Queueing Analysis and Cost Optimization in a Diagnostic--Treatment Hospital Queue with Heterogeneous Referred Patients

Shobha Rani; Rohit Dehru; Raghu Nandan Sengupta

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arXiv · 2608.07967

Queueing Analysis and Cost Optimization in a Diagnostic--Treatment Hospital Queue with Heterogeneous Referred Patients

Shobha Rani·Rohit Dehru·Raghu Nandan Sengupta

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Abstract

This study develops an analytical and decision framework for a pooled hospital service comprising first-time patients who require diagnosis followed by treatment and referred patients who require only their prescribed treatment mode. The system is represented as a Markovian phase-type queue. probability generating functions are derived for two-treatment cases, while a matrix-analytic method is developed for an arbitrary number $n$ of treatment modes. The key performance measures are derived and interpreted. A load-triggered control is designed to determine the minimum capacity increment required to achieve a prescribed utilization level. Numerical experiments are conducted to validate the analytical results. Furthermore, the total-cost problem admits a strictly convex reformulation in reciprocal service-time variables and has a unique global minimum. Particle Swarm Optimization (PSO), Simulated Annealing (SA), and the Sine Cosine Algorithm (SCA) are additionally used as independent heuristic solvers.

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Shobha Rani, Rohit Dehru, Raghu Nandan Sengupta. 2026-08-08. Queueing Analysis and Cost Optimization in a Diagnostic--Treatment Hospital Queue with Heterogeneous Referred Patients. https://arxiv.org/abs/2608.07967

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