Decomposition Theory Meets Reliability Analysis: Processing of Computation-Intensive Dependent Tasks Over Vehicular Clouds With Dynamic Resources

Vehicular cloud (VC) is a promising technology for processing computation-intensive applications (CI-Apps) on smart vehicles. Implementing VCs over the network edge faces two key challenges: (C1) On-board computing resources of a single vehicle are often insufficient to process a CI-App; (C2) The dynamics of available resources, caused by vehicles’ mobility, hinder reliable CI-App processing. This work is among the first to jointly address (C1) and (C2), while considering two common CI-App graph representations, directed acyclic graph (DAG) and undirected graph (UG). To address (C1), we consider partitioning a CI-App with
$m$
dependent (sub-)tasks into
$k\le m$
groups, which are dispersed across vehicles. To address (C2), we introduce a generalized reliability metric called conditional mean time to failure (C-MTTF). Subsequently, we increase the C-MTTF of dependent sub-tasks processing via introducing a general framework of redundancy-based processing of dependent sub-tasks over semi-dynamic VCs (
RP-VC
). We demonstrate that
RP-VC
can be modeled as a non-trivial semi-Markov process (SMP). To analyze this SMP model and its reliability, we develop a novel mathematical framework, called event stochastic algebra (
$\langle e\rangle $
-algebra). Based on
$\langle e\rangle $
-algebra, we propose decomposition theorem (DT) to transform the presented SMP to a decomposed SMP (D-SMP). We subsequently calculate the C-MTTF of our methodology. We demonstrate that
$\langle e\rangle $
-algebra and DT are general mathematical tools that can be used to analyze other cloud-based networks. Simulation results reveal the exactness of our analytical results and the efficiency of our methodology in terms of acceptance and success rates of CI-App processing.