Modeling Group Scheduling Problems in Space and Time by Timed Petri Nets

Abstract

Dealing with cyber-physical systems CPS puts a strong emphasis on the interaction between computing and non-computing elements. Since the physical world is characterized by being strongly distributed and concurrent, this is also reflected in the computational world making the design of such systems a challenging task. If a number of tasks shall be executed on a CPS which are bound to time and space, may have dependencies to other tasks and requires a specific amount of computing devices, a solution requires a four-dimensional space-time schedule which includes positioning of the devices resulting in an NP-hard problem. In this paper, we address the problem of spatial-temporal group scheduling using Timed Petri nets. We use Timed Petri nets in order to model the spatial, temporal, ordered and concurrent character of our mobile, distributed system. Our model is based on a discrete topology in which devices can change their location by moving from cell to cell. Using the time property of Petri nets, we model movement in a heterogeneous terrain as well as task execution or access to other resources of the devices. Given the modeling, we show how to find an optimal schedule by translating the problem into a shortest path problem, which is solvable with the known method of dynamic programming.