Public Transport Capacity Analysis Procedures for Developing Cities


Appendix B - Sample Rail Operations Analysis Problems



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Appendix B - Sample Rail Operations Analysis Problems



Problem Statement
A rail transit operating agency is expecting a 40% increase in ridership over the next two years. The system is currently operating at a peak hour headway of 3 minutes. Calculate the current capacity and establish options that will increase capacity to account for this anticipated increase in ridership
Current Operating Conditions
The following are the current operating conditions:

  • Peak direction, peak hour flow = 16,000 passengers per hour

  • Peak Hour Factor = 0.75

  • Average dwell time = 30 sec.

    • Standard deviation of dwell times = 12 sec

    • Train consist – 8 cars

    • Train car length – 20 meters, 3 doors per side

    • Acceptable loading standard – 6 persons/square meter

    • Advanced signal control system with train control separation of 45 seconds


Step 1 – Computer current capacity

1.1 Compute operating margin

The operating margin is:



 = 24 sec

where,

tom = operating margin (s)
s = standard deviation of dwell times

1.2 Compute train station capacity
The train station capacity is:

where,
Tl = loading area bus capacity (bus/h)


3,600 = number of seconds in 1 hour
tcs = train control separation time (s)
td = mean dwell time (s)
tom = operating margin (s) (from task 1.1)


Calculation 1

 

 

tcs

60

td

30

tom

24

Tl (bus/h)

30

headway (sec)

120

The scheduled train frequency of 20 trains per hour is less than the line capacity of 30 trains per hour.


1.3 Estimate person capacity
The person capacity is:

where,

P = person capacity (p/h)
Pmax = maximum schedule load per traincar (see table below)

C = consist length



T = Station capacity (trains/hour)
PHF = Peak hour factor
Table 1. Rail Vehicle Capacity


Passengers/ sq.m

Rail Car Length (m) and number of doors per side

 

13

20

25

 

3

3

4

4

127

146

172

5

138

157

186

6

148

167

200

7

159

177

214

8

169

188

228




Calculation 2

Pmax

167

T

30

C

8

PHF

0.75

P

30,000

The current maximum person capacity is 30,000 passengers per hour. This is the maximum capacity if the trains were scheduled at the line’s maximum capacity of 30 trains per hour.


Step 2- Enumerate and Assess Alternatives
If the system is currently at its maximum capacity, a 40% increase in ridership will require a design for at least 22,400 passengers per hour. Four alternatives were reviewed to determine if they were feasible in increasing capacity. These included:

      1. introduce longer traincars

      2. introduce longer train consists

      3. increase the acceptable load factor

      4. reduce the headway.


Step 2.1 Assess the introduction of longer traincars
Using longer traincars (25 meter) at the current loading standard changes only Calculation 2. The existing Pmax, (maximum load per train car) is 167. If longer (25 m) train cars are introduced, Pmax will be 200.


Calculation 2

Pmax

200

T

20

C

8

PHF

0.75

P

24,000

From this chart, the person capacity at the current frequency of 20 trains per hour is 24,000 passengers per hour. This increased capacity will be able to accommodate the expected ridership increase to 22,400 passengers per hour.


Step 2.2 Assess the introduction of longer train consists
Using longer train consists changes only Calculation 2. The consist length can be increased to 10 and the calculation of capacity is shown below.


Calculation 2

Pmax

167

T

20

C

10

PHF

0.75

P

25,000

From this chart, the person capacity is increased to 25,000 passengers per hour at the current frequency and loading standard. This increased capacity will be able to accommodate the expected ridership increase to 22,400.


Step 2.3 Assess increasing the acceptable loading standard
If the acceptable loading standard is increased to 8 customers per square meter, the line person capacity is computed as follows.


Calculation 2

Pmax

188

T

20

C

8

PHF

0.75

P

22,560

This is just enough capacity to accommodate the target peak load of 22,400 passengers per hour. It should be noted that operating at a higher load standard will likely increase the stop dwell time since the passenger flow rate on and off trains is diminished due to crowding. Given that the computed line capacity is about 20 trains per hour, in the instant case this is not problematic.


Step 2.4 Assess increasing the service frequency
The current scheduled headway necessary to meet the demand is about 180 seconds or 3 minutes (calculated in original calculation 1). This is a frequency of 20 trains per hour. Increasing the frequency by 40% would require scheduling about 28 trains per hour at the current acceptable load factor. From previous calculations, this is determined to be feasible since the flow capacity of the line is 30 trains per hour. The number of trains per hour to meet the requirement is:
T = P/(Pmax C PHF )
where all terms have been defined previously


Calculation 2

P

22,400

Pmax

167

C

8

PHF

0.75

T

23

This suggests that scheduling 23 trains per hour will be able to accommodate the passenger demand. This is less than the line capacity of 30 trains per hour.






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