and header vector length L L is constant C M cost of match tables depending on

And header vector length l l is constant c m cost of

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and header vector length L ( L is constant) C M : cost of match tables, depending on match width W and depth D C A : cost of the action processor of each HA table Inequality (2) indicates that the number of HA tables should be larger than the required HA resources, in which function x / y denotes rounding up the value of x / y . Generally, function C M ( W , D ) is not linear with respect to the two parameters, thus for different VNFs set and different implementation platforms, the optimal W and D would be different. Generally, the hardware implementation should consider the most representative and commonly used VNFs, and carefully select suitable HA table volumes. 3. Mathematical Model and Problem De fi nition Based on the details of VNF-HA mapping mentioned above, we introduce a mathematical model for our system and formally de fi ne the VNF-HA mapping and traf fi c routing problem. Network Topology. The physical network is represented as an undirected graph G = ( N , L ), where N and L denote the set of FE nodes and links, respectively. As de fi ned in the HSN FE structure, each FE node n 2 N has HA tables to hold the VNF rules, and the idle HA table rule space is represented by C n . The set S represents these VNF servers and binary variable h s , n 2 { 0, 1 } indicates whether server s 2 S is attached to FE n 2 N . VNFs. Different types of VNFs can be provided in a network. We assume that VNFs have been deployed on commodity servers located within the network. Let set P = ( P AS , P AL , P UA ) represent possible VNF types, where P AS is the set of VNF types that require state connection and can only be accelerated in the FE node connected to its server, P AL is the set of VNF types that are stateless and can be accelerated in any FE node, P UA is the set of VNF types that cannot be accelerated in any FE node. Let the binary variable h s , p 2 { 0, 1 } represent if VNF type p has been deployed on server s , and C p represent the rule space requirement of VNF p if p is mapped into hardware. Traf fi c Requests. We assume that there are several requests for setting up paths for different kinds of traf fi c. A traf fi c request is represented by a 4-tuple t = < u t , v t , Ψ t , b t > , where u t , v t 2 N denote the ingress and egress nodes, respectively, b t is the volume of traf fi c to be processed (occupied bandwidth) and Ψ t represents the ordered VNF sequence the traf fi c must pass through (for example, the FW- IDS-Proxy). For simplicity, a speci fi c NF instance cannot be commonly used to handle two or more traf fi c requests because of the different traf fi c processing demand. The VNF-HA mapping and traf fi c routing problem can be described as follows: given K traf fi c requests ( t 1 , t 2 , . . . , t n ), calculate the binary variable h s , n , p , t 2 { 0, 1 } that represents whether the VNF p deployed in server s is to be accelerated in node n for traf fi c request t , while achieving the total optimization goals. Generally, the optimization goal is to minimize the overall operation cost by (i) mapping VNFs that need acceleration to the optimal FEs
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