Service Function Chaining (SFC) is the problem of deploying various network service instances over geographically distributed data centers and providing inter-connectivity among them. The goal is to enable the network traffic to flow smoothly through the underlying network, resulting in an optimal quality of experience to the end-users. Proper chaining of network functions leads to optimal utilization of distributed resources. This has been a de-facto model in the telecom industry with network functions deployed over underlying hardware. Though this model has served the telecom industry well so far, it has been adapted mostly to suit the static behavior of network services and service demands due to the deployment of the services directly over physical resources. This results in network ossification with larger delays to the end-users, especially with the data-centric model in which the computational resources are moving closer to end users. A novel networking paradigm, Network Function Virtualization (NFV), meets the user demands dynamically and reduces operational expenses (OpEx) and capital expenditures (CapEx), by implementing network functions in the software layer known as virtual network functions (VNFs). VNFs are then interconnected to form a complete end-to-end service, also known as service function chains (SFCs). In this work, we study the problem of deploying service function chains over network function virtualized architecture. Specifically, we study virtual network function placement problem for the optimal SFC formation across geographically distributed clouds. We set up the problem of minimizing inter-cloud traffic and response time in a multi-cloud scenario as an ILP optimization problem, along with important constraints such as total deployment costs and service level agreements (SLAs). We consider link delays and computational delays in our model. The link queues are modeled as M/D/1 (single server/Poisson arrival/deterministic service times) and server queues as M/M/1 (single server/Poisson arrival/exponential service times) based on the statistical analysis. In addition, we present a novel affinity-based approach (ABA) to solve the problem for larger networks. We provide a performance comparison between the proposed heuristic and simple greedy approach (SGA) used in the state-of-the-art systems. Greedy approach has already been widely studied in the literature for the VM placement problem. Especially we compare our proposed heuristic with a greedy approach using first-fit decreasing (FFD) method. By observing the results, we conclude that the affinity-based approach for placing the service functions in the network produces better results compared against the simple greedy (FFD) approach in terms of both, total delays and total resource cost. We observe that with a little compromise (gap of less than 10% of the optimal) in the solution quality (total delays and cost), affinity-based heuristic can solve the larger problem more quickly than ILP.
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