Causal delivery protocols in real-time systems: A generic model

The objective of this paper is to introduce a model for causal delivery protocols in real-time systems. We start by showing that temporal order properties of real-time protocols are independent of whether they are timer-driven or clock-driven, being instead related to their degree of synchronism, that we call steadiness. Then, we derive a set of correctness conditions for such protocols to secure causal delivery order. To achieve this objective, we use an extension of Lamport's model of time-stamp based order. We show that both timer- and clock-driven protocols have order correctness limits dictated by the environment and the target applications, and define those limits, through a set of working formulas. We show that in extremely adverse cases, timer-driven protocols will perform as well as clock-driven ones, due to the restrictions imposed on the operation of the latter, which is perhaps surprising. These results open the door to exploring new forms of communication in time-critical systems, for example, supporting clock-and time-driven communication, and event-and time-triggered operation. We expect that the results of this paper will give insight to that problem, and will be useful in real-life systems, such as distributed computer control.