Online Admission Control and Embedding of Service Chains

TL;DR

This paper introduces an online algorithm for maximizing service chain embeddings in networks, achieving near-optimal competitive ratio, and explores the computational complexity of the offline problem.

Contribution

It presents a deterministic O(log L)-competitive online algorithm for OSCEP and establishes hardness results for offline approximations, including NP-completeness.

Findings

The online algorithm is asymptotically optimal among deterministic and randomized algorithms.

The offline problem is APX-hard for small L and Poly-APX-hard in general.

The offline SCEP is NP-complete for constant L.

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 L)-competitive online algorithm, under the assumption that capacities are at least logarithmic in L. 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 L > 2, and even Poly-APX-hard in general, when there is no bound on L. 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 L.