Discrete time stochastic petri nets for modeling and evaluation of real-time systems

Abstract

The design of real-time systems requires modeling and analysis techniques, to ensure their correct and timely operation. In many cases a realistic model should be able to cover both fixed and stochastic times. Stochastic Petri nets are a promising description technique in this field, but mixing deterministic and randomly distributed times in one model makes the analysis often impossible. This paper shows that Petri net models with an underlying discrete time can be advantageous for the modeling and analysis of real-time systems. For a demonstration a simple application example is modeled and its behavior computed using the software tool TimeNET.

Discrete time stochastic and deterministic Petri box calculus

“…Let us introduce a class of labeled discrete time stochastic and deterministic PNs (LDTSDPNs), which are essentially a subclass of DTSPNs [44,45] (since we do not allow the stochastic transition probabilities to be equal to 1) extended with transition labeling and deterministic transitions. LDTSDPNs resemble in part discrete time deterministic and stochastic PNs (DTDSPNs) [61,62,64,65], as well as discrete deterministic and stochastic PNs (DDSPNs) [63]. DTDSPNs and DDSPNs are the extensions of DTSPNs with deterministic transitions (having fixed delay that can be zero), inhibitor arcs, priorities and guards.…”

Stochastic equivalence for performance analysis of concurrent systems in dtsiPBC

“…Let us introduce a class of labeled discrete time stochastic and immediate Petri nets (LDTSIPNs), a subclass of DTSPNs Molloy (1981Molloy ( , 1985 (we do not allow the transition probabilities to be equal to 1) extended with transition labeling and immediate transitions. LDTSIPNs resemble in part discrete time deterministic and stochastic PNs (DTDSPNs) Zimmermann et al (2001), as well as discrete deterministic and stochastic PNs (DDSPNs) Zijal et al (1997). DTDSPNs and DDSPNs are the extensions of DTSPNs with deterministic transitions (having fixed delay that can be zero), inhibitor arcs, priorities and guards.…”

“…The process is the underlying SMC Ross (1996); Kulkarni (2009), denoted by SMC (G), which can be analyzed by extracting from it the embedded (absorbing) discrete time Markov chain (EDTMC) corresponding to G, denoted by EDTMC (G). The construction of the latter is analogous to that applied in GSPNs Marsan (1990); Balbo (2001Balbo ( , 2007, DTDSPNs Zimmermann et al (2001) and DDSPNs Zijal et al (1997). EDTMC (G) only describes the state changes of SMC (G) while ignoring its time characteristics.…”

Performance analysis of concurrent systems in algebra dtsiPBC

“…LDTSIPNs resemble in part discrete time deterministic and sto chastic PNs (DTDSPNs) [21], as well as discrete deterministic and stochastic PNs (DDSPNs) [22]. DTDSPNs First, we present a formal definition of LDTSIPNs.…”

“…This process is the underlying semi Markov chain SMC(G) [17], which can be analyzed by extracting from it the embedded (absorbing) discrete time Markov chain EDTMC(G) corresponding to G. The construction of the latter is similar to that used in the context of the generalized stochastic PNs (GSPNs) in [19], as well as in the frameworks of discrete time deterministic and sto chastic PNs (DTDSPNs) in [21] and discrete deter ministic and stochastic PNs (DDSPNs) in [22]. The EDTMC(G) only describes state changes of SMC(G), while ignoring its time characteristics.…”