Deployment of One- vs. Two-Officer Patrol Units: A Comparison of Travel Times

In this paper we compare the performance of one-officer and two-officer police patrol units using travel time as the measure of performance. We estimate travel times under two different models of dispatch operations. The first model reflects most existing dispatch systems in which patrol units are assigned to specific beats. Under this beat system, the dispatcher does not know the precise location of each police unit, so he often does not dispatch the closest unit. The second model treats a dispatch operation that is supported by an automatic vehicle monitoring system (AVM). With this system, police units can patrol an overlapping region and the closest available unit to a call can always be dispatched. Probabilistic models are used to derive formulae for estimating travel times to calls requiring only one officer (Type 1) and to calls requiring two officers (Type 2) for each of the two dispatch models. We compared the deployment of the same number of officers in either one- or two-officer units over a wide range of unavailability rates. The general findings are summarized as follows: (1) The average travel time of one-officer units to Type 1 calls is at least 30% less than the average travel time of two-officer units. The difference between the two average travel times increases as the unavailability rate increases. (2) The average travel time of the first-arriving one-officer unit at a Type 2 call is at least 40% less than that of the first-arriving two-officer unit. (3) With non-AVM dispatching and normal patrol beats, the difference between the average travel time of the second-arriving one-officer unit and the first-arriving two-officer unit is sensitive to the unavailability rate. For low unavailability rates the two-officer unit is preferred, and for high unavailability rates two one-officer units are preferred. (4) With AVM dispatching and no beats, the average travel time of the second-arriving one-officer unit to a Type 2 call is almost always less than the average travel time of the first-arriving two-officer unit. Again the difference between the two travel times increases as the unavailability rate increases. We also used our models to explore the impact of manpower reductions that might accompany a switch to one-officer units. Our results suggest that the existence of an AVM system can be a critical factor when considering manpower reductions. Without an AVM system, the changeover is likely to have mixed results; shorter average travel times for the first-arriving officer and longer travel times for the second-arriving officer. With an AVM system, it appears that manpower can be reduced in a changeover while reducing the average travel times for both the first- and second-arriving officers. In addition, the results suggest that the existence of an AVM system can significantly affect the average time between the arrival of the first and second one-officer units. This statistic is a measure of the exposure to danger of the first officer to arrive at the scene. Thus, it may be attractive for a police decision-maker to consider the introduction of an AVM system combined with a changeover from two-officer to one-officer units and a manpower reduction. This is one of the few examples in which new technology can be used to reduce the manpower needs of a police department. At the close of the paper some of the results of our analysis are illustrated with an example. For this specific example we estimate travel time statistics for both dispatch models and discuss manpower reductions and tradeoffs among different travel time measures. We conclude with a discussion of future research directions.