Stochastic HYPE is a novel process algebra that models stochastic, instantaneous and continuous behaviour. It develops the flow-based approach of the hybrid process algebra HYPE by replacing non-urgent events with events with exponentially-distribute
d durations and also introduces random resets. The random resets allow for general stochasticity, and in particular allow for the use of event durations drawn from distributions other than the exponential distribution. To account for stochasticity, the semantics of stochastic HYPE target piecewise deterministic Markov processes (PDMPs), via intermediate transition-driven stochastic hybrid automata (TDSHA) in contrast to the hybrid automata used as semantic target for HYPE. Stochastic HYPE models have a specific structure where the controller of a system is separate from the continuous aspect of this system providing separation of concerns and supporting reasoning. A novel equivalence is defined which captures when two models have the same stochastic behaviour (as in stochastic bisimulation), instantaneous behaviour (as in classical bisimulation) and continuous behaviour. These techniques are illustrated via an assembly line example.
We demonstrate the modelling of opportunistic networks using the process algebra stochastic HYPE. Network traffic is modelled as continuous flows, contact between nodes in the network is modelled stochastically, and instantaneous decisions are modell
ed as discrete events. Our model describes a network of stationary video sensors with a mobile ferry which collects data from the sensors and delivers it to the base station. We consider different mobility models and different buffer sizes for the ferries. This case study illustrates the flexibility and expressive power of stochastic HYPE. We also discuss the software that enables us to describe stochastic HYPE models and simulate them.
Semantic equivalences are used in process algebra to capture the notion of similar behaviour, and this paper proposes a semi-quantitative equivalence for a stochastic process algebra developed for biological modelling. We consider abstracting away fr
om fast reactions as suggested by the Quasi-Steady-State Assumption. We define a fast-slow bisimilarity based on this idea. We also show congruence under an appropriate condition for the cooperation operator of Bio-PEPA. The condition requires that there is no synchronisation over fast actions, and this distinguishes fast-slow bisimilarity from weak bisimilarity. We also show congruence for an operator which extends the reactions available for a species. We characterise models for which it is only necessary to consider the matching of slow transitions and we illustrate the equivalence on two models of competitive inhibition.
The process algebra HYPE was recently proposed as a fine-grained modelling approach for capturing the behaviour of hybrid systems. In the original proposal, each flow or influence affecting a variable is modelled separately and the overall behaviour
of the system then emerges as the composition of these flows. The discrete behaviour of the system is captured by instantaneous actions which might be urgent, taking effect as soon as some activation condition is satisfied, or non-urgent meaning that they can tolerate some (unknown) delay before happening. In this paper we refine the notion of non-urgent actions, to make such actions governed by a probability distribution. As a consequence of this we now give HYPE a semantics in terms of Transition-Driven Stochastic Hybrid Automata, which are a subset of a general class of stochastic processes termed Piecewise Deterministic Markov Processes.
We use activity networks (task graphs) to model parallel programs and consider series-parallel extensions of these networks. Our motivation is two-fold: the benefits of series-parallel activity networks and the modelling of programming constructs, su
ch as those imposed by current parallel computing environments. Series-parallelisation adds precedence constraints to an activity network, usually increasing its makespan (execution time). The slowdown ratio describes how additional constraints affect the makespan. We disprove an existing conjecture positing a bound of two on the slowdown when workload is not considered. Where workload is known, we conjecture that 4/3 slowdown is always achievable, and prove our conjecture for small networks using max-plus algebra. We analyse a polynomial-time algorithm showing that achieving 4/3 slowdown is in exp-APX. Finally, we discuss the implications of our results.
