Concurrency interpretation Clause Samples

Concurrency interpretation. The stochastic process calculi proposed in the literature are based on interleaving, as a rule, and parallelism is simulated by synchronous or asynchronous execution. As a semantic domain, the interleaving formalism of transition systems is often used. However, to properly support intuition of the behaviour of concurrent and distributed systems, their semantics should treat parallelism as a primitive concept that cannot be reduced to nondeterminism. Moreover, in interleaving semantics, some important properties of these systems cannot be expressed, such as simultaneous occurrence of concurrent transitions [33] or local deadlock in the spatially distributed processes [71]. Therefore, investigation of stochastic extensions for more expressive and powerful algebraic calculi is an im- portant issue. The development of step or “true concurrency” (such that parallelism is considered as a causal independence) SPAs is an interesting and nontrivial prob- lem that has attracted special attention in the last years. Nevertheless, not so many formal stochastic models of parallel systems were defined whose underlying stochas- tic processes were based on DTMCs. As mentioned in [36], such models are more difficult to analyze, since several events can occur simultaneously in discrete time systems (the models have a step semantics) and the probability of a set of events cannot be easily related to the probability of the single ones. Therefore, parallel executions of actions are often not considered also in the discrete time SPAs, such as TCP dst, whose underlying stochastic process is DTMCs with rewards (DTMRCs). As observed in [48], even for stochastic models with generally distributed time delays, some restrictions on the concurrency degree were imposed to simplify their analysis techniques. In particular, the enabling restriction requires that no two generally distributed transitions are enabled in any reachable marking. Hence, their activity periods do not intersect and no two such transitions can fire simultaneously, this results in interleaving semantics of the model. Stochastic models with discrete time and step semantics have the following im- portant advantage over those having just an interleaving semantics. The underlying Markov chains of parallel stochastically timed processes have additional transitions corresponding to the simultaneous execution of concurrent (i.e. non-synchronized) activities. These additional transitions allow us one to bypass a lot of inter...
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