This thesis collects two papers proposing systematic frameworks for dynamic (i.e. state dependent) resource allocation in healthcare delivery. The first focuses on disaster response, and the second, on care delivery in an Emergency Department (ED) triage and treatment process. The first paper considers how should Emergency Medical Services (EMS) vehicles be allocated in the aftermath of a catastrophic event. The control of EMS vehicles is modeled as a multi-server parallel queueing system and classical results from the queueing theory literature are used to determine how many vehicles can be made available to the affected region. In addition, we propose that a centralized decision-maker coordinate the transfer of resources from the unaffected region to the affected region. A knapsack model is developed to determine how many vehicles to allocate in the different areas within the affected region and a Markov decision process formulation is developed to dynamically reallocate these added resources within each area until a return to normalcy is achieved. We compare our approach to several other reasonable approaches in a numerical study. The second paper considers how should a medical provider be allocated in a two-phase stochastic service system. To do this, we first propose a single-server tandem queueing model where patients can abandon before receiving treatment during the second phase of service. We then use a Markov decision process formulation and sample path arguments to determine optimal dynamic policies for the medical service provider. In particular, we provide sufficient conditions under which it is optimal to prioritize phase-one service (triage) and sufficient conditions under which it is optimal to prioritize phase-two service (treatment). In addition, we introduce a new class of threshold policies as reasonable alternatives to priority rules. Using data from an actual hospital, we compare the aforementioned policies and several other potential service policies in a simulation study.