Performance evaluation with temporal rewards

Software/Hardware Engineering with the Parallel Object-Oriented Specification Language

“…Real-time temporal logics like MTL [18] or MITL [1] are used to specify qualitative and quantitative real-time correctness properties (metrics that are expressible as a reachability property). In addition, temporal reward functions [41] are used to specify delay-type performance metrics (such as long-run time-averages and variances). In case of run-time verification or simulation-based analysis, SHE uses POOSL for extending the formal model of a system with monitors.…”

“…Several guidelines are provided to ensure that such 'reflexive' monitors are non-intrusive. The mathematical link between for example performance monitors expressed in POOSL and the formalism of temporal reward functions from [41] is established in [36]. The term validation in Figure 1 refers to the process of checking that the formal model and monitors properly reflect the informal model and required properties.…”

“…The timed probabilistic labelled transition system defined by a POOSL model can be interpreted as a Markov decision process [41,36], which expresses both the non-deterministic and probabilistic choices in the model. In case non-determinism is not resolved, a performance metric gives rise to a collection of results since different policies for doing so may imply different results for that metric.…”

“…We remark that this implies that there exists at most one action transition =⇒ C holds if configuration C can be entered after advancing the time with t units. This is the case if C t −→ C and no actions can be performed from C. By shifting the action and time labels for the transitions of the new transition system into its configurations, a discretetime Markov chain is obtained [41,36]. From the states of this Markov chain, one can deduct information about the actual occurrence of actions and progress of time (from the transition system, it can only be concluded that an action or time transition can occur).…”

“…Next to evaluating traditional probabilistic and expected reachability properties and long-run sample averages, SHE allows analysing long-run averages that can only be expressed as an accumulation of reward values over a sequence of states. Using temporal rewards [41], one can express for example the difference in time between two subsequent visits of a state in which a certain event occurred (possibly with intermediate visits to other states). Such expressive power is required for denoting delay-type metrics like throughput and jitter.…”