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Chapter 26
Corridor Analysis
26.1 Introduction
Transport problems are very critical one to be solved frequently, sequentially and economically for all sectors of one nation. Even though these solutions are mandatory, they are continuous and expensive so needs to be planned systematically. These all requirements will lead us to Transportation System Planning. Transportation System Planning is a tool that attempts to provide feasible and systematic method for solving transport problems of the society. Trans- portation system planning starts from the problem of the society which is the difference of users desire to the existing condition of the system. Afterwards following its stages it will attempt to meet its goals and objectives. While in the process so many analyses are required to be done from them the one is done to know the performance of the existing system. This can be expressed as either individual component performance or the whole system performance. Doing this is dependent on the type of transportation system. Among them multimodal multi facility system is the one which requires aggregate performance measurement for all components which constitutes. According to our study area we can choose from the two methods of performance measurement alternatives which are Corridor analysis and Area wide analysis. Corridor Analysis is the method of combining Point, Segment and Facility analysis to esti- mate the overall performance of multimodal corridor. Mostly the performance measures of any corridor are determined by calculating its capacity, the travel time and queue delay in the given section. Since this tool is required for multi facility and multimodal transportation system mostly it covers Highway subsystems (Freeways, Rural highways and urban streets) and Transits.
Segment
Point Freeway
Arterials
Figure 26:1: (a) Showing the Point Segment and Corridor Model
Figure 26:2: (b) Showing some common real pictures of a Corridor
26.2 Terminologies
While describing the concept of Corridor analysis we are going to use frequently new words so to develop a better communication here under wards given the terminologies of basic ones.
26.2.1 Corridor, Segment, Point and Facility
- Corridor: A corridor is a set of essentially parallel and competing facilities and modes with cross-connectors that serve trips between two designated points. A corridor may contain several subsystems of facilities freeway, rural highway, urban street, transit, pedes- trian, and bicycle. Below some sample pictures are given showing what Corridor is shown in Figs. 26:1 to 26:4 as:
- Segment: Segments are stretches of a facility in which the traffic demand and capacity
Figure 26:5: Some Facility types with different function, (a) Through put movement on free way (Mobility)
Figure 26:6: Some Facility types with different function, (b) On-street Parking in urban areas (Accessibility)
conditions are relatively constant.
- Point: Points are locations at the beginning and end of each segment, at which traffic enters, leaves, or crosses the facility.
- Facility: is a structure built or road design modification to increase the efficiency of the two main road way services (accessibility and Mobility).
Some of common facility types are shown in Figs. 26:5 to 26:8.
26.2.2 Highway sub systems
- Freeway: A freeway is defined as a divided highway with full control of access and having two uninterrupted flow or more lanes for the exclusive use of traffic in each direction. All the access is through a ramp a separate entrance or exit way to or from the Freeway.
Figure 26:7: Some Facility types with different function, (c) Right turning movement from free way (Accessibility)
Figure 26:8: Some Facility types with different function, (d) Channelized Intersection to increase throughput flow safely on rural two lane (Mobility)
to the following hour. The downstream demands are reduced by the amount of excess demand stored on the segment. The algorithm starts with the entry gate segments on the periphery of the corridor and works inward until all segment demands have been checked against their capacity.
26.3.1 Procedures Demand Adjustment Algorithm
The following steps are used to adjust demand when excess demand occurs in a time period.
- Step 1. Select the entry gate segment with the highest priority and the highest v/c ratio.
- Step 2. Select the first time period.
- Step 3. If demand ≤ capacity or the initial queue, Queue = 0, go to Step 7.
- Step 4. If demand > capacity or Queue > 0, then calculate new Queue by using eqn. 26.1. Queuei = Queuei− 1 + demand − capacity (26.1)
where, i = the current analysis period, i − 1 = the previous analysis period, Queuei− 1 = queue remaining from the preceding analysis period.
- Step 5. Reduce downstream segment demand by the amount that the demand exceeds the capacity. Propagate this reduction to all connecting downstream segments in pro- portion to the ratio of each downstream segment demand to all segments exiting from the subject segment. Continue the process downstream until the reduction is less than 5 percent of capacity.
- Step 6. Add the excess demand - the amount by which the demand exceeds the capacity
- to the next time period demand for the subject segment.
- Step 7. Apply the increment to the next time period. Repeat Steps 3 through 6 until the processes for all the time periods are finished.
- Step 8. Go to next gate tree with unanalyzed segments in current Rank. Repeat Steps 2 through 7 until all segments of current rank have been analyzed.
- Step 9. Apply the increment to current Rank (the new one). Go to the segment with the highest v/c ratio among those of the new rank. Repeat Steps 2 through 8 until all segments are analyzed.
26.4 Free flow Travel time
The segment free-flow traversal times are obtained by dividing the length of the segment by the estimated free-flow speed (FFS), as shown in Eqn. 26.
Rf = (^) SL f
where, Rf : Segment free-flow travel time for given Direction of Segment and Time Period, (hr). L : Length of segment (km), and Sf : Segment free-flow speed computed (km/hr). The FFS is computed according to the Part III methods using the adjusted demands determined in the previous step. The computation is repeated for each direction of each segment for each time subperiods.
26.5 Queue Delay
The queuing delay only the amount due to demand exceeding capacity is computed for all segments. The queuing delay is computed for each direction of each segment and time period only when demand is greater than Capacity by eqn. 26.3.
Di = T 2 × Di− 1 + [V − c] × T^
2 2 (26.3)
where, Di = total delay due to excess demand (veh-hr) for direction, segment, and time period; T = duration of time subperiod (hr); Di− 1 = queue left over at end of previous time period (veh); V = demand rate for current time period (veh/hr); and c = capacity of segment in subject direction (veh/hr). These the above steps are repeated for any additional time periods to be analyzed. For example, if the peak period lasts for 4 hours, it might be divided into four 1hr periods (or 16 quarter hr periods), with each time period analyzed in sequence. The first and the last analysis periods must be uncongested for all delay to be included in the performance measures. Once all time periods have been analyzed, the performance measures are computed.
P kmT = person-kilometres of travel, PHT = person-hours of travel, AV O = average vehicle occupancy, V = vehicle demand in the given Direction on a Segment and Period (veh), and L = length of segment (km).
- The mean trip delay is computed by subtracting the PHT under free-flow conditions from the PHT under congested conditions and dividing the result by the number of person- trips. The person-hours of travel under free-flow conditions is computed like PHT for congested conditions, but using free-flow traversal times and zero queuing delay. It can be determined using eqn. 26.7 given below:
d = 3600 × (P HT^ − P^ P HTf^ ) (26.7)
where, d = mean trip delay (s/person), P HT = person-hours of travel, P HTf = person-hours of travel under free-flow conditions, and P = total number of person trips.
26.6.2 Duration
Performance measurements of duration can be computed from the number of hours of conges- tion observed on any segment. The duration of congestion is the sum of the length of each analysis subperiods for which the demand exceeds capacity. The duration of congestion (i.e., oversaturation) for any link is computed using Eqn. 26.8 as:-
Hi = Ni × T (26.8)
where, Hi = duration of congestion for Link i(h), Ni = number of analysis subperiods for which v/c > 1 .00 on Link i, and T = duration of analysis subperiods (h). The maximum duration on any link indicates the amount of time before congestion is completely cleared from the corridor.
26.6.3 Extent
Performance measures of the extent of congestion can be computed from the sum of the length of queuing on each segment. One can also identify segments in which the queue overflows the
Table 26:1: QUEUE DENSITY DEFAULTS(Source HCM 2000, chapter 29,Exihibit 29.6) Sub system Storage Density Vehicle Spacing (veh/Km/ln) (m) Freeway 75 13. Two lane highway 130 7. Urban Street 130 7.
storage capacity; this is particularly useful for ramp metering analyses. To compute the queue length, an assumption must be made about the average density of vehicles in a queue. Default values are suggested in Table. 26: To compute queue length, Eqn. 26.9 is used.
QL = T^ N× [×v^ −d^ c] s
where, QL = queue length (km) for the given Direction, of Segment, for Time Subperiod; v = segment demand (veh/h); c = segment capacity (veh/h); N = number of lanes; ds = storage density (veh/km/ln); and T = duration of analysis period (h). Note that if v < c, then QL = 0, and if QL > L, then the queue overflows the storage capacity. The queue lengths for all segments then can be added up to obtain the length of queuing in kilometres in the subsystem during the analysis period. The number of segments in which the queue exceeds the storage capacity also might be reported. This statistics is particularly useful for identifying queue overflows that result from ramp metering.
26.6.4 Variability
Variability is a sensitivity measure. The variability or sensitivity of the results can be deter- mined by substituting higher and lower demand estimates. For example assuming 110 percent of the original demand estimates for all segments and repeating the calculations.
Table 26:3: Capacity, length and Speeds input
link length Capacity FFS Actual
Figure 26:10: Showing how the flow allocation is done
Solution:
- Step 1. Because we have Traffic count data we should convert it as link data. This can be done by allocating the flow and adding the volume as per its logical direction (Table 4 col (3)). The flow allocation overview is as shown below. In Fig. 26:
- Step 2. Calculate V/C ratio demand by capacity for each link which is as shown below in Table. 26.7 col (5).
- Step 3. For V/C > 1 find the Queued vehicles simply the difference of demand to capacity.
- Step 4. Adjust the demand downstream till it reaches 10% of the volume before doing further check up. Until all V/C ratios are below 1.
- Step 5. Determination of person hour delay (PHD), person hours travel (PHT), person kilometre hour travel (PkmT). Note that in Table. 26. - None of them(V/C) is greater of unity. - No Adjustment is required. - Indicates No Queue delay Determination
- Step 6. Free VHT (col(7))= (col (3) × col (4))/col (5)
- Step 7. Actual VHT (col(8))= Qd +(col (3) × col (4))/col (6) where, Qd is the queue delay in our case zero.
- Step 8. Free PHT (col(9))= AVO × col (7)
Table 26:5: PHD and PHT calculation
Link length demand FFS Actual free actual Free Actual Delay (km) (veh/hr) (km/hr) speed(km/hr) VHT(hr) VHT(hr) PHT(hr) PHT(hr) PHT(hr) veh. Km /hr
Table 26:6: Performance measurement Facility type Length PkmT PHT PHD Speed(S) (Km) Pers. Km Pers. Hr Pers. Hr km/hr Arterial sub. system 12.8 15795 396.8 114.75 39.
- Step 9. Actual PHT (col(10))= AVO × col (7)
- Step 10. Travel Delay (PHD) (col(11))= Actual PHT (col(10)) - Free PHT (col(9))
- Step 11. Calculation of PkmT P kmT = AV O × ΣV × L where, V is adjusted volume L is length of the Link ΣV L = col(12) last cell in Table. 26:
- Step 12. Intensity measures P HT = ΣactualP HT = 396. 8 pers.hr t = 60 ×^ P HT AV O × ΣV
= 1. 43 min/pers
S = P kmT P HT = AV O × (Σd,l,h[V × L])/P HT = 39. 6 km/hr d = 3600 × (P HT^ −^ P HTf^ ) P = 24. 9 sec/pers.
26.8 Conclusion
- Delay due to traffic congestion accounts 28.9% (PHD/PHT) of the total number of travel.
- No any over saturation (i.e., no Queue delay). So that the sub system is good.
- As per the traversal delay (24.9sec/veh/1.2 ≈ 21sec/veh) LOS of the system is C.
- Though many vehicles are passing without stopping there is operational failure (there are few vehicles passing the section with stopping).
Table 26:8: Length, Capacity, Free flow speed and Actual speed data for each segment
Link length Capacity Free flow Actual speed
- 1 2 1.06 (km) (veh/hr) (km/hr) speed(km/hr)
- 2 1 1.06
- 2 4 1.67
- 4 2 1.67
- 2 8 1.21
- 8 2 1.21
- 2 3 0.09
- 3 2 0.09
- 4 7 1.21
- 7 4 1.21
- 4 6 0.76
- 6 4 0.76
- 4 5 0.09
- 5 4 0.09
- 1 2 1181 1400 0. (1) (2) (3) (4) (5)
- 2 1 1008 3400 0.
- 2 4 1375 1400 0.
- 4 2 1141 1400 0.
- 2 8 541 1400 0.
- 8 2 1090 1700 0.
- 2 3 701 3400 0.
- 3 2 355 1400 0.
- 4 7 942 1400 0.
- 7 4 1107 1200 0.
- 4 6 1318 3400 0.
- 6 4 1216 1400 0.
- 4 5 1017 3400 0.
- 5 4 836 1400 0.
- 1 2 1.06 1181 56 40 22.35 31.30 26.83 37.56 10.73 1251. col(1) col(2) col(3) col(4) col(5) col(6) col(7) col(8) col(9) col(10) col(11) col(12)
- 2 1 1.06 1008 56 56 19.08 19.08 22.90 22.90 0.00 1068.
- 2 4 1.67 1375 56 41 41.00 56.01 49.21 67.21 18.00 2296.
- 4 2 1.67 1141 56 46 34.03 41.42 40.83 49.71 8.88 1905.
- 2 8 1.21 541 56 43 11.69 15.22 14.03 18.27 4.24 654.
- 8 2 1.21 1090 56 26 23.55 50.73 28.26 60.87 32.61 1318.
- 2 3 0.09 701 56 40 1.13 1.58 1.35 1.89 0.54 63.
- 3 2 0.09 355 56 12 0.57 2.66 0.68 3.20 2.51 31.
- 4 7 1.21 942 56 43 20.35 26.51 24.42 31.81 7.38 1139.
- 7 4 1.21 1107 56 43 23.92 31.15 28.70 37.38 8.68 1339.
- 4 6 0.76 1318 56 56 17.89 17.89 21.46 21.46 0.00 1001.
- 6 4 0.76 1216 56 33 16.50 28.00 19.80 33.61 13.80 924.
- 4 5 0.09 1017 56 40 1.63 2.29 1.96 2.75 0.78 91.
- 5 4 0.09 836 56 11 1.34 6.84 1.61 8.21 6.60 75.
- 12.18 13828 Sum 282.05 396.81 114.76 13162.
- 1 A 0.9 (km) (veh/hr) speed(km/hr) (km/hr)
- A C 1.3
- C 7 2.1
- 7 C 2.1
- C A 1.3
- A 1 0.9
- 2 B 0.9
- B D 1.3
- D 8 2.1
- 8 D 2.1
- D B 1.3
- B 2 0.9
- 3 A 1.1
- A B 1.85
- B
- 4 B
- B A 1.85
- A 3 1.1
- 5 C 1.1
- C D 1.85
- D
- 6 D
- D C 1.85
- C 5 1.1
Solution:
- Step 1. Because we have Traffic count data we should convert it as link data. This can be done by allocating the flow and adding the volume as per its logical direction (Table. 26:9 col (3)).
- Step 2. Calculate V/C ratio demand by capacity for each link which is as shown below in Table. 26:9 col (5).
- Step 3. For V/C > 1 find the Queued vehicles simply the difference of demand to capacity.
- Step 4. Adjust the demand downstream till it reaches 10% of the volume before doing further check up. Until all V/C ratios are below 1.
- Step 5. Determination of person hour delay (PHD), person hours travel (PHT), person kilometre hour travel (PkmT). Note that in Table. 26: - None of them (V/C) is greater of unity. - No Adjustment is required. - Indicates No Queue delay Determination.
All Calculations below refers to Table. 26:
- Step 6. Free VHT (col(7))= (col (3) × col (4))/col (5)
- Step 7. Actual VHT (col(8))= Qd +(col (3) × col (4))/col (6) where, Qd is the queue delay in our case zero.
- Step 8. Free PHT (col(9))= AVO × col (7)
- Step 9. Actual PHT (col(10))= AVO × col (7)
- Step 10. Travel Delay (PHD) (col(11))= Actual PHT (col(10)) - Free PHT (col(9))
- Step 11. Calculation of PkmT
P kmT = AV O × ΣV × L
