Optimizing queueing systems with metaheuristics: a comparative analysis of genetic algorithms and traffic flow inspired optimization

Abstract

Queueing system inefficiencies present critical operational challenges in service industries, particularly in healthcare where extended patient wait times and suboptimal resource utilization directly impact service quality and operational costs. While traditional analytical models (e.g., M/M/1, M/M/c) offer theoretical solutions, they frequently fail to accommodate dynamic real-world complexities. This study comparatively evaluates two metaheuristic approaches the established Genetic Algorithm (GA) and the novel Traffic Flow Inspired Optimization Algorithm (TFIOA), which models adaptive behaviors observed in transportation systems to optimize physician scheduling at Baquba Hospital’s Internal Medicine Clinic. Using empirical patient arrival and service time data collected over three-hour operational windows, we implemented both algorithms across three physician allocation scenarios (1-3 doctors). Performance was assessed through five metrics: patient waiting time, physician idle time, convergence rate, computational cost, and total operational expenditure. Results demonstrate TFIOA’s superior performance, achieving a 9.96% improvement in optimal solutions, 11.02% reduction in average costs, 33.6% faster convergence, and 17.1% higher success rate compared to GA. The dual objective cost function effectively balanced patient and physician time considerations, enabling practical policy evaluation. While TFIOA shows significant promise for realtime queue management, this study is limited by its single clinic focus and condensed observation period. Future research should validate these findings across diverse healthcare settings and extended timeframes.