
• bimodal, distribution with two mode
• 51,55,55,57,57,58,58,58,59,59,60,61,61,62,63,
• 63,63,63,63,64,65,65,66,68,68,68,69,69,70,72,
• 72,72,73,74,74,75,75,78
• MODE SPEED IS 63km/h

11
MEDIAN SPEED

• Middle speed in an ordered sequence (ascending or
  descending)
• it divides the speed data into two parts, one
  half of observed values are higher than the
  median speed and the other half are lower than
  the median speed.
• Also known as 50th percentage speed (P50)

12
MEDIAN SPEED

• First array the data in ascending or descending
• If odd number of item, choose the middle item of
  an array. If even item, the median is the average
  of 2 middle items.
• Median the (n1) / 2) th item in a data array
• 51,55,55,57,57,58,58,58,59,59,60,61,61,62,63,
• 63,63,63,63,64,65,65,66,68,68,68,69,69,70,72,
• 72,72,73,74,74,75,75,78
• MEDIAN SPEED IS 63.5 km/h

13
STANDARD DEVIATION SPEED

• Measure the dispersion or variability in the
  speed data
• if the speed data are nearly equal to each other,
  the standard deviation is close to zero otherwise
  the standard deviation will be larger than zero

14
STANDARD DEVIATION

• S v ? a2 / (n 1) ( ? a) 2 / (n (n-1))
• a speed of vehicle
• n number of observation
• S v ? a2 / (n 1) ( ? a) 2 / (n
  (n-1))
• v 161297 / (38 1) (2463) 2 / (38
  (38-1))
• v 161297 / (37) (6066369 / (38
  (37))
• v 4359.378 4314.629
• v 44.749
• 6.689 km/h

15
GROUPED DATA
16
GROUPED DATA

• Class boundary - endpoints or limits for each
• class
• 28 30 (lower class boundary 28 ,
• 30 32 upper class boundary 30)
• 28 30 (lower class boundary 27.5 ,
• 31 33 upper class boundary 30.5)

17
GROUPED DATA

• Class Interval
• Example 28 - 30
• 30 - 32
• 32 34
• Equal class interval of 2
• Example 28 30
• 31 33
• 34 36
• Equal class interval of 3

18
GROUPED DATA

• Size of class interval (C) (largest data
  smallest data) / class number
• Class limit the beginning and endpoints of the
  classes
• 28 30 (lower class limit 28 , upper class
  limit 30)
• 31 40 (lower class limit 31 , upper class
  limit 40)

19
GROUPED DATA

• Class Mark midpoint between two class
• boundaries/class limit
• Eg 28 30
• 30 40
• Class mark (28 30) /2
• 29

20
GROUPED DATA

• Let class interval is 5

21
MEAN SPEED

• Average speed of all the observed vehicles
• a ? fv / n
• f frequency of observation in group
• n number of observation
• v class mark of group
• a 53(3) 58(8) 63(11) 68(7) 73(8)
  78(1) / 38
• 2454 / 38
• 64.579 km/h

22
MODE SPEED

• First, find where mode speed class (biggest no of
  observation or frequency)
• â L C (fm fb) / (2fm (fb fa))
• L Lower class boundary
• fm No of observaton in mode speed group
• fb No of observation before mode speed group
• fa No of observation after mode speed group

23
MODE SPEED

• â L C (fm fb) / (2fm (fb fa))
• 60.5 5 (11 8) / (2(11) (8 7))
• 60.5 5 3 / (22 15)
• 60.5 5 3 / 7
• 60.5 2.143
• 62.643 km/h

24
MEDIAN SPEED

• First, find where median speed group the (n/2)
  th no of observation
• ã L ((n / 2 fL )/ fm) x C
• L Lower class boundary
• n Number of observation
• C class interval
• fL Cummulative no of observation before
• median speed group
• fm no of observaton in median speed group

25
MEDIAN SPEED

• ã L ((n / 2 fL )/ fm) x C
• 60.5 ((38 / 2 11 )/ 11) x 5
• 60.5 (8/11) x 5
• 60.5 3.636
• 64.136 km/h

26
STANDARD DEVIATION

• S v ( ? fv 2 / ? f) ( ? fv / f) 2
• f No of observation
• v Class mark
• S v ( 160082/ 38) (2454 / 38) 2
• v 4212.684 (64.579) 2
• v 4212.684 4170.447
• v 4212.684 4170.447
• v 42.237
• 6.499 km/h

27
COEFFICIENT OF VARIATION

• V S / a x 100
• S Standard deviation speed
• a Mean speed
• V 6.499 / 64.579 x 100
• 10.064

28
GRAPHICAL REPRESENTATION

• HISTOGRAM
• FREQUENCY POLYGON
• OGIVES

29

HISTOGRAM

• ? Consist of a set of joined vertical bar,
  frequency distribution (width of bar class
  width, height of barclass frequency)
• ? Used to present distribution of data speed
• ? Must have a title on the top , title for both
  axis and scaled
• Size of class interval (C) (largest data
  smallest data) / class number

30
HISTOGRAM

• HOW TO GET MODE?

31
FREQUENCY POLYGON

• A line graph of a class frequency plotted against
  class mark
• Can be obtained by connecting mid-points of the
  histogram
• It extends the curve to the midpoints of the
  lowest class (frequency zero) and the highest
  class

32
FREQUENCY POLYGON
33
OGIVES

• Also know as cumulative frequency curve
• Construction of ogive
• - compute the cumulative frequency
• distribution
• - start at zero for y-axis and lower class
• limit or class mark for x-axis
• can be used to determine percentile() P15
  15, P50 50, P85 85, P95 95

34
OGIVES
35
WHAT WE GET FROM OGIVE ?

• MEDIAN SPEED P50
• STANDARD DEVIATION
• (P85 P15) /2
• ROAD DESIGN SPEED P95
• ROAD SPEED LIMIT P85