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Network Function Virtualization (NFV) changes the way that we implement network services, or middleboxes, from expensive hardwares to software functions. These software middleboxes, also called Virtual Network Functions (VNFs), run on switch-connected commodity servers. Efficiently placing such middleboxes is challenging because of their traffic-changing effects and dependency relations. Private (used by one single flow) middleboxes can save more link bandwidth resources while shared (used by multiple flows) middleboxes cut down server resource expenses. This paper formulates the resource usage trade-off between bandwidth consumption and cost of middlebox placement as a combined cost minimization problem. After proving the NP-hardness of our problem in general topologies, we narrow down to a specific kind of topology: tree-structured networks. We study two kinds of constraints: traffic-chaining ratio and middlebox dependency relations. With homogeneous flows, we propose optimal greedy algorithms for the placement of a single middlebox first, and then multiple middleboxes without order. We also introduce a dynamic programming algorithm for the placement of a totally-ordered middlebox set. A performance-guaranteed algorithm is designed to handle heterogeneous flows. Extensive simulations are conducted to evaluate the performance of our proposed algorithms in various scenarios.

NFV Middlebox Placement with Balanced Set-up Cost and Bandwidth Consumption