Modeling prison populations

Various stochastic models such as the transient and steady state versions of the infinite server queueing system are employed for the representation of the input-output dynamics of correctional institutions. These models determine in stochastic terms the ensuing prison population size that occurs after perturbations in the values of certain parameters have been made. The parameters are: the average inmate admission rate, the average time of incarceration, the elapsed time, and the initial number of inmates. The models’ quantitative results are reported in the form of probabilities of intervals of two standard deviations about the mean of prison population size. Because of the models used, the prison population size is not normally distributed, nevertheless, it is shown that this random variable can be considered approximately normally distributed.