Network Diffuser for Placing-Scheduling Service Function Chains with Inverse Demonstration

TL;DR

The paper tackles online joint placement and scheduling of Service Function Chains (SFCs) in NFV-enabled networks, modeling the problem as NP-hard and sequentially arriving. It introduces a Network Diffuser, a conditional diffusion model operating on state trajectories augmented with graph diffusion to generate future system states and extract SFC placement and scheduling decisions. To overcome the scarcity of expert demonstrations, it proposes inverse demonstration, generating problem instances that render random decisions feasible and refining them via a lexicographic separable-convex optimization. Empirical results show substantial improvements over baselines in SFC reward and reductions in waiting time and blocking, validating the approach and its potential applicability to broader network-optimization tasks.

Abstract

Network services are increasingly managed by considering chained-up virtual network functions and relevant traffic flows, known as the Service Function Chains (SFCs). To deal with sequential arrivals of SFCs in an online fashion, we must consider two closely-coupled problems - an SFC placement problem that maps SFCs to servers/links in the network and an SFC scheduling problem that determines when each SFC is executed. Solving the whole SFC problem targeting these two optimizations jointly is extremely challenging. In this paper, we propose a novel network diffuser using conditional generative modeling for this SFC placing-scheduling optimization. Recent advances in generative AI and diffusion models have made it possible to generate high-quality images/videos and decision trajectories from language description. We formulate the SFC optimization as a problem of generating a state sequence for planning and perform graph diffusion on the state trajectories to enable extraction of SFC decisions, with SFC optimization constraints and objectives as conditions. To address the lack of demonstration data due to NP-hardness and exponential problem space of the SFC optimization, we also propose a novel and somewhat maverick approach -- Rather than solving instances of this difficult optimization, we start with randomly-generated solutions as input, and then determine appropriate SFC optimization problems that render these solutions feasible. This inverse demonstration enables us to obtain sufficient expert demonstrations, i.e., problem-solution pairs, through further optimization. In our numerical evaluations, the proposed network diffuser outperforms learning and heuristic baselines, by $\sim$20\% improvement in SFC reward and $\sim$50\% reduction in SFC waiting time and blocking rate.

Figures (9)

• Figure 1: An illustration of the SFC placing-scheduling optimization problem for a toy network of 6 nodes and 8 links. Three SFCs, denoted by Blue, Green, and Yellow, arrive sequntially, one at each time step. A naive greedy approach will result in SFC Yellow being blocked, while a solution jointly optimizing both SFC placement and scheduling can accomadate all three SFCs. We propose a network diffuser to solve it using generative models, by generating a sequence of system states as shown in this figure with constraint-guided diffusion and then extracting optimal placing-scheduling decisions from them.
• Figure 2: An illustration of our proposed network diffuser for SFC optimization. Each state $s_{t}$ in the trajectory encapsulates server state $V_{t}$ (such as server utilization), link state $E_{t}$ (such as link utilization and network topology), and SFC information $F_{t}$ (such as SFC parameters, placement, and schedules), with respect to the SFC optimization variables $x_{i,t}$ and $z_{i,j}^p$. The SFC optimization constraints and objective/reward value are represented by conditions as guidance/input to the diffusion model. Given the current state $s_t$ and conditioning, our network diffuser generates a sequence of future system states. It then extracts and executes the SFC placement and scheduling actions (i.e., $x_{i,t}$ and $z_{i,j}^p$) at that leads to the immediate future state $s_{t+1}$.
• Figure 3: A visualization of our state sequence representation in our network diffuser, for the optimal SFC placing-scheduling solution shown previously in Figure \ref{['fig:example2']}. We will perform diffusion over these state trajectories, to generate future states and extract SFC placing-scheduling decisions from them.
• Figure 4: An illustration of our proposed inverse demonstration approach to generate problem-solution pairs for training. Instead of solving a given instance of SFC problem that is NP-hard and has exponential problem space, we start with a randomly generated SFC placement/schedule and then find an appropriate SFC problem that renders the placement/schedule a feasible solution. Further optimization of the demonstration via an integer programming with separable convex objectives yields expert demosntrations for training our network diffuser.
• Figure 5: Achieved reward during training. The SFC placing-scheduling reward (i.e., $\sum_i I_i$) converges within about 100 epochs of training. The reward variance tends to be small and diminishes around 350 epochs, as network size grows from 5 to 15 nodes, showing stable performance.

Theorems & Definitions (3)

• Theorem 1
• Lemma 1
• Lemma 2