摘要 :
In process mining, extensive data about an organizational process is summarized by a formal mathematical model with well-grounded semantics. In recent years a number of successful algorithms have been developed that output Petri n...
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In process mining, extensive data about an organizational process is summarized by a formal mathematical model with well-grounded semantics. In recent years a number of successful algorithms have been developed that output Petri nets, and other related formalisms, from input event logs, as a way of describing process control flows. Such formalisms are inherently constrained when reasoning about the probabilities of the underlying organizational process, as they do not explicitly model probability. Accordingly, this paper introduces a framework for automatically discovering stochastic process models, in the form of Generalized Stochastic Petri Nets. We instantiate this Toothpaste Miner framework and introduce polynomial-time batch and incremental algorithms based on reduction rules. These algorithms do not depend on a preceding control-flow model. We show the algorithms terminate and maintain a deterministic model once found. An implementation and evaluation also demonstrate feasibility.
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摘要 :
In process mining, extensive data about an organizational process is summarized by a formal mathematical model with well-grounded semantics. In recent years a number of successful algorithms have been developed that output Petri n...
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In process mining, extensive data about an organizational process is summarized by a formal mathematical model with well-grounded semantics. In recent years a number of successful algorithms have been developed that output Petri nets, and other related formalisms, from input event logs, as a way of describing process control flows. Such formalisms are inherently constrained when reasoning about the probabilities of the underlying organizational process, as they do not explicitly model probability. Accordingly, this paper introduces a framework for automatically discovering stochastic process models, in the form of Generalized Stochastic Petri Nets. We instantiate this Toothpaste Miner framework and introduce polynomial-time batch and incremental algorithms based on reduction rules. These algorithms do not depend on a preceding control-flow model. We show the algorithms terminate and maintain a deterministic model once found. An implementation and evaluation also demonstrate feasibility.
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摘要 :
In process mining, extensive data about an organizational process is summarized by a formal mathematical model with well-grounded semantics. In recent years a number of successful algorithms have been developed that output Petri n...
展开
In process mining, extensive data about an organizational process is summarized by a formal mathematical model with well-grounded semantics. In recent years a number of successful algorithms have been developed that output Petri nets, and other related formalisms, from input event logs, as a way of describing process control flows. Such formalisms are inherently constrained when reasoning about the probabilities of the underlying organizational process, as they do not explicitly model probability. Accordingly, this paper introduces a framework for automatically discovering stochastic process models, in the form of Generalized Stochastic Petri Nets. We instantiate this Toothpaste Miner framework and introduce polynomial-time batch and incremental algorithms based on reduction rules. These algorithms do not depend on a preceding control-flow model. We show the algorithms terminate and maintain a deterministic model once found. An implementation and evaluation also demonstrate feasibility.
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摘要 :
In process mining, extensive data about an organizational process is summarized by a formal mathematical model with well-grounded semantics. In recent years a number of successful algorithms have been developed that output Petri n...
展开
In process mining, extensive data about an organizational process is summarized by a formal mathematical model with well-grounded semantics. In recent years a number of successful algorithms have been developed that output Petri nets, and other related formalisms, from input event logs, as a way of describing process control flows. Such formalisms are inherently constrained when reasoning about the probabilities of the underlying organizational process, as they do not explicitly model probability. Accordingly, this paper introduces a framework for automatically discovering stochastic process models, in the form of Generalized Stochastic Petri Nets. We instantiate this Toothpaste Miner framework and introduce polynomial-time batch and incremental algorithms based on reduction rules. These algorithms do not depend on a preceding control-flow model. We show the algorithms terminate and maintain a deterministic model once found. An implementation and evaluation also demonstrate feasibility.
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摘要 :
Many algorithms, now exist for discovering process models from event logs. These models usually describe a control flow and are intended for use by people in analysing and improving real-world organizational processes. The relativ...
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Many algorithms, now exist for discovering process models from event logs. These models usually describe a control flow and are intended for use by people in analysing and improving real-world organizational processes. The relative likelihood of choices made while following a process (i.e., its stochastic behaviour) is highly relevant information which few existing algorithms make available in their automatically discovered models. This can be addressed by automatically discovered stochastic process models. We introduce a framework for automatic discovery of stochastic process models, given a control-flow model and an event log. The framework introduces an estimator which takes a Petri net model and an event log as input, and outputs a Generalized Stochastic Petri net. We apply the framework, adding six new weight estimators, and a method for their evaluation. The algorithms have been implemented in the open-source process mining framework ProM. Using stochastic conformance measures, the resulting models have comparable conformance to existing approaches and are shown to be calculated more efficiently.
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摘要 :
Many algorithms, now exist for discovering process models from event logs. These models usually describe a control flow and are intended for use by people in analysing and improving real-world organizational processes. The relativ...
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Many algorithms, now exist for discovering process models from event logs. These models usually describe a control flow and are intended for use by people in analysing and improving real-world organizational processes. The relative likelihood of choices made while following a process (i.e., its stochastic behaviour) is highly relevant information which few existing algorithms make available in their automatically discovered models. This can be addressed by automatically discovered stochastic process models. We introduce a framework for automatic discovery of stochastic process models, given a control-flow model and an event log. The framework introduces an estimator which takes a Petri net model and an event log as input, and outputs a Generalized Stochastic Petri net. We apply the framework, adding six new weight estimators, and a method for their evaluation. The algorithms have been implemented in the open-source process mining framework ProM. Using stochastic conformance measures, the resulting models have comparable conformance to existing approaches and are shown to be calculated more efficiently.
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摘要 :
A multidimensional stochastic process is considered which is a function of a parametric process. The parametric process may be multidimensional as well. Two such processes that differ only in their parametric processes are compare...
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A multidimensional stochastic process is considered which is a function of a parametric process. The parametric process may be multidimensional as well. Two such processes that differ only in their parametric processes are compared. The known stochastic convexity results for one-dimensional stochastic processes, which were developed by M. Shaked and J.G. Shanthikumar (1988), are extended to multidimensional processes. These results are then used to obtain comparison results for various queuing systems that are subject to different processes, which may be the arrival processes, service processes, etc. Based on these comparison results it is shown how the performances of queuing systems can be affected by the variability of parametric processes.
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摘要 :
A multidimensional stochastic process is considered which is a function of a parametric process. The parametric process may be multidimensional as well. Two such processes that differ only in their parametric processes are compare...
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A multidimensional stochastic process is considered which is a function of a parametric process. The parametric process may be multidimensional as well. Two such processes that differ only in their parametric processes are compared. The known stochastic convexity results for one-dimensional stochastic processes, which were developed by M. Shaked and J.G. Shanthikumar (1988), are extended to multidimensional processes. These results are then used to obtain comparison results for various queuing systems that are subject to different processes, which may be the arrival processes, service processes, etc. Based on these comparison results it is shown how the performances of queuing systems can be affected by the variability of parametric processes.
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摘要 :
The system considered in this paper operates with a feedback that is characterized by a gain and a desired final state (DFS), which is the main parameter of interest in the present study. The system is, however, subjected intermit...
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The system considered in this paper operates with a feedback that is characterized by a gain and a desired final state (DFS), which is the main parameter of interest in the present study. The system is, however, subjected intermittently to stochastic inputs according to a Markov process. Since the system operates in two modes | under the feedback to the DFS and under a stochastic input|the Interacting Multiple Model (IMM) estimator is used. Two approaches are considered: (i) the DFS is a discrete-valued random variable | one of a finite number of possible states | with an a priori probability mass function (pmf), and (ii) the DFS is a continuous-valued random variable with an a priori probability density function (pdf). For Approach (i), we use a multiple IMM estimator (MIMM) that features one IMM for each one of the possible DFS. The a posteriori probability of the model for each IMM, i.e., of each DFS, will be computed based on the likelihood function (LF) of the corresponding IMM. For Approach (ii), we design a single IMM to handle the unknown DFS to be estimated (mode M_1), and the random inputs (mode M_2). Simulation results explore several scenarios and investigate the degree of observability of this stochastic problem.
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This paper studies task assignment in a network of resource constrained computing platforms (called microservers). A task is an abstraction of a computational agent or data that is hosted by the microservers. For example, in an ob...
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This paper studies task assignment in a network of resource constrained computing platforms (called microservers). A task is an abstraction of a computational agent or data that is hosted by the microservers. For example, in an object tracking scenario, a task represents a mobile tracking agent, such as a vehicle location update computation, that runs on microservers, which can receive sensor data pertaining to the object of interest. Due to object motion, the microservers that can observe a particular object change over time and there is overhead involved in migrating tasks among microservers. Furthermore, communication, processing, or memory constraints, allow a microserver to only serve a limited number of objects at the same time. Our overall goal is to assign tasks to microservers so as to minimize the number of migrations, and thus be kinetically stable, while guaranteeing that as many tasks as possible are monitored at all times. When the task trajectories are known in advance, we show that this problem is NP-complete (even over just two time steps), has an integrality gap of at least 2, and can be solved optimally in polynomial time if we allow tasks to be assigned fractionally. When only probabilistic information about future movement of the tasks is known, we propose two algorithms: a multi-commodity flow based algorithm and a maximum matching algorithm. We use simulations to compare the performance of these algorithms against the optimum task allocation strategy.
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