Adaptive Petri Net Based on Learning Automata

Abstract

This chapter contributes toward proposing adaptive Petri nets which evolve under the control of a number of learning agents. To this end, we utilize learning automata as learning agents and propose a number of hybrid machines, which are constructed by the fusion of Petri nets and learning automata. To justify the suitability of the proposed hybrid machines, we use them for modeling, simulating, analyzing, and problem solving in a variety of applications from different fields, such as queuing systems, graphs, and wireless sensor networks. The first hybrid machine, which is proposed in this chapter, is called APN-LA. In this machine, learning automata are used in a Petri net for adaptive decision making, whenever required. A decision making point is raised when two or more transitions are simultaneously enabled in a given marking. The decision to be made at such a point is the selection of an enabled transition for firing. Decision making in Petri nets is referred to as controlling mechanisms. Thus, in the APN-LA, learning automata are used to provide an adaptive controlling mechanism for the Petri net. APN-LA is the basic machine, from which other hybrid machines are proposed. One machine, which is constructed atop of the APN-LA, is ASPN-LA. The ASPN-LA is an APN-LA where the underlying Petri net is a Stochastic Petri net (SPN). This hybrid machine is used for representing and analyzing a number of priority assignment algorithms in queuing systems and a number of sleep scheduling algorithms in wireless sensor networks. The ASPN-LA is also used for analyzing an algorithm in the shortest path problem in stochastic graphs. Another hybrid machine, which is proposed in this chapter, is APN-ICLA. The idea behind constructing APN-ICLA is that in some situations, having a mean of cooperation between learning automata within a single Petri net may be beneficial. This cooperation is not available in the APN-LA; that is, in the APN-LA, each learning automaton acts independently from the others. The APN-ICLA can be regarded as a Petri net, in which the controlling mechanism is cooperative. The last proposed hybrid machine in this chapter is CAPN-LA. The CAPN-LA can be utilized to represent cellular algorithms, in which an identical algorithm must be executed in each cell and the solution of the problem is achieved from the cooperation of such identical algorithms. The CAPN-LA consists of a cellular structure and a number of identical APN-LAs; each APN-LA represents the identical algorithm, which must be executed in each cell. The required cooperation between the neighboring cells in the CAPN-LA is handled by the means of cooperation between the APN-LAs in the corresponding cells. The idea behind proposing CAPN-LA is that designing a single APN-LA for representing cellular algorithms is a tedious work and results in a large and complex model. This hybrid machine has been used for representing a number of cellular algorithms for solving vertex coloring graph problem. Furthermore, the notion of expediency has been defined for the CAPN-LA and the sufficient condition under which a CAPN-LA is expedient has been proposed.