Development of a parametric-decomposition methodology for solving queueing networks with simultaneous resource possession under capacity restrictions

Motivated by applications in health care systems, this study focused on queueing network models with instances of simultaneous resource possession under capacity restrictions in different stages. Customers during service at certain nodes in the first-level or primary system may simultaneously need service from a second-level server. In this simultaneous resource possession situation, the time the customer spends waiting for the second-level server will impact the overall service time at first-level server and consequently the performance of the entire system. Closed queueing networks and fork/join approximations for one and two-stage systems were used to capture the capacity restriction effects in different sections of the primary system. An iterative algorithm was developed to incorporate the effect of the second-level server on the performance of the entire system. This study used a modular approach rooted in the parametric-decomposition method and two-moment approximations. Different systems showing the proposed building blocks and their combinations to solve more complex systems illustrated the application of the proposed modeling approach.To evaluate the performance prediction accuracy of the solution algorithms, the analytical results were compared to simulation estimates for several configurations with single and multi-server nodes, a wide range of service time variability, and different levels of capacity constraints. The analytical results tracked the simulation estimates well with errors less than 10% in more than 80% of the configurations simulated. Higher errors in the 15% to 20% range were observed for system with low capacity limits, high service time variability (SCV=2), and high demand (p=0.75) for the second-level server