Influenza A viruses (IAV) have been the cause of several influenza pandemics in history and are a significant threat for the next global pandemic. Hospitalized influenza patients often have excess interferon production and a dysregulated immune response to the IAV infection. Obtaining a better understanding of the mechanisms of IAV infection that induce these harmful effects would help drug developers and health professionals create more effective treatments for IAV infection and improve patient outcomes. IAV stimulates viral sensors and receptors expressed by alveolar epithelial cells, like RIG-I and TLR3. These two pathways coordinate with one another to induce expression of type III interferons to combat the infection. Presented here is a queuing theory-based model of these pathways that was designed to analyze the timing and amount of interferons produced in response to IAV ssRNA and dsRNA detection. The model accurately represents biological data showing the necessary coordination of the RIG-I and TLR3 pathways for effective interferon production. This model can serve as the framework for future studies of IAV infection and identify new targets for potential treatments.