INTERSECTION MODEL COMPONENTS TTE 6815 K. Courage

TOPICS n Queue accumulation polygon n Uniform delay, stops & queue n Effects of random arrivals n Effects of oversaturation n Effects of coordination n Unsignalized control

QUEUE ACCUMULATION POLYGON (QAP) ASSUMPTIONS n Cyclical repetition n Uniform arrivals over the whole cycle

QUEUE ACCUMULATION POLYGON (QAP)

Maximum queue accumulation

DELAY n Uniform delay n Incremental delay n Deterministic queue delay

UNIFORM DELAY (sec/veh) n C = Cycle length 8 = Green / cycle n X = Degree of Saturation

HCM 94/97

NCHRP 3-48

STOPS n Arrival on red n Arrival on green before queue has cleared

Not stopped Stopped

UNIFORM STOPS 8 = Green / cycle n X = Degree of Saturation

EFFECT OF RANDOM ARRIVALS n Different QAP each cycle n Probability of overflow

QUEUE SIZE n Maximum queue accumulation n Maximum queue reach

Max Accumulation Max Reach Back of queue Front of queue

UNIFORM QUEUE REACH n q= arrival rate per sec = Volume (vph) / 3600

What Happens When The Demand Exceeds The Capacity?

TpTp Time

UNDERSATURATION ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ TpTp Time

OVERSATURATION ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^ TpTp ^^^^^^^^^^^^^^^^^^^ Deterministic Queue Delay DQD

OVERSATURATED DELAY DEFINITIONS n Delay per vehicle within the analysis period n Delay to each vehicle arriving during the analysis period

DEFINITION # 1

DEFINITION #2 # of vehicles in queue

DEFINITION #2 Delay to nth vehicle

DELAY MODEL 1.0 X DELAY Uniform DQD

GENERALIZED INCREMENTAL DELAY EQUATION

OPPOSED MOVEMENTS n Capacity n Delay

OPPOSED MOVEMENT APPLICATIONS n Permitted left turns n RTOR n Yield signs n Two-way stop signs n Roundabouts

DEFINITIONS n Critical gap, g c n Follow up time, t f n Opposing Volume, q o (veh per sec)

CAPACITY (Q emax )

# of Gaps

# of vehicles expected per gap

UNIFORM DELAY ON UNSIGNALIZED APPROACHES D u = 3600 / Capacity

TRAFFIC-ACTUATED SIGNALS n Estimation of phase times n Estimation of delay

TRAFFIC-ACTUATED DELAY n Uniform: Based on average cycle and phase times. n Incremental: Reduced effect of randomization

EFFECT OF SIGNAL COORDINATION n Uniform: QAP arrivals n Incremental: Reduced randomization

QUANTIFICATION OF PROGRESSION QUALITY n Arrival type n Time-space diagram n Flow profile n Implicit treatment by simulation

MODELING OF COORDINATED SIGNALS n Performance n Platoon dispersion n Optimization criteria and procedures

ASSIGNMENT Deterministic queue delay n Derive the general expression for Residual queue Residual queue service time Delay