Predicting Inmate Populations from Arrest, Court Disposition, and Recidivism Rates

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Abstract
Mathematical models, incorporating arrest and indictment rates and conviction and incarceration percentages, are developed for pre dicting the number of inmates incarcerated (before and after sen tence) and on parole. The models are derived from deterministic differential equations arising from a basic input-output analysis of the correction subsystem. The deterministic projection equation is shown to be identical with that for the expected value of the number in service for an infinite server queuing system with exponential ser vice times. Results are also given for the case of general service-time distribution (the M/GI/∞ case). A generalized recidivism rate is incorporated as well as specific feedback from parole. The model applications use data from the criminal justice sys tem in Washington, D.C. Predictions are validated for sentenced inmates in facilities at Lorton, Va., and for presentence detainees at the D.C. Jail. Finally, quantified versions of the models are devel oped for sentenced inmates, parolees, and presentence detainees.

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