# Decomposition Theory Meets Reliability Analysis: Processing of Computation-Intensive Dependent Tasks over Vehicular Clouds with Dynamic Resources

arXiv: https://arxiv.org/abs/2210.07337 · HTML: https://mlsanity.com/paper/2210.07337/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Oct 2022.

## Built on by (most cited first, 1 of 1)

- [DNN Partitioning, Task Offloading, and Resource Allocation in Dynamic Vehicular Networks: A Lyapunov-Guided Diffusion-Based Reinforcement Learning Approach](https://mlsanity.com/paper/2406.06986/) (2024)

## Abstract (arXiv)

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≤ 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 erangle-algebra). Based on langle erangle-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 erangle-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.