Performance evaluation of an emergency call center: tropical polynomial systems applied to timed Petri nets

We analyze a timed Petri net model of an emergency call center which processes calls with different levels of priority. The counter variables of the Petri net represent the cumulated number of events as a function of time. We show that these variables are determined by a piecewise linear dynamical system. We also prove that computing the stationary regimes of the associated fluid dynamics reduces to solving a polynomial system over a tropical (min-plus) semifield of germs. This leads to explicit formul{\ae} expressing the throughput of the fluid system as a piecewise linear function of the resources, revealing the existence of different congestion phases. Numerical experiments show that the analysis of the fluid dynamics yields a good approximation of the real throughput.Comment: 21 pages, 4 figures. A shorter version can be found in the proceedings of the conference FORMATS 201

Satellite inventory of Minnesota forest resources

The methods and results of using Landsat Thematic Mapper (TM) data to classify and estimate the acreage of forest covertypes in northeastern Minnesota are described. Portions of six TM scenes covering five counties with a total area of 14,679 square miles were classified into six forest and five nonforest classes. The approach involved the integration of cluster sampling, image processing, and estimation. Using cluster sampling, 343 plots, each 88 acres in size, were photo interpreted and field mapped as a source of reference data for classifier training and calibration of the TM data classifications. Classification accuracies of up to 75 percent were achieved; most misclassification was between similar or related classes. An inverse method of calibration, based on the error rates obtained from the classifications of the cluster plots, was used to adjust the classification class proportions for classification errors. The resulting area estimates for total forest land in the five-county area were within 3 percent of the estimate made independently by the USDA Forest Service. Area estimates for conifer and hardwood forest types were within 0.8 and 6.0 percent respectively, of the Forest Service estimates. A trial of a second method of estimating the same classes as the Forest Service resulted in standard errors of 0.002 to 0.015. A study of the use of multidate TM data for change detection showed that forest canopy depletion, canopy increment, and no change could be identified with greater than 90 percent accuracy. The project results have been the basis for the Minnesota Department of Natural Resources and the Forest Service to define and begin to implement an annual system of forest inventory which utilizes Landsat TM data to detect changes in forest cover

Testing real-time systems using TINA

The paper presents a technique for model-based black-box conformance testing of real-time systems using the Time Petri Net Analyzer TINA. Such test suites are derived from a prioritized time Petri net composed of two concurrent sub-nets specifying respectively the expected behaviour of the system under test and its environment.We describe how the toolbox TINA has been extended to support automatic generation of time-optimal test suites. The result is optimal in the sense that the set of test cases in the test suite have the shortest possible accumulated time to be executed. Input/output conformance serves as the notion of implementation correctness, essentially timed trace inclusion taking environment assumptions into account. Test cases selection is based either on using manually formulated test purposes or automatically from various coverage criteria specifying structural criteria of the model to be fulfilled by the test suite. We discuss how test purposes and coverage criterion are specified in the linear temporal logic SE-LTL, derive test sequences, and assign verdicts

Synthesis of Bounded Integer Parameters for Parametric Timed Reachability Games

International audienc

Integer Parameter Synthesis for Timed Automata

International audienceInteger Parameter Synthesis for Timed Automat