New Developments in Closed-Form Computation for GSPN Aggregation
New Developments in Closed-Form Computation for GSPN Aggregation
复制标题
GSPN 聚合闭式计算的新进展
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
J. Billington
中科院分区：
文献类型：
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作者：
J. Freiheit;J. Billington
Petri网对于复杂并发系统的建模非常有用。使用Petri网的建模侧重于局部状态和动作，而分析方法则关注全局状态及其转换。完全状态空间的生成存在众所周知的状态空间爆炸问题。提出了一种克服一类广义随机Petri网（gspn）状态空间爆炸问题的方法。将大型复杂GSPN模型转化为比原始模型更小、更简单、状态空间更小的模型。这种转换称为聚合。聚合的目的是减少状态空间，同时保留原始模型的期望行为。在本文中，我们利用最近的[5,6]和新开发的变换规则研究了gspn保持时间依赖行为的聚合。这些规则用于将多个单定时转换合并为一个合并转换。合并跃迁的发射速率取决于网的标记。除了引入一种固定射速的指数跃迁聚合新方法外，还给出了与射速相关的指数跃迁聚合新公式。连续聚合可以将非常复杂的模型转换为可以使用稳态分布的封闭形式计算或具有非常小的状态空间的模型。通过一个原型实现演示了该方法对合适模型的状态空间的大幅缩减以及该方法的一般限制。
Petri nets are useful for modelling complex concurrent systems. While modelling using Petri nets focusses on local states and actions, the analysis methods are concerned with global states and their transitions. Unfortunately generation of the complete state space suffers from the well-known state space explosion problem. This paper presents a method to overcome the state-space explosion problem for a class of Generalised Stochastic Petri Nets (GSPNs). Large complex GSPN models are transformed into smaller, less complex ones with smaller state spaces than the original models. This transformation is called aggregation. The aim of aggregation is to reduce the state space while preserving the desired behaviour of the original model. In this paper we investigate the aggregation of GSPNs preserving time dependent behaviour by using recent [5,6] and newly developed transformation rules. These rules are used to merge several single timed transitions into one merged transition. The firing rate of the merged transition turns out to be dependent on the marking of the net. Beside the introduction of a new method for the aggregation of exponential transitions with fixed firing rates, new formulae to aggregate transitions with marking-dependent firing rates are presented. Successive aggregation becomes possible to transform very complex models into models in which either a closed-form computation of the stationary state distribution is available or which has a very small state space. A prototype implementation is used to demonstrate both the drastically reduced state space for suitable models and the general limits of the method.