TCE 327 · TRANSPORTATION ENGINEERING · DR. AMIN RAD
Quiz 1 Cheat Sheet — Traffic Flow & Signal Timing
PEAK HOUR FACTOR (PHF)
SIDE A
SIGNAL TIMING TERMINOLOGY
CAPACITY & V/C RATIO
PHF = V60 / (4 · V15,max)
Interval
period all indications unchanged
Cycle (C)
total time for one full sequence (s)
DHV = Vpeak-hr / PHF
Phase (Ø)
G+Y+AR for an independent movement
PHF = 1.0 → perfectly uniform flow
Change interval
PHF < 1 → spiked demand in peak 15 min
Y + AR (clearance)
C = ΣGi + ΣYi + ΣARi
Min PHF = 0.25 (all volume in 1 interval)
More phases → longer C → lower capacity
Use PHF to convert hourly vol → design flow rate (DHV = V/PHF)
Minimum yellow to eliminate dilemma zone:
Adjust mixed traffic to PCE before applying PHF:
E = 1.0
Truck (general)
E = 1.5
tr = perception-reaction time (1.0 s)
Left turn
E = 2.5
v = approach speed (ft/s) → mph × 1.467
Right turn
E = 1.5
a = deceleration rate (11.2 ft/s²)
g = grade (decimal; + uphill, − downhill)
G = 32.2 ft/s² (gravitational accel)
W = intersection width (ft)
VD = Vadj / PHF
Lv = avg vehicle length (20 ft)
SIGNAL CONTROLLER MODES
Pre-timed: Fixed cycle/phase; good for coordinated systems &
constant demand
Semi-actuated: Detection on minor street only; variable cycle;
good for coordinated systems
Fully-actuated: Detection all approaches; variable cycle &
phase order; best for isolated intersections
No grade adjustment: drop ±2gG term. All-red provides extra
clearance after yellow.
Protected: Exclusive green, no yield to opposing
VLT·Vopp ≥ 50,000
2 opposing lanes
VLT·Vopp ≥ 90,000
3+ opposing lanes
VLT·Vopp ≥ 110,000
Or LT vol
≥ 240 veh/h
Leading LT most common. Lagging can cause Yellow Trap — avoid
lagging unless needed for queue clearance.
WEBSTER & HCM OPTIMAL CYCLE
Webster Method:
Co = (1.5L + 5) / (1 − ΣYci)
L = total lost time per cycle
ΣYci = sum of critical flow ratios
HCM Critical v/c (whole intersection):
Xc = (Σ v/sci) · C / (C − L)
Green Splitting:
Gi = gi − Yi − ARi + tL,i
PEDESTRIAN MINIMUM GREEN
tp = 3.2 + L/Sp + 2.7·Nped/WE (WE>10ft)
t2 (clearance): last ~1s yellow + all-red
tp = 3.2 + L/Sp + 0.27·Nped (WE≤10ft)
Gte = C − L (effective green per cycle)
1 opposing lane
Yi = vij / sj (flow ratio)
Critical group = highest v/s in concurrency group
t1 (start-up): reaction lag when green appears
Total L = Σ li (sum over all phases)
Use Protected LT when (peak hour):
X ≤ 1.0 desired; X > 1 → oversaturated
tL = t1 + t2 (start-up + clearance lost time)
Permissive: Must yield to opposing traffic
Protected-Permissive: Both in same cycle
Xi = degree of saturation (v/c ratio)
gi = (v/s)ci · Gte / Σ(v/s)ci
LOST TIME & EFFECTIVE GREEN
g = G + Y + AR − tL
LEFT-TURN PHASING MODES
ci = capacity of lane group i (veh/hr)
Y = tr + v/(2a ± 2gG) + (W+Lv)/v
Passenger car
Vadj = V + VLT(ELT−1) + VRT(ERT−1) + VTR(ETR−1)
Xi = vi / ci = (vi·C) / (si·gi)
Critical Lane Group Yi:
CHANGE / YELLOW INTERVAL
PASSENGER CAR EQUIVALENTS
ci = si · (gi / C)
3.2 s = pedestrian startup time
L = curb-to-curb crossing distance (ft)
Sp = walking speed (ft/s); default 3.5 ft/s
Nped = # peds crossing per interval
SATURATION FLOW RATE
s = 3600 / h (veh/hr/lane)
WE = effective crosswalk width (ft)
DON'T WALK flash = L/Sp (from end of all-red)
so = 3600 / 1.895 ≈ 1900 pc/hr/lane
h = saturation headway (s/veh)
LANE GROUPING RULES
so = ideal rate (HCM, single/multi-lane)
Exclusive turn lane → separate lane group
Multilane: multiply by # of lanes
Remaining lanes after excl. LT/RT → one group
Each shared lane → separate lane group
Phasing Types (fewer = better service):
2-phase: simple; thru + permissive LT
3-phase: excl. LT for 1 direction
4-phase: split phasing or excl. LT both dirs
Split phasing: all movements one approach → opposing
approach
TCE 327 · TRANSPORTATION ENGINEERING · DR. AMIN RAD
Quiz 1 Cheat Sheet — Delay, LOS & NEMA Phasing
CONTROL DELAY COMPONENTS
di = d1i + d2i + d3i
d1 Uniform Delay:
d1 = 0.5C(1 − g/C)² / [1 − min(1,X)·g/C]
SIDE B
NEMA PHASE NUMBERING SCHEME
Movement #s:
SIGNAL DESIGN SUMMARY CHECKLIST
Phase #s (Ø):
1=NB LT
2=NB thru+RT Ø1=NB LT
Ø2=NB thru
3=SB LT
4=SB thru+RT Ø3=SB LT
Ø4=SB thru
5=EB LT
7=WB LT
6=EB thru+RT Ø5=EB LT
8=WB thru+RT Ø7=WB LT
Ø6=EB thru
Ø8=WB thru
d2 Incremental Delay:
d2 = 900T[(X−1) + √((X−1)²+8kIX/(cT))]
RING-BARRIER DIAGRAM (STANDARD DUAL-
① Determine LT phasing (protected vs. permissive
threshold)
② Build ring-barrier diagram (NEMA phases, lead/lag)
③ Establish lane groups
④ Compute change interval Y (yellow eq.)
⑤ Estimate lost times t1, t2, L per phase
RING)
⑥ Identify critical lane groups (max v/s per
concurrency group)
k = 0.5 (pretimed, isolated)
Standard 4-leg, protected LT leading:
⑦ Calculate optimal cycle length C (Webster or HCM)
I = 1.0 (isolated)
Ring 1
Ø1
Ø2
|
Ø3
Ø4
d3 Initial Queue Delay:
Ring 2
Ø5
Ø6
|
Ø7
Ø8
= 0 when no initial queue (default in class)
LT = LT phases
TH = Thru phases
barrier (must cross simultaneously)
T = analysis period (h); usually 0.25 h
Class assumption: isolated, pretimed, no initial queue →
k=0.5, I=1.0, d3=0
⑧ Split the green (gi proportional to Yi)
⑨ Check pedestrian minimum green
| =
Rules: (1) Phases in same ring run
sequentially. (2) Phases in different rings can
overlap. (3) Both rings must cross barrier at
same time. (4) Ø1&Ø2 concurrent with Ø5&Ø6
WEIGHTED AVERAGE DELAYS
(EW+NS together). (5) Ø3&Ø4 concurrent with
Ø7&Ø8.
⑩ Compute capacity, v/c, delay, LOS
UNIT CONVERSIONS & CONSTANTS
mph → ft/s
× 1.467
ft/s → mph
× 0.682
32.2 ft/s²
Gravity g
1.895 s/veh
Ideal sat. headway
Approach delay (dA):
dA = Σ(di·vi) / Σvi
Intersection delay (dint):
dint = Σ(dAi·vAi) / ΣvAi
Weight each lane group by its volume (veh/hr)
CONFLICTING / COMPATIBLE PHASES
1.0 s
Std. PRT (tr)
Ø conflicts (cannot run simultaneously):
AASHTO decel (a)
Ø1 conflicts: 3,4,5,6,7,8
Avg. vehicle length
Ø2 conflicts: 3,4,5,6,7,8
1900 pc/hr/lane
Ideal sat. flow so
Ø3 conflicts: 1,2,5,6,7,8
Ped walking speed Sp
Ø4 conflicts: 1,2,5,6,7,8
Analysis period T
11.2 ft/s²
20 ft
3.5 ft/s (default)
0.25 h (15 min)
Ø1 compatible with: Ø2, Ø5, Ø6
LEVEL OF SERVICE (LOS) — CONTROL DELAY
LOS
Delay
(s/veh)
< 10
Free flow; minimal delay
B
10 – 20
Stable; occasional wait
C
20 – 35
Stable; moderate delays
E
F
35 – 55
55 – 80
> 80
Ø5 compatible with: Ø1, Ø2, Ø6
Approach unstable; long
queues
Unstable; frequent oversat.
Forced flow; excessive delay
Same thresholds for lane group, approach, and intersection
LOS
ROAD HIERARCHY — MOBILITY VS. ACCESS
Arterials: high mobility, low access
Condition
A
D
Ø2 compatible with: Ø1, Ø5, Ø6
LEAD VS. LAG LEFT TURN
Lead LT: LT phase before thru — most common,
preferred
Lag LT: LT phase after thru — use when bay gets
blocked; risk of yellow trap
One approach lead + opposing lag is acceptable if
operationally better
Yellow Trap: lagging LT sees green while opposing sees
yellow — can create unsafe conflict
Collectors: balance of mobility & access
Local roads: low mobility, high access
US Roadway Facts:
Total road miles
4.2 million mi
~70–72%
Rural %
Interstates
<1% miles, >24% VMT
KEY AGENCIES & LEGISLATION
FHWA, FTA, FAA, NHTSA → under USDOT
NTSB → National Transportation Safety Board
IIJA 2021 → latest funding act ($1.2T)
HCM → Highway Capacity Manual (TRB)
NEMA → National Electrical Manufacturers Assoc.
Textbook (Quiz source):
Mannering & Washburn, Principles of Highway Eng. & Traffic
Analysis, 7e — Ch.1 & Ch.6 §6.1–6.4; FHWA Signal Timing
Manual Ch.4 §4.1–4.4