A timeband framework for modelling real-time systems

Abstract

Complex real-time systems must integrate physical processes with digital control, human operation and organisational structures. New scientific foundations are required for specifying, designing and implementing these systems. One key challenge is to cope with the wide range of time scales and dynamics inherent in such systems. To exploit the unique properties of time, with the aim of producing more dependable computer-based systems, it is desirable to explicitly identify distinct time bands in which the system is situated. Such a framework enables the temporal properties and associated dynamic behaviour of existing systems to be described and the requirements for new or modified systems to be specified. A system model based on a finite set of distinct time bands is motivated and developed in this paper.

Deriving real-time action systems with multiple time bands using algebraic reasoning

“…Each of these phases takes time. Furthermore, the components operate at different time granularities and hence have different notions of precision (the amount of time that may be regarded as instantaneous [9,10]). For example, water 1 may have a precision of 30 seconds (i.e., there is no significant change in the water level in Tank 1 within 30 seconds) and Pump 2 turns on/off with precision 1 second (i.e., it takes Pump 2 at most 1 second to reach its operating speed or to come to a stop).…”

“…We assume that the set of all time bands is given by the primitive type TimeBand [9,10]. Each time band may be associated with events that execute within the precision of the time band.…”

“…2, variables are sampled at most once, hence, if a variable occurs multiple times within an expression, the same sampled value is used for each occurrence of the variable. Hence, expression x = x is guaranteed to evaluate to true regardless of how x changes within the evaluation interval, however, x > y may evaluate to false even if (x > y) holds [10,18,30] as in sa 3 in Figure 4.…”

“…Our framework incorporates a logic of time bands [9,10,49], which allows one to formalise properties at different time granularities and define relationships between these properties. Behaviours of components at fine levels of granularity often involve interactions that may not necessarily be observed when assuming a coarse level of atomicity.…”

“…On the other hand, consideration of fine-grained interactions results in an increase in the complexity of the reasoning. In this paper, we use a high-level logic that allows one to describe the observable states that may occur when sampling variables at finer time-bands [10,19,21,30].…”