Online Admission Control and Embedding of Service Chains

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.Comment: early version of SIROCCO 2015 pape

Exact finite approximations of average-cost countable Markov Decision Processes

For a countable-state Markov decision process we introduce an embedding which produces a finite-state Markov decision process. The finite-state embedded process has the same optimal cost, and moreover, it has the same dynamics as the original process when restricting to the approximating set. The embedded process can be used as an approximation which, being finite, is more convenient for computation and implementation.Comment: Submitted to Automatic

On the Benefit of Virtualization: Strategies for Flexible Server Allocation

Virtualization technology facilitates a dynamic, demand-driven allocation and migration of servers. This paper studies how the flexibility offered by network virtualization can be used to improve Quality-of-Service parameters such as latency, while taking into account allocation costs. A generic use case is considered where both the overall demand issued for a certain service (for example, an SAP application in the cloud, or a gaming application) as well as the origins of the requests change over time (e.g., due to time zone effects or due to user mobility), and we present online and optimal offline strategies to compute the number and location of the servers implementing this service. These algorithms also allow us to study the fundamental benefits of dynamic resource allocation compared to static systems. Our simulation results confirm our expectations that the gain of flexible server allocation is particularly high in scenarios with moderate dynamics