The Information Entropy Performance Indicator (IEPI): A Deterministic Analytics Engine for Quantifying Routing Uncertainty in BPMN Process Models

Business Process Management (BPM) models represent routing behavior through control-flow constructs but do not provide a quantitative mechanism for evaluating uncertainty at decision points. This study introduces the Information Entropy Performance Indicator (IEPI) as a deterministic analytics artifact that maps BPMN 2.0 routing structures and externally specified probability assignments to uncertainty-based diagnostics. The IEPI engine takes as input a BPMN 2.0 process representation, a routing-probability map, and predefined viability thresholds, and computes (i) construct-level quantities based on normalized entropy and responsiveness, (ii) block-level propagated uncertainty measures using fixed composition rules, and (iii) a bounded process-level reporting index. The evaluation is conducted on analytically constructed BPMN scenarios with controlled routing configurations and fixed inputs, without reliance on statistical estimation or learning. Results show that construct-level classifications and process-level scores are well-defined and vary deterministically with threshold parameters and routing structure. Sensitivity analysis confirms consistent behavior under controlled parameter variation. The IEPI provides a reproducible analytical mapping from process structure to quantified uncertainty for evaluating routing behavior in BPMN-based models.