Intro: A new Advanced Queueing Mechanism (AQM) powered by AI for telemedicine triage and doctor assignment promises smarter scheduling and lower costs, backed by real data and simulations.

Methodology: The approach fuses AI triage classification, reinforcement learning (Q-learning), time-dependent differential equations, and classical queueing theory to model triage and doctor queues.

Context: There is a literature gap in real-time, adaptable telemedicine queue management that ties assessments directly to pricing dynamics and scheduling.

Data and setting: Validation uses 48 hours of DHRC Hospital Jaipur data covering patient arrivals, triage levels, and doctor availability.

Cost efficiency and validation: A cost-benefit analysis, paired t-tests, and simulations indicate AI-driven scheduling reduces wait times and improves resource utilization.

Research aim: Develop an Advanced Queueing Mechanism (AQM) integrated with AI-driven smart scheduling to optimize triage, doctor assignment, resource use, and overall costs.

Q-learning specifics: The update rule and parameters—learning rate alpha, discount factor gamma, and exploration rate epsilon—drive adaptive doctor allocation across Emergency, Moderate, and Routine queues.

Implementation: A Python-based methodology simulates queues, applies Q-learning, and evaluates performance across scenarios.

Mathematical formulation: Stepwise ODE-based queue dynamics for triage and doctor queues, with a RL component that uses state, action, reward, policy, and Q-function; rewards reflect wait time, delays, and rejections.