A note on the square root law for urban police travel times

Abstract

The classical Square Root Law formula for emergency travel times consists of one observable component, the density of patrol coverage, and one unknown component that must be estimated empirically, the effective travel speed. The effective travel speed is typically assumed to be an empirical constant. We test whether this simplifying assumption is justified empirically. We propose a modern machine-learning approach and a Least Absolute Shrinkage and Selection Operator regression to incorporate into a travel speed model various exogenous factors such as call type, incident location, weather conditions and traffic congestion. The value of the proposed analytical approach and some practical implications are demonstrated using operational data from a large urban police jurisdiction based in British Columbia, Canada. Although the analysis is framed within the context of urban emergency police operations, the proposed approach has the potential to be useful for other emergency services or roving business units that deal with unscheduled service calls.

Keywords:

• artificial intelligence
• manpower planning
• practice of OR
• regression
• traffic
• urban studies

Acknowledgements

The research assistance provided by Alex Eastwood and Correen Yedon is gratefully acknowledged. The authors are also appreciative of the insightful feedback and suggestions provided by Tim Szkopek-Szkopowski and two anonymous referees on an earlier version of the manuscript.

Notes

1 The other five topics were computerized information systems, effectiveness measures for crime prevention programs, other measures of police effectiveness, promotional standards for sworn officers, and surveys of public attitudes towards police.