The problem of blood delivery has been a critical concern in past decades. However, the unsteady behavior of blood donors, along with the uncertainties associated with demands in a crisis imposes several challenges for resource management. In this research work, we analyze the blood delivery behavior in a crisis modeled by coupled queues of patients and blood sources. Using Markovian modeling and results associated with G-network, we derive two critical probabilities, namely lack of unit of blood (unit of donations) or not having any storage capacity left to accept new donors' blood. We propose a closed-form solution to calculate the optimal blood storage size, and also we suggest sufficient conditions that guarantee the feasibility of the model. Finally, we conduct a sensitivity analysis to investigate the impact of model parameters on storage size and the proportion of time that storage is full.