Bus Service ReliabilityDeveloping new performance

measures

Unreliability Vs. Bus Bunching

Meead Saberi K.

meead@pdx.edu

Bus Trip AutopsyBus Trip Autopsy

Bus Trip AutopsyBus Trip AutopsyUnreliability sourcesUnreliability sources

Bus closes Bus closes the door and the door and is ready to is ready to

leaveleave

Bus stops Bus stops and opens and opens the doorthe door

Bus Bus leavesleaves

Non-stop tripNon-stop tripNon-stop tripNon-stop trip

Dwell timeDwell time Clearance timeClearance time

Delay in Delay in ArrivingArriving

Study AreaStudy Area

105 scheduled trips per weekday

64 stops

Scheduled trip times range 40-45 minutes

Scheduled headways range 3-55 minutes

Data: Tuesday, February 1, 2001

Route-Level Trip TimeRoute-Level Trip Time(inbound trip)(inbound trip)

0:20

0:30

0:40

0:50

1:00

1:10

0:00 6:00 12:00 18:00 0:00

Time of Day

Rou

te T

rave

l Tim

e (m

in)

Average trip time = 42:03

Standard deviation = 05:11

Coefficient of Variation = 0.12

90th% - 40th% (Layover) = 08:51

Route-Level Trip TimeRoute-Level Trip Time(outbound trip)(outbound trip)

0:20

0:30

0:40

0:50

1:00

1:10

0:00 6:00 12:00 18:00 0:00

Time of Day

Rou

te T

rave

l Tim

e (m

in)

Average trip time = 45:25

Standard deviation = 07:58

Coefficient of Variation = 0.17

90th% - 40th% (Layover) = 16:31

Developing New Developing New Reliability MeasuresReliability Measures

Current Reliability MeasuresCurrent Reliability MeasuresProposed by HCM and TCQSMProposed by HCM and TCQSM

On-Time PerformanceOn-Time Performance

Headway AdherenceHeadway Adherence

Stop-level Delay = Actual Arrive Time – Scheduled Arrive Time

Stop-level Delay = Actual Headway – Scheduled Headway

Current Reliability MeasuresCurrent Reliability MeasuresProposed by HCM and TCQSMProposed by HCM and TCQSM

On-Time PerformanceOn-Time Performance

Stop-level Delay = Actual Arrive Time – Scheduled Arrive Time

Current Reliability MeasuresCurrent Reliability MeasuresProposed by HCM and TCQSMProposed by HCM and TCQSM

Headway AdherenceHeadway Adherence

Stop-level Delay = Actual Headway – Scheduled Headway

Current Reliability MeasuresCurrent Reliability MeasuresProposed by HCM and TCQSMProposed by HCM and TCQSM

Why current measures, based on coefficient of variation and simply counting the number of late buses, do not tell the whole story?

Based on preliminary analysis of empirical data, delay distribution both in terms of headway for frequent services and scheduled arrival time for not frequent services is often wide and skewed specially when congestion occurs. Large delays cause “bus bunching”, no matter what the delay source is and in which link it occurs.

To find out the possible delay source(s), link level analysis should be done to find the “problem causing” link in terms of variation in travel time. A stop level analysis should also be done to measure reliability.

New Reliability New Reliability MeasureMeasure

Cumulative Frequency Distribution

0%

20%

40%

60%

80%

100%

0 100 200 300 400

Delay (sec)

Cumulative Frequency Distribution

0%

20%

40%

60%

80%

100%

-400 -300 -200 -100 0

Delay (sec)

Cumulative Frequency Distribution

0%

20%

40%

60%

80%

100%

-200 -100 0 100 200

Delay (sec)

Which distribution is ideal from the perspective of a passenger?

%100 Early%100 Early %100 Late%100 Late%50 Early & %50 %50 Early & %50 LateLate

New Reliability New Reliability MeasureMeasure

Cumulative Frequency Distribution

0%

20%

40%

60%

80%

100%

-150 -50 50 150 250

Delay (sec)

0% xthD

Earliness IndexEarliness Index

1000 x

All lateAll late

All earlyAll early

0x

100x

New Reliability New Reliability MeasureMeasure

Which distribution is ideal from the perspective of a passenger?

SlimSlim WideWideNormalNormal

Cumulative Frequency Distribution

0%

20%

40%

60%

80%

100%

-350 -150 50 250

Delay (sec)

Cumulative Frequency Distribution

0%

20%

40%

60%

80%

100%

-350 -250 -150 -50 50 150 250 350

Delay (sec)

Cumulative Frequency Distribution

0%

20%

40%

60%

80%

100%

-350 -250 -150 -50 50 150 250 350

Delay (sec)

Cumulative Frequency Distribution

0%

20%

40%

60%

80%

100%

-150 -50 50 150 250

Delay (sec)

New Reliability New Reliability MeasureMeasureWidth IndexWidth Index

%90th%90th

%10th%10th

HeadwayScheduled

DD 1090

A Real ExampleA Real Example

Width IndexWidth Index

Stop ID: Stop ID: 26092609

Earliness IndexEarliness Index

1.39%WI

For not frequent services “delay” should be usedFor not frequent services “delay” should be used

2.37%xI

0%

20%

40%

60%

80%

100%

-200 0 200 400 600

Delay (sec)

Cu

mu

lati

ve F

req

uen

cy

Average Headway = 13:30Average Headway = 13:30

Average Delay (sec) = 60Average Delay (sec) = 60

On-time Performance = %90.5On-time Performance = %90.5

LOS grade = BLOS grade = B

A Real ExampleA Real Example

Width IndexWidth Index

Stop ID: Stop ID: 26092609

Earliness IndexEarliness Index

3.81%WI

For frequent services “headway” should be usedFor frequent services “headway” should be used

6.47%xI

0.00%

20.00%

40.00%

60.00%

80.00%

100.00%

-400 -200 0 200 400 600

Headway Deviation (sec)

Cu

mu

lati

ve F

rew

uen

cy

Average Headway = 6:41Average Headway = 6:41

Average Delay (sec) = 51Average Delay (sec) = 51

Headway Adherence = Headway Adherence = 0.410.41

LOS grade = ELOS grade = E

Thank youThank you