UAID: Unconventional Arterial Intersection Design 1
Content Overview of Unconventional Arterial Intersection Design System Structure Continuous Flow Intersection Diverging Diamond Interchange Analysis System: MUID 2
Overview of Unconventional Arterial Intersection Design 3
Unconventional Arterial Intersection Design refers to a class of innovative intersection designs that attempt to increase the intersection capacity by reducing the impact of turning movements at the major intersection through various geometric design and management strategies. 11/15/2012 4
Roundabout Median U-Turn Unsignalized Superstreet Superstreet Unsignalized Median U-Turn At Grade & Unsignalized At Grade & Signalized Continuous Flow Windmill Interchange Grade- Separated & Unsignalized Grade- Separated & Signalized Echelon Single Roundabout Interchange Double Roundabout Interchange Center Turn Overpass Diverging Diamond 11/15/2012 5
Rerouting of turning movement paths Emphasis on predominant movements Reduction in signal phases Reduction in conflicting points Separation of intersection planes 11/15/2012 6
System Structure 7
Start Planning Evaluation Signal Design Operation Anlaysis Input: Demand pattern Preliminary geometry design Input: Demand pattern Detail geometry of intersections Input: Demand pattern Detail geometry of intersections Signal settings Output: Estimated delay Queue spill back locations Q/L ratios of each critical segment Output: Optimal offset Optimal green split and cycle length Output: Accurate delay Time-dependant queue configuration Overall level of service 11/15/2012 8
At the planning stage, this system offers a set of empirical equations for engineers to compute the overall interchange delay and to identify potential queue spillback locations in a DDI design. The second stage is to help traffic professionals develop the optimal signal timing plan, so as to synchronize traffic flows at those intersections and to prevent any potential queue blockage. Based on the recommended geometric features and signal plans, the system subsequently offers a function to employ VISSIM-based simulation model for users to assess the resulting queues and delays. 9
Continuous Flow Intersection (CFI) 10
The main feature of CFI is to eliminate the conflict between left-turn and opposing through traffic by relocating the left-turn bay to several hundred feet upstream of the primary intersection so that the through and left-turn flows can move concurrently. 11
Planning Evaluation Identify all the geometric factors contributing to delay and queue Build simulation models using VISSIM Calibrate VISSIM model parameters with field data Random sampling of different demand scenarios Build simulation datasets Perform regression analysis for each type of queue 12
CFI Delay Analysis For the convenient of discussion, we define a set of QL ratios to indicate the queue occupancy rate at each link: QL ratio = Maximum Queue Length Bay Length If QL ratio of a bay is less than one, it indicates that the design provides a sufficient storage capacity to accommodate all volumes approaching the target bay. If QL ratio of a bay is greater than one, then it implies that queue spillback may incur due to insufficient bay capacity and the service quality of the entire system may be deteriorated. 13
CFI Delay Analysis 250 200 Average Delay Per Vechicle Delay 150 100 50 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Average Queue-to-bay Ratio QL Ratio The figure illustrates the relationship between the average delay and queuing size within CFI, which reveal that the QL ratio has significant impacts on the CFI delay. 14
CFI Delay Analysis Delay= Congestion levels at four crossover intersections X= Degree of Saturation of the intersection 0.047 XX 1 1 XX 1 + 0.028 XX 2 1 XX 2 + 0.025 XX 3 1 XX 3 + 0.033 XX 4 1 XX 4 + 0.062 XX 5 1 XX 5 Congestion level of the primary intersection +0.167ββ 1 + 0.182ββ 2 + 0.192ββ 3 + 0.195ββ 4 +0.23θθ 1 + 0.196θθ 2 + 0.207θθ 3 + 0.219θθ 4 +0.072γγ 1 + 0.091γγ 2 + 0.101γγ 3 + 0.049γγ 4 +0.213ωω 1 + 0.229ωω 2 + 0.187ωω 3 + 0.281ωω 4 QL ratio of sixteen queues R 2 = 0.9142, Sample size N: 800 15
CFI Delay Analysis Ranking for the intersection degree of saturation impacts Level 1: Primary intersection degree of saturation (0.062) Level 2: Crossover intersection degree of saturation (0.047; 0.028; 0.025; 0.033) Ranking for Queue Impacts (Parameters analysis) Level 1: Type-4 Queues (0.213; 0.229; 0187; 0.281) Level 2: Type-3 Queues (0.23; 0.196; 0.207; 0.219) Level 3: Type-1 Queues (0.167; 0.182; 0.192; 0.195) Level 4: Type-2 Queues (0.072; 0.091; 0.101; 0.049)
Queue Length Estimation Type-1 Queue: Through queues at the primary intersection Type-2 Queue: Left-turn queues at the crossover intersections Type-3 Queue: Left-turn queues at the primary intersection Type-4 Queue: Through queues at the crossover intersections 17
Full CFI Queue Regression (1) Type-1 Queue: D (1-G )s s-d t t t θρ Queue=0.92γ +5.14 +1.72e t D s-cv m 2 d Qd Deterministic queue determined by demand and estimated green ratio Downstream queue-to-bay ratio The ratio between demand and the remaining capacity of the primary intersection D γ is a weighted factor between deterministic queue and correction components 18
Full CFI Queue Regression (2) Type-2 Queue: D (1-G )s s-d l l l θρ Queue=1.03γ +6.28 +1.13e l D s-cv n 2 d Deterministic queue determined by the demand and estimated green ratio Downstream queue-to-bay ratio Qd The ratio between the demand and the remaining capacity of the crossover intersection D 11/15/2012 19
GC: Estimated green time at the upstream intersection Full CFI Queue Regression (3) Type-3 Queue: Downstream queue-to-bay ratio θρd ( ) l Queue=0.729γ 1-α 1-G u D l+0.61e (s-d l) D D Qd Demand Estimated green time ratio at the primary intersection W: Estimated green time at the primary intersection 20
W:Estimated green time at the crossover intersection Full CFI Queue Regression (4) Dl Dt Type-4 Queue: (βd +D )(1-G )s βd +D Queue=0.78γ +5.62 s-(βd t+d l) s-cvn Dt, Dl : through and left-turn demands t l t t l Estimated green time ratio at the crossover intersection The ratio between total demand and the remaining capacity at the crossover intersection For the possible coordination of signals along the through movement, only part of through traffic may stop in the queue. Given by: βdt 11/15/2012 21 2
Delay Analysis of CFI-T CLV of the primary and crossover intersections X1 log(d) = 2.316 + 0.049 X 1 1 X 1 + 0.035 X 2 1 X 2 +0.132ρ 1 + 0.151ρ 2 + 0.213ρ 3 + 0.200ρ 4 X2 + 0.514ρ 5 + 0.196ρ 6 +0.23ρ 7 + 0.251ρ 8 R 2 = 0.897, Sample size N: 800 22
Delay Analysis of Two-leg CFI Primary Intersection Crossover Intersection X2 log(d) = 2.554 + 0.059 X 1 1 X 1 + 0.031 X 2 1 X 2 + 0.033 X 3 1 X 3 X1 +0.167ρ 1 +0.177ρ 6 +0.213ρ 4 +0.245ρ 9 +0.178ρ 3 +0.201ρ 8 +0.315ρ 12 +0.297ρ 14 +0.072ρ 2 +0.082ρ 7 X3 +0.182ρ 5 +0.169ρ 10 +0.210ρ 11 +0.228ρ 13 23
Signal Optimization for CFI Crossover Space Five Signalized intersections involved in one full CFI network Traffic flow generation node Central signalized node Minor signalized node Traffic flow entry node Traffic flow entry link
Signal Optimization for CFI Compared with conventional traffic networks, a CFI network has its own characteristics: (1) only left-turn and opposing through traffic volumes involved in the sub-intersections; (2) conflict between left-turn and opposing through traffic volumes has been eliminate at the primary intersection; and (3) those intersections are quite close to each other due to the high construction cost of larger footprint. (4) the special design of CFI provides a simplified two-phase signal control while also brings some new problems, such as the interaction of queues among neighboring intersections. 25
Signal timing plan
Signal Correlations The left-turn vehicles have to pass three intersections; The trough vehicles have to pass two intersections. T A good plan to coordinate those signal timings can reduce the delay significantly. L
Blockage and Spillback Correlation between Downstream and Upstream movements Correlation between parallel Left-turn and Through movements
Critical Issues Cycle Length optimization Green Ratio optimization. Offset Optimization Integrate geometry constraints
Network Flow Formulation If the spillback or blockage occur, the oversaturated vehicles would be stored in the traffic flow entry links. Crossover Space Traffic flow generation node Left-turn bay Central signalized node Minor signalized node Traffic flow entry node Traffic flow entry link
Traffic Queue Modeling The analysis time period has been divided into a set of discrete time intervals. # of arrival vehs Basic Point Queue at Formulation time step k # of Vehs in the queue At time step k+1 D q + = q + A D k 1 k k k m m m m # of Vehs in the queue At time step k 0 During Red Time = min( sm* t, Am + qm) During Green Time k m k k # of discharged vehs at time step k Saturation Flow Rate # of potential departing vehs
Traffic Flow modeling j i For those traffic flow entry link Total Arrival Vehs A = λ + λ k k k i L T R Left-turn volume Through- Right turn Volume m D = D + D k k k i im ij Crossover Space Left-turn bay Traffic flow generation node Central signalized node Minor signalized node Traffic flow entry node Departing Vehs Departing Vehs from i to m Traffic flow entry link Without the occurrence of blockage, the # of arrival vehs would equal to the # of discharged vehs. No traffic queue would accumulated in the entry link.
Blockage Modeling In order to take blockage into account, we introduce a set of binary variables to indicate the occurrence of blockage. Β 1 if Q >= L = 0 otherwise k 1 k m m m Available storage space on the link is given by: N = L Q k k m m m
When blockage is happening: j i Crossover Space Left-turn bay m Traffic flow generation node Central signalized node Minor signalized node Traffic flow entry node k k k k 1 k im = (1 m)(1 j ) min( il + λl, m ) D B B q ns t Scenario 1 happened Scenario 2 happened # of lanes at link m Traffic flow entry link k k If Scenario 1 happen, B = 1, then the departure flow form i to m D = 0; k k If Scenario 2 happen, B = 1, then the departure flow form i to m D = 0; Otherwise, D k im m j = min{total stored left-turn vehicles in i; capacity of m} im im
When blockage is happening: j i Crossover Space m k k k k 1 k ij m j itr λtr j D = (1 B )(1 B ) min( q +, ns t) k k k 1 k m(1 j ) ϕmin( itr λtr, ( j 1) ) + B B q + n s t Traffic flow generation node Left-turn bay Traffic flow entry link Central signalized node Minor signalized node Traffic flow entry node Scenario 1 Partially blockage One lane is blocked k k If Scenario 1 happen (Partially blockage), B = 1, B = 0then the departure flow form i to j is computed by: D k ij = min{total stored left-turn vehicles in i; reduced capacity of j}; m k k k If Scenario 2 happen(completely blockage), B = 0, B = 1, then the departure flow form i to j D = 0; k k k Otherwise,B = 0,B = 0, D = min{total stored left-turn vehicles in i; capacity of j} m j ij j m j ij
For the other links A C Upstream Downstream B D The arrival and departure process are correlated to the upstream and downstream links Crossover Space A k m = k t D up t : travel time from upstream stop line to the end of queue at link m Left-turn bay Traffic flow entry link Traffic flow generation node Central signalized node Minor signalized node Traffic flow entry node k k k k D = (1 B ) * min( q + A, ns t) m down m m m To indicate if blockage occurs at downstream
Flow merging m Crossover Space j Left-turn bay i Traffic flow generation node Central signalized node Minor signalized node Traffic flow entry node Flows from different direction may merge into one lane group Discharged vehs at link j Total arrivals at link m A = D + D k k τ k µ m im jm Discharged vehs at link i τ : Travel Time from link i to link m µ : Travel Time from link j to link m Traffic flow entry link
Signal Optimization Model Objective: Minimize the total delay of the entire intersection min D = k m q k m t Control parameters, decision variables and constraints C Min min, C minimal and maximal cycle length; Max g minimal green time for each phase; C common cycle length of the entire CFI design; θ i offset of intersection i; g effective green time for Φ2 at intersection i; I i i sum of inter-green time at intersection i. st.. C < C < C Min Max g < g < C, for i=1,2,...,5 Min i 0 < θ < C, for i=1,2,...,4 i
How to solve it? Objective is non-linear function The Optimal solution is really appropriate for application? Two-Stage solution algorithm 1: MAXBAND Optimization algorithm to provide an initial feasible solution II: Adjust this obtained solution to come out the final optimal solution
Stage 1 Green Ratio Optimization
Stage 1 How to synchronize those movements and optimize the offsets? Some literatures adopt the greedy heuristic method Those movements with higher demand level would take the priority to be synchronized. It may yield a local optimize solution when demand differences between movements are small
MAXBAND Optimization To optimize the offsets, a typical phase plan of CFI is: NORTH INTERSECTION Ø2 Ø4 WEST INTERSECTION MAIN INTERSECTION EAST INTERSECTION Ø2 Ø4 Ø2 Ø4 Ø2 Ø4 SOUTH INTERSECTION Ø2 Ø4 x mi, 1, if traffic flow m obtain the ROW in Φ2 at intersection i; = 0, o.w. e.g.: Northbound Left-turn flow and West bound Through flow x = 0; x = 0; x = 1; x NL,1 NL,0 NL,2 = 1; x = 1; WT,2 WT,0
Distance Westbound Through 2 θ 2 WT w2 WT b NL w0 NL w 2 = 0 NL b Northbound Left 0 1 θ 1 NL w1 Green time for Phase Φ2 Green time for Phase Φ4 Time NL : θ + g + w + t = CL + g + w NL NL 1 1 1 1,0 0 0 CL + g + w + t = θ + w + 2CL NL NL 0 0 0,2 2 2 NL NL wi + b gi for i=0,1,2
Distance Westbound Through 2 θ 2 WT w2 WT b NL w0 NL w 2 = 0 NL b Northbound Left 0 1 θ 1 NL w1 Green time for Phase Φ2 Green time for Phase Φ4 Time WT : t = θ + w WT 0,2 2 2 w + b ( C g ) WT WT 2 2
Stage I Max : st.. i V u b i i V i u i = 1 Ui is the weight factor Constraints for each movements. This is a linear programming optimization problem, could be solved efficiently by simplex method. Output: Common Cycle Length, offsets
Stage II Hari(1995) proposed a simplified and efficient method for offset optimization. Similarly, for each particular intersection, we shift the offset by 1 secs, and check the corresponding total delay: + 1 0 1 0 D= D D (or D= D D ) If ΔD<0, the offset would be shift continually at the same direction until the total delay begins to increase; otherwise the offset would be shift in the opposite direction.
Green ratio In this step, green ratio would be reoptimized based on the given offsets and cycle length; Adopt the decomposition approach developed by Heydecker (1955), each intersection is treated individually. The green ratio could be easily reoptimized with the given offsets and cycle length.
Stage II Step1: Start from one sub-intersection, shift the offset and update the new optimal one; Step 2: Repeat Step 1 until all the subintersections have been re-optimized; Step 3: Re-optimize the green times of each intersection; define the current signal plan as Φ(k); Step 4: Check if Φ(k)-Φ(k-1) <δ; yes, stop; no, go back to step 1.
Diverging Diamond Interchange (DDI) 50
The key logic of DDI is to provide efficient navigation for both left-turn and through movements between highway ramps, and to accommodate left-turning movements onto the arterial without using a left-turn bay. Off-Ramp Freeway On-Ramp Arterial Bridge Arterial On-Ramp Off-Ramp 51
Planning Evaluation The procedures of the planning stage include the following steps: Step 1: Identifying all factors contributing to the DDI total delay, including external factors such as demand, and internal factors such as intersection geometric features; Step 2: Generating a comprehensive set of data set with all identified factors for simulating analysis; Step 3: Deriving the quantitative relationships between intersection delays and contributing factors; Step 4: Estimating the impact of queues on the overall intersection performance and developing a set of statistical models for queues length prediction at each critical location within a DDI. 52
DDI Delay Analysis Delay= 2.549 + 0.154 XX 1 1 XX 1 + 0.149 XX 2 1 XX 2 Congestion level of intersections +0.206ρρ 1 + 0.212ρρ 4 +0.213ρρ 2 + 0.197ρρ 5 + +0.253ρρ 3 + 0.251ρρ 6 Queue-to-bay ratio of each location + 0.201ρρ 7 + 0.217ρρ 8 X1 X2 53
DDI Queue Regression (1) Type-1 Queue: 2 D t(1-g t)s Dt 4ρ Queue=0.64 +5.14 +1.72e s-d t s-cv d Deterministic queue determined by demand and estimated green ratio Downstream queue-to-bay ratio The ratio between demand and the remaining capacity of the target intersection D 54
DDI Queue Regression (2) Type-2 Queue (Left-turn or Right-turn): D t(1-g t)s Dt Queue=0.73 +5.54 s-d s-cv t 2 Deterministic queue determined by the demand and estimated green ratio The ratio between the demand and the remaining capacity of the target intersection D 11/15/2012 55
DDI Queue Regression (3) Type-3 Queue: (D +D )(1-G )s D +D Queue=0.61γ +5.62 s-(d t+d l) s-cvn t l t t l 2 D Deterministic queue determined by the demand and estimated green ratio The ratio between the demand and the remaining capacity of the target intersection 11/15/2012 56
Signal Optimization for DDI Due to the unique geometry features, a DDI typically has two signalized intersections, controlled with two-phase signals. East Intersection West Intersection Φ2 Φ4 Φ2 Φ4 Note: Φ1 and Φ3 denote the yellow time and all-red time. To optimize a DDI s signal timings, one shall concurrently addresses the following three issues: green split at each intersection, cycle length, and offset. 57
Green Split Optimization One important issue for signal design is to maximize the capacity of an intersection given the geometric layout. Based on the assumption that traffic demand matrix can be multiplied with a common flow multiplier μ to represent the maximum amount of volume increased that would still allow the intersection to perform reasonably well. the optimization problem is becoming an issue of determining the maximum multiplier μ. Apply a multiplier μ to the demand pattern 58
Green Split Optimization With the increased demand, the flow conservation constraints could be set as: q = µβ Q i, j j ij i i Where Q = {Q i ; i N T } denotes the traffic demand of the entire DDI; q j is the assigned traffic flow (multiplied by μ) on lane group j; a set of binary variables {β ij } are used to indicate the resulting traffic assignment: 1 βij = 0 if flow i is assigned to j otherwise For Example: q = μq1+ μq2 59
Green Split Optimization Two kinds of DDI design DDI with left-turn only lane DDI without left-turn only lane For those DDIs with left-turn only lane, the left-turn on-ramp volume is allowed to move continuously without any signal delay. For those DDIs without left-turn only lane, the through traffic queue may block the entry of the on-ramp. Therefore, for those DDIs without a left-turn only lane, the left-turn volume is multiplied by a parameter γ i and equivalently converted to through volume during the optimization process. 60
Green Split Optimization Based on the same assumption as mentioned above, the following constraints should be satisfied to ensure that the degree of saturation in each movement is below the maximum acceptable limit q s α g j j j mnj mn m n Assigned flow < saturation flow rate * total obtained green time α mnj 1 if j obtains its right of way in phase m at int er sec tion n = 0 otherwise gmin g 1 mn, mn 61
Green Split Optimization Thus, one can present the optimization model as follows: Maxmize µ S.t. q = µβ Q i, j j ij i i q s α g j j j mnj mn m n gmin gmn 1 mn, m g mn = 1 n 62
Cycle Length and Offset Optimization Distance West intersection (0) θ w SL = 0 b NL bsl w ET b WT bet NL: Northbound Left ET: Eastbound Though SL: Southbound Left WT: Westbound Though East Intersection (1) w NL = 0 w WT Green time for Phase Φ2 Green time for Phase Φ4 Time 63
Cycle Length and Offset Optimization Similar to the MAXBAND model in CFI, a set of constraints are given by: 64
Cycle Length Optimization Delay increases rapidly when the CL is below the optimal CL (Co); Exact CL not critical as long as not less than Co; To minimize the delay, Webster formulated an equation: (1.5* LostTime + 5) Cwebster = 1.0 CLV / s Then the range of cycle length (a constraint for the MAXBAND Model) is: C webster C C + C webster C is the given constant, and C + C indicates the upper bound of CL webster 65
Cycle Length and Offset Optimization Thus, the objective function is: S.t. Max ϕ b : i i i V C C C + C webster webster 66
Maryland Unconventional Intersection Design 67
Step 0: Start 11/15/2012 68
Step 1: Create a new case for analysis Click Full CFI to select the design 11/15/2012 69
Interface File Edition Tool Box Input and Display Tool Box Output Tool Box, unable at the beginning Intersection Display Platform 70
Step 2: Input Demands Change the demand settings of the intersection 11/15/2012 71
Step 3: Edit Geometric Parameters Change # of lanes, link Length The selected link would be highlighted for convenience 11/15/2012 72
Buttons enable now The display of intersection changed according to the input 11/15/2012 73
Functions Rotate the figure clockwise (counterclockwise) 11/15/2012 74
Functions Change the figure color and background color 11/15/2012 75
Step 4: Planning Analysis Planning Analysis result (Queue length, QL Ratio, CLV) Buttons enable now 11/15/2012 76
Step 5: Signal Optimization Optimization for cycle length, green split and offset 11/15/2012 77
Output Functions Display demands 11/15/2012 78
Output Functions Display link length 11/15/2012 79
Output Functions Display Phase Plan 11/15/2012 80
Output Functions Display Queue Length 11/15/2012 81
Output Functions Display Queue-tobay Ratios 11/15/2012 82
Output Functions Display Signal settings 11/15/2012 83
Other Designs User can perform analysis of different design at the same time 11/15/2012 84
Other Designs 11/15/2012 85
Thank You! 86