How it's built
Both trips start where the Turnpike and the Parkway split at exit 11. The GWB leg runs 31.5 miles up the Turnpike to the Manhattan end of the bridge (31.5 min with no traffic). The Tappan Zee leg runs 55 miles up the Garden State, the Parkway connector, and the Thruway to the Tarrytown landing (52 min).
On the New York side, a hand-built network of about 120 highway segments (Cross Bronx, Deegan, Thruway, Henry Hudson, Saw Mill, Bronx River, Sprain, Hutch, I-95, I-287, I-684, Taconic, 9A, US-9) carries each trip to the exit nearest the destination, and local streets finish it at 13 mph in the Bronx, 18 to 23 mph in southern and central Westchester, and 29 mph up north, with a 35% detour factor.
The map is crude on purpose: interchange positions are approximate, tolls are ignored, and the Palisades Parkway and Bear Mountain Bridge are left out.
Where the traffic numbers come from
The delay assumptions are loose calibrations, not measurements. Reported NY-bound GWB congestion runs 30 to 35 minutes from I-95 to the Alexander Hamilton Bridge, against about 6 minutes clear, and incidents push it near two hours (Patch, Patch). INRIX ranks the Cross Bronx the most congested corridor in the country, averaging 9.8 mph in its congested hours and costing about 29 minutes a trip (NBC New York, NY Sun). Mario Cuomo Bridge crashes can back traffic up seven miles (CBS New York), but day-to-day spikes there are smaller.
The GWB being spikier is built into these inputs. The map shows what follows from that assumption. It cannot confirm the assumption itself.