基于NFV的网络中函数计算的最佳传输延迟：网络编码和冗余计算的作用
Optimum Transmission Delay for Function Computation in NFV-based Networks: the role of Network Coding and Redundant Computing
摘要：
在本文中，我们研究了基于NFV的网络中的延迟最小化问题。在这样的系统中，任何请求的最终目标都是计算网络中的函数序列，其中每个函数只能在网络节点的特定子集上计算。在传统方法中，对于每个函数，我们从节点的相应子集中选择一个节点来计算该函数。相比之下，在这项工作中，我们允许每个函数在多个节点中计算，冗余并行，以响应给定的请求。我们认为，这种冗余的计算不仅提高了网络的可靠性，但也会，也许令人惊讶的是，减少整体传输延迟。特别是，我们建立，通过明智地选择计算每个函数的节点的子集，结合线性网络编码方案，以提供每个计算的结果，我们可以表征和实现最佳的端到端传输延迟。此外，我们表明，使用这种技术，我们可以显着减少传输延迟相比，传统的方法。在某些情况下，这种减少甚至可以随着网络的大小而扩展。更准确地说，通过将可以并行计算给定函数的节点数量增加一个乘法因子，端到端延迟也将减少相同的因子。此外，我们发现，而每个计算的节点的子集，在一般情况下，是一个复杂的整数规划，近似算法可以提出，以减少计算复杂性。事实上，对于给定函数的计算节点数由常数上界的情况，可以提出动态规划方案以在多项式时间内找到最优子集。我们的数值模拟证实，与传统的方法相比，实现的性能增益。
英文摘要：
In this paper, we study the problem of delay minimization in NFV-based networks. In such systems, the ultimate goal of any request is to compute a sequence of functions in the network, where each function can be computed at only a specific subset of network nodes. In conventional approaches, for each function, we choose one node from the corresponding subset of the nodes to compute that function. In contrast, in this work, we allow each function to be computed in more than one node, redundantly in parallel, to respond to a given request. We argue that such redundancy in computation not only improves the reliability of the network, but would also, perhaps surprisingly, reduce the overall transmission delay. In particular, we establish that by judiciously choosing the subset of nodes which compute each function, in conjunction with a linear network coding scheme to deliver the result of each computation, we can characterize and achieve the optimal end-to-end transmission delay. In addition, we show that using such technique, we can significantly reduce the transmission delay as compared to the conventional approach. In some scenarios, such reduction can even scale with the size of the network. More precisely, by increasing the number of nodes that can compute the given function in parallel by a multiplicative factor, the end-to-end delay will also decrease by the same factor. Moreover, we show that while finding the subset of nodes for each computation, in general, is a complex integer program, approximation algorithms can be proposed to reduce the computational complexity. In fact, for the case where the number of computing nodes for a given function is upper-bounded by a constant, a dynamic programming scheme can be proposed to find the optimum subsets in polynomial times. Our numerical simulations confirm the achieved gain in performance in comparison with conventional approaches.
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