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 time-inhomogeneous semi-Markov process (I-SMP). To analyze I-SMP 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 I-SMP to a decomposed time-homogeneous 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.

翻译：车载云（VC）是一种在智能车辆上处理计算密集型应用的潜力技术。在网络边缘实现VC面临两个关键挑战：（C1）单辆车的车载计算资源通常不足以处理计算密集型应用；（C2）车辆移动性导致的可用资源动态性阻碍了计算密集型应用的可靠处理。本研究率先联合解决（C1）和（C2），同时考虑两种常见的计算密集型应用图表示形式：有向无环图（DAG）和无向图（UG）。为应对（C1），我们将一个包含$m$个依赖（子）任务的计算密集型应用划分为$k \leq m$个组，并分散放置到多辆车中。为应对（C2），我们提出一种称为条件平均失效时间（C-MTTF）的广义可靠性度量指标。随后，通过引入基于冗余的依赖子任务处理通用框架（RP-VC）在半动态车载云上处理依赖子任务，从而提高其C-MTTF。我们证明RP-VC可建模为一个非平凡的时间非齐次半马尔可夫过程（I-SMP）。为分析I-SMP及其可靠性，我们开发了一种名为事件随机代数（$\langle e\rangle$-代数）的新型数学框架。基于$\langle e\rangle$-代数，我们提出分解定理（DT）将I-SMP转化为分解后的时间齐次SMP（D-SMP），进而计算我们方法的C-MTTF。我们证明$\langle e\rangle$-代数和DT是可用于分析其他基于云的网络的通用数学工具。仿真结果揭示了分析结果的精确性以及我们方法在计算密集型应用处理接受率和成功率方面的有效性。