Analysis of Petri net based scheduling models

Abstract

Scheduling based on specialised scheduling models is one of the main stages of project management. It allows setting deadlines, budgeting, optimising resource allocation, identifying risks, implementing proactive risk management, and improving quality performance. This article discusses interrelated projects represented by scheduling network models. It also proposes mechanisms to study scheduling network models when some parameters of work are stochastic. The mechanisms developed within the study involve the analysis of critical paths of scheduling graphs with the help of coloured Petri nets with predicate transitions and specific markings represented by functions of random variables. Petri nets tools allow building models to describe project dynamics and to simulate the execution of jobs within the project schedule under certain restrictions or resource allocation rules. The resources allocated for jobs are assumed to be random variables, while time and the quality are functions of these random variables. Each job resource has sets value ranges, which, under certain assumptions about the distribution law, allow obtaining characteristics of the resources and their functions as random variables. The results of the simulation modelling are used to estimate time parameters of the project events and jobs and the possibility of completing the project within the deadline. The paper examines two ways to distribute project resources. The first model does not take into account the competition between jobs for the resources. According to the second model, the resources are distributed dynamically from a single centre. As a result, the random nature of job execution can cause a shortage of resources.