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:
introduce longer traincars
introduce longer train consists
increase the acceptable load factor
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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