Four-Way Stop Delay Calculator

Calculator inputs

Enter your traffic and behavior assumptions. Values are checked and capped to keep results stable.

Peak Hour Factor (PHF)

Adjusts hourly counts to demand flow rate (v/PHF).

Demand growth factor

Use 1.00 for existing, or >1.00 for forecast.

Arrival variability (Ca²)

1.0 = random arrivals; lower means more platooned.

Service variability (Cs²)

Represents turning, hesitation, and driver differences.

Stop penalty (sec/veh)

Approx. time lost due to mandatory stop behavior.

Accel/decel add-on (sec/veh)

Adds control delay components beyond pure queueing.

HV impact per 1% (hv_k)

Headway multiplier: 1 + HV% × hv_k.

Grade impact per 1% (grade_k)

Uses absolute grade value for a conservative effect.

Compliance impact (comp_k)

Headway multiplier: 1 + (1 − compliance) × comp_k.

Ped effect per crossing (sec)

Distributed across vehicles: (peds/hr × ped_sec) ÷ vph.

Northbound approach Inputs

Volume (veh/h)

Approach lanes

Base departure headway (s/veh)

Heavy vehicles (%)

Grade (%)

Stop compliance (0.70–1.00)

Ped crossings (per hour)

Tip: If you have observed saturation headway, use it as the base headway input.

Eastbound approach Inputs

Volume (veh/h)

Approach lanes

Base departure headway (s/veh)

Heavy vehicles (%)

Grade (%)

Stop compliance (0.70–1.00)

Ped crossings (per hour)

Tip: If you have observed saturation headway, use it as the base headway input.

Southbound approach Inputs

Volume (veh/h)

Approach lanes

Base departure headway (s/veh)

Heavy vehicles (%)

Grade (%)

Stop compliance (0.70–1.00)

Ped crossings (per hour)

Tip: If you have observed saturation headway, use it as the base headway input.

Westbound approach Inputs

Volume (veh/h)

Approach lanes

Base departure headway (s/veh)

Heavy vehicles (%)

Grade (%)

Stop compliance (0.70–1.00)

Ped crossings (per hour)

Tip: If you have observed saturation headway, use it as the base headway input.

Reset

Example data table

A simple example scenario for quick checks.

Approach	Volume (vph)	Lanes	Base headway (s)	HV (%)	Ped/hr
Northbound	250	1	2.6	6	10
Eastbound	300	1	2.6	6	10
Southbound	260	1	2.6	6	10
Westbound	290	1	2.6	6	10

Suggested global settings: PHF 0.92, Growth 1.00, Ca² 1.00, Cs² 0.20, Stop penalty 2.0 s, Add-on 4.0 s.

Formula used

This calculator uses a planning-level queueing approximation to estimate average control delay at a four-way stop. It converts volumes to demand flow rate using v = volume / PHF, then applies the growth factor.

Adjusted headway (sec/veh): h = h0 × (1 + HV%×hv_k) × (1 + |grade%|×grade_k) × (1 + (1−compliance)×comp_k) + ped_delay
Pedestrian delay (sec/veh): ped_delay = (peds/hr × ped_sec) ÷ v
Capacity (veh/h): c = 3600 × lanes ÷ h
Utilization: ρ = v / c
Queue delay (Kingman G/G/1): Wq ≈ (ρ/(1−ρ)) × ((Ca² + Cs²)/2) × (h/lanes)
Control delay (sec/veh): d = Wq + stop_penalty + accel/decel_addon

Important: When ρ ≥ 1, the queue is unstable in this model. The calculator flags oversaturation and caps displayed delay to prevent misleading “infinite” values.

How to use this calculator

Enter hourly approach volumes for north, east, south, and west.
Set PHF to convert counts into demand flow rate.
Choose base headway from observations or conservative defaults.
Adjust heavy vehicles, grade, compliance, and pedestrian crossings.
Press Calculate delay to view results above the form.
Use the CSV/PDF buttons to export your scenario outputs.

Notes for construction planning

For temporary traffic control and work zones, small changes in headway assumptions can strongly affect delay. Consider running multiple scenarios: baseline, constrained geometry, increased heavy vehicles, and higher pedestrian activity.

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