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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&#x2019; 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.

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