Applications of queuing theory to some problems in neuronal circuitry*

摘要

This paper discusses mathematical models for neurons and neuron-pair networks. Models are developed in which the parameters are related to basic physiological properties. Single-neuron models are treated first. The membrane-potential decay is modeled as a linear function, making it analogous to the virtual waiting time in a queue. Both spatial and temporal summation are incorporated into the model. Networks consisting of two neurons are then analyzed. It is shown that even though each neuron generates a renewal process, the interaction of the spike trains produces a nonrenewal process. A feedback inhibitory network is found to generate a bursting pattern of spikes. Expressions for the interspike-interval density function and the serial correlogram are derived based on the points of regenerating in the process, and verified by computer simulation. Finally, the feedback neuron-pair model is applied to spike-train data from the hippocampus of a rabbit.