NCJ Number
11211
Date Published
1973
Length
133 pages
Annotation
EXPANSION AND OPTIMIZATION OF THE SPATIALLY DISTRIBUTED QUEUING OR 'HYPERCUBE', MODEL USED IN THE DISPATCHING OF EMERGENCY VEHICLES.
Abstract
URBAN EMERGENCY SERVICES, SUCH AS FIRE, POLICE, AND AMBULANCE SYSTEMS, ARE COMPLEX FUNCTIONS NOT READILY DESCRIBED WITH SIMPLE ANALYTIC MODELS. THE OPERATIONAL EFFECTIVENESS OF THESE SYSTEMS DEPENDS ON MANY DIVERSE AND OFTEN CONFLICTING PERFORMANCE CRITERIA. A SPATIALLY DISTRIBUTED QUEUING MODEL, THE 'HYPERCUBE', HAS RECENTLY BEEN PROPOSED AS A TOOL FOR EXAMINING SUCH SYSTEMS. J.P. JARVIS BEGINS HIS TECHNICAL ATTEMPT TO OPTIMIZE THIS METHOD BY PROVIDING A PRECISE FORMULATION OF THE HYPERCUBE MODEL. THE DESCRIPTION IS EXTENDED TO VIEW THE MODEL AS A MARKOV DECISION PROCESS AND SOME SIMPLE EXAMPLES ARE PRESENTED AS ILLUSTRATIONS. THE COMPUTATIONAL EFFORT REQUIRED TO SOLVE THE PROBLEM IS EXAMINED AND FOUND TO BE PROHIBITIVE. THE AUTHOR DETAILS AN EXPANDED MODEL OF THE QUEUING SYSTEM WHICH IS SHOWN TO BE EQUIVALENT TO THE HYPERCUBE MODEL. USING THE EXPANDED DESCRIPTION, A CHARACTERISTIC OF THE OPTIMAL POLICY IS FOUND WHICH GREATLY REDUCES THE SIZE OF THE PROBLEM. A GEOGRAPHIC INTERPRETATION OF THE RESULT IS GIVEN. THE CHARACTERIZATION OF THE OPTIMAL POLICY IS COMPARED TO AN ANALYTIC RESULT DEVELOPED FOR A TWO SERVER SYSTEM. THE USE OF THE MODEL IN SOLVING A SAMPLE PROBLEM IS DESCRIBED. ALTERNATE FORMULATIONS OF THE PROBLEM STRUCTURE ARE DISCUSSED IN TERMS OF THE IMPLEMENTATION OF A COMPUTER PROGRAM TO SOLVE THE MARKOV DECISION PROBLEM. THE USEFULNESS OF THE OPTIMIZATION IS EXAMINED IN TERMS OF ITS EFFECT ON VARIOUS PERFORMANCE MEASURES FOR THE SAMPLE PROBLEM. THE REPORT CONCLUDES WITH A SUMMARY OF THE BASIC RESULTS AND CONCLUSIONS REGARDING THE USEFULNESS OF THIS APPROACH TO DESCRIBING URBAN SERVER SYSTEMS. (AUTHOR ABSTRACT MODIFIED)