Stochastic Bifurcation in Resource-Constrained Networks: Quantifying Soft-Edge Volatility (SEVI) during Monte Carlo Simulation

Abstract

The application of Monte Carlo simulation to stochastic resource-constrained project scheduling (SRCPSP) relies fundamentally on what we term the Topological Continuity Assumption [1]–the implicit hypothesis that the underlying directed acyclic graph (DAG) structure remains invariant across simulation iterations. We demonstrate that resource-leveling heuristics systematically violate this assumption. We introduce the Soft-Edge Volatility Index (SEVI), a metric quantifying the probability of precedence relation reversal during simulation. Empirical analysis across 10,000 Monte Carlo iterations reveals density-dependent bifurcation: networks exhibit SEVI values approaching unity at sufficient scale, producing multimodal duration distributions that compromise the reliability of standard percentile forecasts. This so-called "Ghost P90" – an 82-day discrepancy between baseline and simulated percentiles at N = 3000 – emerges not from input variance but from topological discontinuity. We demonstrate that applying continuous statistical metrics to discretely bifurcating state-spaces introduces significant methodological limitations in risk quantification, particularly in highly dynamic networks, with implications extending to enterprise-level schedule forecasting under resource constraints.