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• W14550196 abstract "In the last few years computers have become a much larger part of our daily lives. Because of this it has also gotten more important for computer programs to be correct. Nobody would want the medical software in hospitals to be incorrect. If such software has to be patched or recalled because it is incorrectly working, it can cost a large amount of money to fix the flaws in the software. Using computer models and so called model checkers, it has become possible to verify if a computer model is working as intended or not. However due to the complexity or size of certain computer models it becomes hard to completely verify if a computer program does what it is supposed to do. Simulation can help in this case. In simulation we run a model several thousands of times and see whether or not certain failures occur. Statistical tests on the results can be done to see how often a failure occurs. A problem arises when the probability of a certain failure occurring is very low (a rare event). When rare events are present it could take a very large number of simulation runs before the rare event is even perceived. This is where importance sampling comes in. With importance sampling we increase the probability that a certain failure is triggered so we can reduce the number of simulation runs needed to make an accurate estimate. Afterwards the result is multiplied with a factor to account for the error we create when increasing the probability that a certain failure is triggered. Importance sampling can be applied on a wide number of models. Known techniques such as failure biasing are already applied on models like Discrete/Continuous Time Markov Chains. We have worked on techniques to apply importance sampling on a class of models called probabilistic timed automata (PTA). We used a number of different papers as our basis, however the semantics and definitions of PTA in these papers were not always clear to us. There were also a number of discrepancies between the papers. Due to these definition problems, we had to perform proper research into the true workings of these PTA during simulation in order to apply importance sampling on them. We found out that semantics and underlying probability distributions normally used for simulating PTA were not behaving as we would expect and that there were several different versions of PTA defined by different people. We supply updated definitions on the real semantics of PTA later on in this thesis. We also supply a number of alternative distributions for simulation of PTA. These alternative distributions behave more logically in our eyes than the distributions used for simulating PTA mentioned in the papers we researched. Another problem was the flexible behavior of timed automata which resulted in the fact that timed automata can cause a range of different kinds of rare events trough for examples very low probabilities on edges, small waiting times (delays), the flexible behavior of the model-checker Uppaal, via networks of PTA influencing other PTA and more. Each kind of rare event possibly requires a different approach in applying importance sampling. We limited ourselves during this master project to only the most important kinds of rare events; rare events caused by the distributions attached to locations and rare events caused by branching edges. We altered a specific importance sampling technique called failure biasing, in which the probabilities of certain edges towards (rare) locations are increased in Discrete/Continuous Time Markov Chain models, in order to apply importance sampling on PTA by performing a number of case studies. We also developed a technique called delay biasing in which we calculate the probability that a certain edge is taken by letting the model wait a specific amount of time, and increase said probability if necessary, also in order to apply importance sampling on a number of case studies. On the case studies we performed for both delay biasing and failure biasing we have seen some good results that show that importance sampling could be a viable alternative and an improvement to regular simulation. Unfortunately we have also seen results where the estimates were incorrect when wrongfully applying importance sampling. This showed that our developed failure biasing technique does not necessarily have to be correct. Both delay biasing and failure biasing were implemented in a Java program capable of simulating PTA, which we named MISS: Marco’s Importance Sampling Simulator for PTA. By using the MISS tool we can simulate PTA via regular Monte Carlo simulation and via importance sampling. Some restrictions do have to be made before the MISS tool can simulate a PTA. As input a specially prepared PTA is taken, created in Uppaal. The estimate of the probability to reach a failure location is given as output. We used the MISS tool to simulate a number of case studies." @default.
• W14550196 created "2016-06-24" @default.
• W14550196 creator A5037001194 @default.
• W14550196 date "2013-01-01" @default.
• W14550196 modified "2023-09-27" @default.
• W14550196 title "Importance sampling for probabilistic timed automata" @default.
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