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In this paper, we study the problem of delay minimization in NFV-basednetworks. In such systems, the ultimate goal of any request is to compute asequence of functions in the network, where each function can be computed atonly a specific subset of network nodes. In conventional approaches, for eachfunction, we choose one node from the corresponding subset of the nodes tocompute that function. In contrast, in this work, we allow each function to becomputed in more than one node, redundantly in parallel, to respond to a givenrequest. We argue that such redundancy in computation not only improves thereliability of the network, but would also, perhaps surprisingly, reduce theoverall transmission delay. In particular, we establish that by judiciouslychoosing the subset of nodes which compute each function, in conjunction with alinear network coding scheme to deliver the result of each computation, we cancharacterize and achieve the optimal end-to-end transmission delay. Inaddition, we show that using such technique, we can significantly reduce thetransmission delay as compared to the conventional approach. In some scenarios,such reduction can even scale with the size of the network. More precisely, byincreasing the number of nodes that can compute the given function in parallelby a multiplicative factor, the end-to-end delay will also decrease by the samefactor. Moreover, we show that while finding the subset of nodes for eachcomputation, in general, is a complex integer program, approximation algorithmscan be proposed to reduce the computational complexity. In fact, for the casewhere the number of computing nodes for a given function is upper-bounded by aconstant, a dynamic programming scheme can be proposed to find the optimumsubsets in polynomial times. Our numerical simulations confirm the achievedgain in performance in comparison with conventional approaches.

Optimum Transmission Delay for Function Computation in NFV-based Networks: the role of Network Coding and Redundant Computing