Queueing Network Modeling of Mental Architecture, Response Time, and Response Accuracy: Reflected Multidimensional Diffusions

Response time (RT) and response accuracy are two of the most commonly used performance measures in cognitive psychology and studies of cognitive architecture. This paper examines the relationship and establishes a bridge between two currently separated groups of mathematical models of RT: models of RT and mental architecture and models of RT and accuracy. The bridge, called QN-RMD, is established by extending the queueing network (QN) architecture model of RT (Liu, 1996), which has successfully integrated a large number of RT-architecture models as special cases, and by representing the state changes in a mental QN as Reflected Multidimensional Diffusions (RMD). More specifically, the “state” of a K-server QN mental architecture is represented as a reflected diffusion space of K dimensions, in which “reflecting barriers” represent and reveal architectural constraints, while “absorbing barriers” represent accuracyrelated response criteria, analogous to diffusion models of RT. This approach moves beyond the current 1-D diffusion models that have successfully accounted for but are limited to single-stage fast responses. 1-D diffusions can only represent the “state” of a single server system in stochastic information accumulation, not multi-server architectures. This approach extends the architectural RT models to account for accuracy, brings the diffusion/accumulator models to the architectural domain, and unifies RT/accuracy/mental architecture modeling in a larger framework.