MARKOV MODELS OF FIXED-POST SENSOR AVL (AUTOMATIC VEHICLE LOCATION) SYSTEMS (FROM POLICE AVM (AUTOMATIC VEHICLE MONITORING) SYSTEM - PHASE 2 EVALUATION 1978, BY G C LARSON AND J W SIMON - SEE NCJ-64852)

• NCJ Number: 64854
• Author(s): R C LARSON
• Date Published: 1977
• Length: 56 pages
• Grant Number(s): 76-NI-99-0095
• Sponsoring Agency: US Dept of Justice; US Dept of Justice NIJ Pub
• Corporate Author: Public Systems Evaluation, Inc
• Publication Format: Document
• Language: English
• Country: United States of America
• Note: APPENDIX B

Annotation

A CLASS OF MODELS SUITABLE FOR MODELING ONE IMPORTANT ERROR CHARACTERISTIC OF FIXED-POST SENSOR SYSTEMS OF AUTOMATIC VEHICLE MONITORING (AVM) IS INTRODUCED AND DEVELOPED USING MARKOV PROCESSES.

Abstract

AVM SYSTEMS HAVE BEEN ESTABLISHED IN BOTH THE UNITED STATES AND EUROPE. A FIXED-POST SENSOR SYSTEM IS CHARACTERIZED BY A NUMBER OF PROXIMITY SENSORS LOCATED AT A PARTICULAR FRACTION OF CITY INTERSECTIONS. EACH SENSOR DETECTS THE PRESENCE OF A VEHICLE ENTERING THE INTERSECTION. BETWEEN PASSINGS OF THE INTERSECTIONS, NO ADDITIONAL POSITION INFORMATION IS AVAILABLE. AT ANY GIVEN TIME THE VEHICLE'S ESTIMATED LOCATION IS THE LAST SENSOR-EQUIPPED LOCATION THROUGH WHICH THE VEHICLE HAS PASSED. TIME (OR DISTANCE TRAVELED) BETWEEN SUCCESSIVE PASSINGS OF SENSORS IS AN IMPORTANT RANDOM VARIABLE WHICH CHARACTERIZES SYSTEM PERFORMANCE; THE LONGER THIS TIME, THE LESS ACCURATE IS THE LAST RECORDED SENSOR EQUIPPED INTERSECTION AS AN ESTIMATE FOR THE VEHICLE'S CURRENT LOCATION. THE MODELS PRESENTED HERE PROVIDE PROCEDURES FOR ANALYZING ALTERNATIVE SENSOR LAYOUTS TO SELECT THE ONE THAT MINIMIZES TIME BETWEEN SENSOR PASSINGS. A GENERAL EXAMPLE ASSUMES THAT THE CITY IS AN INFINITE REGULAR GRID OF TWO-WAY STREETS AND USES MARKOV PROCESSES TO MODEL THE DYNAMICS OF VEHICLE TURNING BEHAVIOR. BY EXAMINING A SUBSET (KERNEL) OF THE INFINITE LATTICE AND INVOKING TURNING PROBABILITIES GENERATED FROM FIELD STUDY, A FINITE STATE MARKOV PROCESS GOVERNING THE VEHICLE'S MOVEMENT CAN BE GENERATED. THE SIX FOLLOWING SENSOR LAYOUTS ARE THEN DESCRIBED AND ANALYZED: REGULAR SQUARE LATTICE, DIAGONAL WALLS OF SENSORS, DIAMOND LATTICE, VERTICAL WALLS OF SENSORS, SQUARE CENTER SYSTEM, AND RANDOM (UNPLANNED) SYSTEM. FOR EACH SYSTEM, THE CORRESPONDING MARKOV MODEL IS DEVELOPED. NEXT, SYSTEM PERFORMANCES ARE COMPARED USING THE COEFFICIENT OF VARIATION AS THE PERFORMANCE MEASURE. ANALYSIS SHOWS THAT DESIGNS OTHER THAN THE SQUARE LATTICE ARE SUPERIOR FOR A RANGE OF TURN PROBABILITY VALUES THAT PROBABLY CHARACTERIZES MOST OPERATING URBAN SYSTEMS. FUTURE RESEARCH SUGGESTED INCLUDES DEVELOPING ADDITIONAL MODELS USING A HOMOGENEOUS INFINITE CITY GRID, MODELING A CITY'S ACTUAL STREET AND VEHICULAR FLOW PATTERNS, OR FOCUSING ON THE PERFORMANCE OF THE AVM DISPATCHING OR CONTROL SYSTEM. FIGURES, FOOTNOTES, AND A REFERENCE LIST ARE PROVIDED. FOR RELATED DOCUMENTS, SEE NCJ 64852-53. (CFW)