New and exciting opportunities are emerging for operational researchers to create and use models that provide managers with solutions to enhance the quality of their services as the importance of the service sector grows in industrialized countries. The key to this process is the creation of time-dependent models that analyze complicated service systems and produce efficient staff schedules, allowing organizations to strike a balance between delivering high-quality services and avoiding unnecessary personnel costs. There is a need, particularly in the healthcare sector, to encourage effective management of an EMS, where the likelihood of survival is strongly correlated with the response time.Motivated by case studies investigating the operation of the Emergency Medical System (EMS), this dissertation aims to examine how operations research (OR) techniques can be developed to determine staff scheduling and maximize the ambulance to decrease service system delays. A capacity planning tool is developed that integrates a combination of queueing theory and optimization techniques to reduce the delay in the service system and maximize ambulance coverage. The research presented in this dissertation is novel in several ways. Primarily, the first section considers the Markovian models with sinusoidal arrival rates and state-dependency of service rate and uses a numerical method known as Stationary Independent Period by Period (SIPP) to determine the staff requirement of the service system. The final section considers the time dependency in locating an ambulance station across the network and allocating the ambulance to the patients to cover more 911 calls.