Parallel Application Scheduling Model Based on Petri Net with Changeable Structure

In Parallel computing environments, each user can submit his job that is represented as a workflow composed of tasks that require multiple types of computational resources. How to develop a mechanism that ensures the success of these workflows is a challenging issue because the resources they use are dynamic and heterogeneous. In order to schedule these workflows conveniently, a model is needed to describe them in a simple, intuitive way. Script-based method is a simple way to describe workflows. However, because those scripts often consist of so many elements with complex syntax that the users cannot understand them quickly. The graphic description for a workflow is an intuitive way, such as directed acyclic graph (DAG) and Petri Net. Compared to scriptbased descriptions, DAG is easier to use and more intuitional. However, DAG offers only a limited expressiveness [1], e.g. loops cannot be expressed directly. Moreover, as DAG only has a single node type, data flowing through the net cannot be modeled easily. Petri net [2] is a modeling tool used for modeling discrete, dynamic, parallel and asynchronous system. Because of the function of simple graphical description and interpretation ability, Petri net is widely used for system modeling and performance analysis in recent years. Many researches have already introduced this method to model workflow [3-5]. In this paper, we model scheduling nets and job nets based on Petri Net techniques. To be convenient to analyze the performance of parallel jobs and to make net models compact and intuitional, we separate the scheduling net from the job net and model them respectively. A hierarchical colored Petri Net is proposed for the scheduling net that is designed into four levels according to the granularity of parallel applications. The hierarchical scheduling model makes each level scheduling only pay attention to its responsibility and it can reduce the structure complexity of the scheduling net at the same time. This paper also designs a extended Petri net with changeable structure for the job net model, which can change its structure dynamically according to the real-time state of running job. This model supports the mergence and division of subtasks and has ability to deal with the abnormity of subtasks. The models are validated with reachability tree techniques and their performances are analyzed with transition trees.