A procedure for dispatching moving mobile servers

This article deals with some dispatching aspects of a system in which the dispatcher, in addition to stationary service units, has also the option to assign service units in motion. The nonstationary servers leave their home location at different times and move on different paths. The response time is the shortest time path of a server from the incident. The objective is to identify efficiently the appropriate unit to dispatch to a random incident. The analysis ends as soon as one of the servers is dispatched. The paper contains an efficient procedure based on the notion of the general time path. The general time path is a single path in which we superimpose the various different paths of all the moving servers. This simplifies the analysis since once the general time path is constructed it contains all the information that is provided by all those different paths. The procedure shows how to divide the general time path to disjoint segments according to the server which is closest to the incident (in each one of the segments exactly one identifiable server is closest to the incident).