Discrete time Sample Clauses

Discrete time. Much fewer SPAs with discrete time semantics were designed. Dts-nets [1] are a class of compositional DTSPNs with generally distributed discrete time transition delays. The denotational semantics of a stochastic extension (we call it stochastic ACP or sACP) of a subset of Algebra of Communicating Processes (ACP) [8] can be constructed via dts-nets. There are two types of transiti- ons: immediate (timeless) ones, with zero delays, and time ones, whose delays are random variables with general discrete distributions. The top-down synthesis of dts-nets consists in the substitution of their transitions by blocks (dts-subnets) corresponding to some composition operators. It was explained how to calculate the throughput time of dts-nets using the service time (holding time or delay) of their transitions. For this, the notions of service distribution for the transitions and throughput distribution for the building blocks were defined. Since the throughput time of the parallelism block was calculated as the maximal service time for its two constituting transitions, the analogue of the step semantics was implemented. Theory of Communicating Processes with discrete stochastic time (TCP dst) [63, 64], later called Theory of Communicating Processes with discrete real and stochastic time (TCP drst) [62], is another stochastic extension of ACP. TCP dst has discrete real time (deterministic) delays (including zero time delays) and discrete stochastic time delays. The algebra generalizes real time processes to discrete sto- chastic time ones by applying real time properties to stochastic time and imposing race condition to real time semantics. TCP dst has an interleaving operational semantics in terms of stochastic transition systems. The performance is analyzed via discrete time probabilistic reward graphs which are essentially the reward transition systems with probabilistic states having finite number of outgoing probabilistic Time Immediate (multi)actions Interleaving semantics Non-interleaving semantics Continuous No MTIPP (CTMC), PEPA (CTMP), sPBC (CTMC) GSPA (GSMP), Sπ, GSMPA (GSMP) Discrete No — dtsPBC (DTMC) Yes TCP dst (DTMRC) sACP, dtsiPBC (SMC, DTMC) transitions and timed states having a single outgoing timed transition. The mentio- ▇▇▇ graphs can be transformed by unfolding or geometrization into discrete time Markov reward chains (DTMRCs) appropriate for transient or stationary analysis. dtsiPBC, sACP and TCP dst, all have zero delays. However, discrete time ...

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