A Node-Selection-Based Sub-Task Assignment Method for Coded Edge Computing

A Node-Selection-Based Sub-Task Assignment Method for Coded Edge Computing

Abstract: Recently, coded computation has emerged as a promising technique to reduce the influence of straggling computing nodes in distributed computing systems.

However, most existing works neglect the time cost of communicating messages from the client to the computing nodes. Besides straggling computing nodes, straggling receivers also have significant influence on the total computing time, especially in edge computing systems, in which the client and the edge computing nodes are connected through wireless links. Motivated by this observation, we propose in this paper a new sub-task assignment method based on edge node selection to reduce the total computing time for coded edge computing systems. In the proposed method, a subtask is assigned to the first computing node which decodes the associated messages of the sub-task successfully. Comprehensive numerical results are presented, which show that, with the proposed assignment method, the overall computing time can be reduced. We also show that further reduction can be achieved if additional edge nodes are available.

Existing system:

Existing works on coded computing were mainly focused on wired networks.

Hence the communication latencies due to distributing the sub-tasks and transmitting back the computing results are neglected. Coded computing also can be incorporated into wireless networks. For wireless computing networks, the communication latencies cannot be ignored due to the time-varying nature of wireless links. In, the authors analyzed the latency of transmitting back the computing results for coded wireless computing systems. In, coded computing for edge and fog computing systems was investigated. However, the latency of distributing the associated messages of the sub-tasks has not been considered.

Motivated by this observation, we propose a node-selection based method to reduce the latency due to distributing subtasks by leveraging the broadcasting nature of wireless signals. In the proposed method, a sub-task is assigned to the first edge node which decodes the associated messages of the sub-task successfully, instead of assigned to a fixed edge node. Analysis and comparisons are presented to show the advantages of the proposed method.

Proposed system: This phenomenon partially weakens the advantages of distributed computing.

Recently, several works in the literature have shown that we can incorporate the idea of coding into distributed computing to mitigate the influence of stragglers at the expense of using more computing units. In coded computing, redundant subtasks are firstly generated by the encoder of an error correction code, such as maximum distance separable (MDS) code. These new subtasks are then computed by the redundant computing units. The authors of investigated the benefits of using sparse encoded matrix in coded matrix multiplication. For large scale matrix multiplication, the authors of proposed to use shorter MDS codes to reduce the latency due to decoding. To make use of the partial results of the stragglers, hierarchical coded computation schemes were proposed. Generalization of coded computation for hierarchical computing system was considered. Practical codes for binary matrix-vector multiplication were constructed Coded computing for privacy is investigated.

Advantages:

This phenomenon partially weakens the advantages of distributed computing.

Recently, several works in the literature have shown that we can incorporate the idea of coding into distributed computing to mitigate the influence of stragglers at the expense of using more computing units.

In coded computing, redundant sub-tasks are firstly generated by the encoder of an error correction code, such as maximum distance separable (MDS) code. These new subtasks are then computed by the redundant computing units. The authors of investigated the benefits of using sparse encoded matrix in coded matrix multiplication.

Disadvantages: Existing works on coded computing were mainly focused on wired networks.

Hence the communication latencies due to distributing the sub-tasks and transmitting back the computing results are neglected. Coded computing also can be incorporated into wireless networks.

For wireless computing networks, the communication latencies cannot be ignored due to the time-varying nature of wireless links. In, the authors analyzed the latency of transmitting back the computing results for coded wireless computing systems. In, coded computing for edge and fog computing systems was investigated.

Modules: Error correction code: Error correction codes have been successfully used in communication and storage systems to combat channel-induced errors. Adding redundancy is the key to the success of error correction codes. Computation offloading has been proposed to tackle the challenges raised by the growth of computation intensive tasks at resource-limited terminals. Existing frameworks for computation offloading include cloud computing, fog computing, edge computing, etc. For computation limited terminals, computation offloading can be used to relieve the computation burden of the users. For power-limited terminals, computation offloading can be used to reduce the power consumption of the users. Recently, mobile edge computing has been proposed to reduce latency for latency-critical applications.

Major information technology companies have invested enormously in the research and development of high-performance computation offloading platforms.

Maximum distanced separable: The computing latency is determined by the slowest computing server, i.e., the straggler. This phenomenon partially weakens the advantages of distributed computing. Recently, several works in the literature have shown that we can incorporate the idea of coding into distributed computing to mitigate the influence of stragglers at the expense of using more computing units. In coded computing, redundant sub-tasks are firstly generated by the encoder of an error correction code, such as maximum distance separable (MDS) code. These new subtasks are then computed by the redundant computing units. The authors of investigated the benefits of using sparse encoded matrix in coded matrix multiplication. For large scale matrix multiplication, the authors of proposed to use shorter MDS codes to reduce the latency due to decoding. To make use of the partial results of the stragglers, hierarchical coded computation schemes were proposed. Generalization of coded computation for hierarchical computing system was considered. Practical codes for binary matrix-vector multiplication were constructed. Coded computing for privacy is investigated.

Wired network: Existing works on coded computing were mainly focused on wired networks.

Hence the communication latencies due to distributing the sub-tasks and transmitting back the computing results are neglected. Coded computing also can be incorporated into wireless networks. For wireless computing networks, the communication latencies cannot be ignored due to the time-varying nature of wireless links. In, the authors analyzed the latency of transmitting back the computing results for coded wireless computing systems. In, coded computing for edge and fog computing systems was investigated. However, the latency of distributing the associated messages of the sub-tasks has not been considered.

Motivated by this observation, we propose a node-selection based method to reduce the latency due to distributing subtasks by leveraging the broadcasting nature of wireless signals. In the proposed method, a sub-task is assigned to the first edge node which decodes the associated messages of the sub-task

successfully, instead of assigned to a fixed edge node. Analysis and comparisons are presented to show the advantages of the proposed method. Comparisons show that, as expected, when the average communication latency is comparable with or larger than the average computing latency, significant reduction in total computing latency is achieved, while when the communication latency is negligible when compared with the computing latency, the reduction is marginal. Our results also show that further reduction can be achieved if additional edge nodes are available.

A Sub-Task Assignment Method for Coded Edge Computing: The transmission time of from the client the edge nodes varies for the following reasons. Firstly, the channel quality of wireless links varies with time. Secondly, thermal noise of the receiver varies with time. Following, we model the transmission time from the client to an edge node as an exponentially distributed random variable with parameter Îť. As the edge nodes are typically physically separated, transmission times of different edge nodes are assumed to be independent. Following, we assume that the computing times of the edge nodes are exponentially distributed with parameter Ď . We also assume that the computing times of the edge nodes are independent.