Rule based solution for a real time applications problem through abstract Petri nets

Abstract

A b s t-r a c tA rule based solution for a real time problem based on Abstract Petri net (apn) is provided. This new extended net type Abstract Petri net provides compact and verifiable models and possesses same descriptive power as that of other extended net types.Various restrictions, activities, and properties of an elevator system (a representative of real time problem) are defined by means of set of behavioral rules to control and manage the functioning of elevator system. This paper demonstrates how these rules can be implemented in terms of entities of apn to get the model of the system and furhter, it is shown how this model provides an efficient solution of the elevator system. I. IntroductionPrevious work on Petri nets resulted into the definition of various restricted, extended, and modified Petri net types models [3].This diversification of net types was made necessary by the inability of a single type to meet the requirements of different application domains. We have proposed a new extended type of net termed as Abstract Petri net [l].This new extended net type which combines the concepts of timed and colored Petri nets provides a compact and verifiable model of system. Further, analysis technique of apn offer various features like consistency, finite state tree, reusability, etc. within the modeled system at various levels of abstract io ns . In this paper we discuss an application of apn to provide rule based solution for a real-time problem. A Petri net solution to elevator problem was given in [2], where the size of the solution increased as number of floors increased. In this paper, we provide a compact and verifiable solution to the above problem based on apn. Apn based models are compact and furthermore, size of the solution is independent of number of floors. In section two a brief introdution of apn and its technique are given, and various notations which will be used in this paper are defined. Section three provides a general description for the elevator problem, and presents its requirements and behavior in terms of predicates/rules. Using behavioral rules of section three, section four provides an apn solution to the elevator problem. Finally, we conclude by summarizing the main points of the paper and propose some interesting extension to this work. II. A brief. introduction of apn: Definitions and notations.We denote by N+, N and R the sets of positive i n t e g e r s , non-negative integers, and real numbers, respectively. Furthermore, we make use of "#" operator, where #(p,x) gives number of items of type x in place p. An Abstract Petri net (apn) is a 5-tuple, an = ( n, K, FP, FT, MO ) where n=(P,T,I,O) is a Petri (plt) net , P is the set of places, T is the set of transitions, I is the transitions input arc function, and 0 is the transition output arc function. K is the set of token types, FP is the properties associated with P, FT is the properties associated with T, and MO is initial token distributions. K = {ki I ki is a token type, 1s i S I", I" E N+ } K is the set of valid token...