Online Admission Control and Embedding of Service Chains

Abstract

The virtualization and softwarization of modern computer networks enables the definition and fast deployment of novel network services called service chains: sequences of virtualized network functions (e.g., firewalls, caches, traffic optimizers) through which traffic is routed between source and destination. This paper attends to the problem of admitting and embedding a maximum number of service chains, i.e., a maximum number of source-destination pairs which are routed via a sequence of to-be-allocated, capacitated network functions. We consider an Online variant of this maximum Service Chain Embedding Problem, short OSCEP, where requests arrive over time, in a worst-case manner. Our main contribution is a deterministic O(log )-competitive online algorithm, under the assumption that capacities are at least logarithmic in . We show that this is asymptotically optimal within the class of deterministic and randomized online algorithms. We also explore lower bounds for offline approximation algorithms, and prove that the offline problem is APX-hard for unit capacities and small ≥ 3, and even Poly-APX-hard in general, when there is no bound on . These approximation lower bounds may be of independent interest, as they also extend to other problems such as Virtual Circuit Routing. Finally, we present an exact algorithm based on 0-1 programming, implying that the general offline SCEP is in NP and by the above hardness results it is NP-complete for constant .

Robust Online Composition, Routing and NF Placement for NFV-Enabled Services

“…Therefore, the competitive-ratio of the admission mechanism for the multicast services is O(2 max{ϕ, φ}) = O(max{ϕ, φ}). Algorithm 2: JRP algorithm for a single service request for n k ∈ F k do 8 Add l ← (n k , n k+1 ) to L I ; 9 C l (r) = C(n k ); 10 end 11 end 12 For multicast services, find an MST-based Steiner tree from s 0 to D | V | , while utilizing the cost functions in (25) and (26), and save on P; 13 For unicast services, find a Dijkstra shortest path from s 0 to t | V | , while utilizing the cost functions in (25) and (26), and save on P; 14 return P; component of the runtime is due to the Dijkstra shortest path for unicast services and MST-based Steiner tree for multicast services that is run over the network transformation which has |N |(K + 1) nodes.…”

“…In the former, all service requests are known a priori, and all service requests are assumed to arrive in one batch. In practice, network services arrive in an online and random manner without knowledge of future requests [12], [13].…”

“…Some relevant studies deal with the online handling of service requests without statistical assumptions [12], [13], [15]- [18]. The NFV-enabled frameworks are based on the seminal work by Awerbuch et al [19], where some new aspects are due to the inclusion of NF instances and the need for an admission mechanism for service requests with multiple resource types.…”

On a virtual network functions placement and routing problem: Some properties and a comparison of two formulations

“…Similarly, a VNE based representation of the problem is proposed in [15], where the focus is on the online version of the VNF chaining problem: three greedy algorithms and a tabu-search based heuristic method are proposed to deal with the VNF online mapping and scheduling. The problem of embedding VNF chains is addressed also in [14], where demands may be rejected and the subset of accepted demands must be maximized while limiting the number of service chains considered. In [12], the authors propose an ILP model based on the mapping of VNF chains on a physical network, although without naming it explicitly.…”

A New Approach for Delivering Customized Security Everywhere: Security Service Chain

“…However, with respect to our work no consideration is made on instance sharing explicitly. Beyond offline problems, Lukovszki and Schmid [30] propose deterministic online algorithms for deploying service chains.…”