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In this paper, we present timing constraint Petri nets (or TCPN's for short) and describe how to use them to model a real-time system specification and determine whether the specification is schedulable with respect to imposed timing constraints. The strength of TCPN's over other time-related Petri nets is in the modeling and analysis of conflict structures. Schedulability analysis is conducted in three steps: <it>specification modeling, reachability simulation, and timing analysis</it>. First, we model a real-time system by transforming its system specification along with its imposed timing constraints into a TCPN; we call this net <math><tmath>N_s</tmath></math>. Then we <it>simulate</it> the reachability of <math><tmath>N_s</tmath></math> to verify whether a marking, <math><tmath>M_n</tmath></math>, is reachable from an initial marking, <math><tmath>M_0</tmath></math>. It is important to note that a reachable marking in Petri nets is not necessarily reachable in TCPN's due to the imposed timing constraints. Therefore, in the <it>timing analysis</it> step, a reachable marking <math><tmath>M_n</tmath></math> found in the <it>reachability simulation</it> step is analyzed to verify whether <math><tmath>M_n</tmath></math> is reachable with the timing constraints. <math><tmath>M_n</tmath></math> is said to be reachable in the TCPN's if and only if we can find at least one firing sequence <math><tmath>\sigma</tmath></math> so that all transitions in <math><tmath>\sigma</tmath></math> are strongly schedulable with respect to <math><tmath>M_0</tmath></math> under the timing constraints. If such <math><tmath>M_n</tmath></math> can be found, then we can assert that the specification is schedulable under the imposed timing constraints, otherwise the system specification needs to be modified or the timing constraints need to be relaxed. We also present a synthesis method for determining the best approximation of the earliest fire beginning time (EFBT) and the latest fire ending time (LFET) of each strongly schedulable transition.
Timing constraints, Petri nets, time Petri nets, timed Petri nets, specification and verification, timing analysis, real-time systems, synthesis.

Y. Chang, J. J. Tsai and S. J. Yang, "Timing Constraint Petri Nets and Their Application to Schedulability Analysis of Real-Time System Specifications," in IEEE Transactions on Software Engineering, vol. 21, no. , pp. 32-49, 1995.
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