On Petri nets with deterministic and exponentially distributed firing times

Marsan, Marco Ajmone; Chiola, Giovanni

doi:10.1007/3-540-18086-9_23

Cited by 281 publications

(96 citation statements)

References 4 publications

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“…Our fdCTMC formalism can be seen as a subclass of deterministic and stochastic Petri nets [24]. The main restriction is that in fdCTMC, at most one fixed-delay event can be enabled at a time (i.e., we cannot have two different "alarm clocks" turned on simultaneously).…”

Section: Related Workmentioning

confidence: 99%

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Efficient Timeout Synthesis in Fixed-Delay CTMC Using Policy Iteration

Korenčiak

Kučera

Řehák

2016

2016 IEEE 24th International Symposium on Modeling, Analysis and Simulation of Computer and Telecommunication Systems (MASCOTS)

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Abstract-We consider the fixed-delay synthesis problem for continuous-time Markov chains extended with fixed-delay transitions (fdCTMC). The goal is to synthesize concrete values of the fixed-delays (timeouts) that minimize the expected total cost incurred before reaching a given set of target states. The same problem has been considered and solved in previous works by computing an optimal policy in a certain discrete-time Markov decision process (MDP) with a huge number of actions that correspond to suitably discretized values of the timeouts.In this paper, we design a symbolic fixed-delay synthesis algorithm which avoids the explicit construction of large action spaces. Instead, the algorithm computes a small sets of "promising" candidate actions on demand. The candidate actions are selected by minimizing a certain objective function by computing its symbolic derivative and extracting a univariate polynomial whose roots are precisely the points where the derivative takes zero value. Since roots of high degree univariate polynomials can be isolated very efficiently using modern mathematical software, we achieve not only drastic memory savings but also speedup by three orders of magnitude compared to the previous methods.

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Section: Related Workmentioning

confidence: 99%

“…), a lot of research effort has been devoted to developing formalisms that generalize CTMC with fixed-delay transitions. Examples include deterministic and stochastic Petri nets [24], delayed CTMC [14], or fixed-delay CTMC (fdCTMC) [20], [5], [21].…”

Section: Introductionmentioning

confidence: 99%

Efficient Timeout Synthesis in Fixed-Delay CTMC Using Policy Iteration

Korenčiak

Kučera

Řehák

2016

2016 IEEE 24th International Symposium on Modeling, Analysis and Simulation of Computer and Telecommunication Systems (MASCOTS)

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“…For communication-free Petri nets with inhibitor arcs, the test-for-zero capabilities are explicitly allowed. Several timed versions of Petri nets have been proposed in the literature to introduce the timing information (either implicitly or explicitly) into the Petri net model (see, e.g., [14], [16]). A common approach is to associate each of the time-related transitions with an upper and lower bounds, defining the interval in which the transition must fire.…”

Section: Context-free Grammars)mentioning

confidence: 99%

Reachability Analysis of Variants of Communication-Free Petri Nets

Chen

Wang²,

Yen

2009

IEICE Trans. Inf. & Syst.

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SUMMARYCommunication-free Petri nets provide a net semantics for Basic Parallel Processes, which form a subclass of Milner's Calculus of Communicating Systems (CCS) a process calculus for the description and algebraic manipulation of concurrent communicating systems. It is known that the reachability problem for communication-free Petri nets is NP-complete. Lacking the synchronization mechanism, the expressive power of communication-free Petri nets is somewhat limited. It is therefore importance to see whether the power of communication-free Petri nets can be enhanced without sacrificing their analytical capabilities. As a first step towards this line of research, in this paper our main concern is to investigate, from the decidability/complexity viewpoint, the reachability problem for a number of variants of communication-free Petri nets, including communication-free Petri nets augmented with

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“…The particular class of Petri nets used for the model construction is called DSPN (Deterministic and Stochastic Petri Net) [10,11]. These are Petri nets with timed transitions, where the transition firing delays can be either deterministic or exponentially distributed.…”

Section: Introductionmentioning

confidence: 99%

Performance Analysis of Data Services over GPRS

Marsan

Gribaudo

Meo

et al. 2001

High Performance Computing — HiPC 2001

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Abstract. In this paper we describe a model for the performance analysis of mobile packet data services sharing a common GSM/GPRS (Global System for Mobile communications/General Packet Radio Service) cellular infrastructure with mobile telephony services. The performance model is developed using the DSPN (Deterministic and Stochastic Petri Net) paradigm. With limited computational cost, the DSPN solution allows the derivation of a number of interesting performance metrics, which can be instrumental for the development of accurate design and planning algorithms for cellular networks offering integrated services.

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On Petri nets with deterministic and exponentially distributed firing times

Cited by 281 publications

References 4 publications

Efficient Timeout Synthesis in Fixed-Delay CTMC Using Policy Iteration

Efficient Timeout Synthesis in Fixed-Delay CTMC Using Policy Iteration

Reachability Analysis of Variants of Communication-Free Petri Nets

Performance Analysis of Data Services over GPRS

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