Distributed computing enables large-scale computation tasks to be processed over multiple workers in parallel. However, the randomness of communication and computation delays across workers causes the straggler effect, which may degrade the performance. Coded computation helps to mitigate the straggler effect, but the amount of redundant load and their assignment to the workers should be carefully optimized. In this work, we consider a multi-master heterogeneous-worker distributed computing scenario, where multiple matrix multiplication tasks are encoded and allocated to workers for parallel computation. The goal is to minimize the communication plus computation delay of the slowest task. We propose worker assignment, resource allocation and load allocation algorithms under both dedicated and fractional worker assignment policies, where each worker can process the encoded tasks of either a single master or multiple masters, respectively. Then, the non-convex delay minimization problem is solved by employing the Markov's inequality-based approximation, Karush-Kuhn-Tucker conditions, and successive convex approximation methods. Through extensive simulations, we show that the proposed algorithms can reduce the task completion delay compared to the benchmarks, and observe that dedicated and fractional worker assignment policies have different scopes of applications.

For in-vehicle application,task type and vehicle state information, i.e., vehicle speed, bear a significant impact on the task delay requirement. However, the joint impact of task type and vehicle speed on the task delay constraint has not been studied, and this lack of study may cause a mismatch between the requirement of the task delay and allocated computation and wireless resources. In this paper, we propose a joint task type and vehicle speed-aware task offloading and resource allocation strategy to decrease the vehicl's energy cost for executing tasks and increase the revenue of the vehicle for processing tasks within the delay constraint. First, we establish the joint task type and vehicle speed-aware delay constraint model. Then, the delay, energy cost and revenue for task execution in the vehicular edge computing (VEC) server, local terminal and terminals of other vehicles are calculated. Based on the energy cost and revenue from task execution,the utility function of the vehicle is acquired. Next, we formulate a joint optimization of task offloading and resource allocation to maximize the utility level of the vehicles subject to the constraints of task delay, computation resources and wireless resources. To obtain a near-optimal solution of the formulated problem, a joint offloading and resource allocation based on the multi-agent deep deterministic policy gradient (JORA-MADDPG) algorithm is proposed to maximize the utility level of vehicles. Simulation results show that our algorithm can achieve superior performance in task completion delay, vehicles' energy cost and processing revenue.