This dissertation addresses key operational challenges in telemedicine through stochastic modeling, with applications that extend beyond healthcare to domains such as customer service, technical support, manufacturing, supply chains, and logistics. The first part presents a simulation-based framework for designing and evaluating physician staffing policies across CVS minute clinic networks. Modeling a nationwide telemedicine system, we construct national staffing policies and compare strategies under restrictive versus flexible state regulations. The subsequent chapters model patient–provider interactions as a Markov Decision Process within a two-stage queueing system with holding costs. After an initial screening, a nurse practitioner must decide whether to proceed independently or collaborate with a general physician (GP)---a more comprehensive option that offers higher service quality but may involve delays due to limited GP availability. We analyze the structural properties of optimal policies and identify conditions under which collaborative care is preferred. To support practical implementation, we develop scalable, accurate, and robust heuristics that achieve near-optimal performance and consistently outperform existing benchmarks across a broad range of system parameters. Together, these contributions offer actionable guidance for healthcare providers, policymakers, and other stakeholders. Applications include regulatory design, operational policy development, workforce planning, resource allocation, and strategic telemedicine investments. The findings support more effective and efficient care delivery in hybrid service systems that combine autonomous and collaborative components.