The Surface Hold Advisor Using Critical Sections is a system and method for providing hold advisories to surface controllers to prevent gridlock and resolve crossing and merging conflicts among vehicles traversing a vertex-edge graph representing a surface traffic network on an airport surface. The Advisor performs pair-wise comparisons of current position and projected path of each vehicle with other surface vehicles to detect conflicts, determine critical sections, and provide hold advisories to traffic controllers recommending vehicles stop at entry points to protected zones around identified critical sections. A critical section defines a segment of the vertex-edge graph where vehicles are in crossing or merging or opposite direction gridlock contention. The Advisor detects critical sections without reference to scheduled, projected or required times along assigned vehicle paths, and generates hold advisories to prevent conflicts without requiring network path direction-of-movement rules and without requiring rerouting, rescheduling or other network optimization solutions.