Graph-theoretic Modeling of Multi-echelon Queueing-inventory Systems with Node and Edge Dependencies
ANUSHA A K
*
Department of Mathematics, Maharaja’s College, Ernakulam, Kerala, India.
*Author to whom correspondence should be addressed.
Abstract
Multi-echelon supply chains and inventory networks are inherently complex, characterized by stochastic demand, variable lead times, and interdependent transportation links. Traditional queueing–inventory models often assume independence among nodes and edges, limiting their applicability in realistic, interconnected supply networks. In this study, we develop a graph-theoretic framework for multi-echelon queueing–inventory systems, where nodes represent warehouses, suppliers, or retailers and edges represent stochastic transportation or information flows with temporal correlations.
By integrating queueing theory, stochastic inventory control, and graph spectral analysis, the framework captures propagation of demand signals, stockouts, and service delays throughout the network, enabling the identification of critical bottlenecks and optimization of inventory allocation. Simulation results demonstrate that the model effectively accounts for node and edge dependencies, reflecting how upstream disruptions or fluctuating lead times influence downstream inventory levels and service performance.
The proposed methodology provides actionable insights for complex logistics systems, including shipyards, multi-warehouse distribution networks, and manufacturing supply chains, supporting resilient, efficient, and responsive inventory management strategies under uncertainty.
Keywords: Multi-echelon inventory, queueing networks, graph theory, stochastic dependencies, network optimization, supply chain management, spectral analysis