Police patrol policies on motorways with unequal patrol lengths

On motorways, and other roads with limited access, emergencies arise which require the presence of police, ambulance, rescue services and breakdown trucks. Of these, only the police make regular patrols of the road; other emergency vehicles are static. The regular police patrols arise because their role is to satisfy multiple objectives, some of which depend on being seen to be mobile. For responding to emergencies these patrols need to be coordinated so that assistance can be supplied as quickly as possible. It is common practice to divide a long motorway into separate stretches of roadway, and assign one vehicle to each. Published analysis of the problem of finding an optimal assignment of patrols to roadway has assumed that these stretches are equal in length. This paper extends earlier work to examine the consequences of having unequal lengths of road. It considers measures of effectiveness and their sensitivity to the choice of divisions of the roadway.