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The psychological refractory period (PRP) is a basic but important form of dual-task information processing. Existing serial or parallel processing models of PRP have successfully accounted for a variety of PRP phenomena; however, each also encounters at least 1 experimental counterexample to its predictions or modeling mechanisms. This article describes a queuing network-based mathematical model of PRP that is able to model various experimental findings in PRP with closed-form equations including all of the major counterexamples encountered by the existing models with fewer or equal numbers of free parameters. This modeling work also offers an alternative theoretical account for PRP and demonstrates the importance of the theoretical concepts of “queuing” and “hybrid cognitive networks” in understanding cognitive architecture and multitask performance.