🌱 Carbon-Aware Service Function Chain Placement

⚡ L-CAVO & QL-CAVO Simulation Framework

---

Carbon-Aware Service Function Chain Placement Under Time-Varying Grid Intensity A Lyapunov-Optimisation and Q-Learning Framework

Yassir Al-Karawi · Department of Communications Engineering · University of Diyala, Iraq

🔭 Overview · 🧠 Algorithms · 🚀 Quick Start · 📊 Results · 🖼️ Figures · 📚 Citation

---

🔭 Overview

Modern NFV-enabled networks can substantially reduce operational carbon emissions by steering VNF placement toward data-centre regions powered by cleaner energy sources. This repository provides the complete simulation framework for reproducing all results in our IEEE TGCN paper.

We propose two online algorithms that jointly optimise carbon emissions, SFC acceptance rate, and end-to-end delay — without requiring future knowledge of grid carbon intensity:

🏷️ Algorithm	🧮 Technique	🌿 Carbon Reduction (vs EA)	✅ SFC Acceptance
L-CAVO	Lyapunov optimisation + Benders decomposition	26 – 27 %	91 – 98 %
QL-CAVO	Tabular Q-learning + greedy placement	17 – 18 %	94 – 99 %

Note

Both algorithms are benchmarked against six baselines — MILP-OPT (offline optimal), Energy-aware, Latency-aware, Carbon-greedy, and Random — on two real-world topologies (NSFNET and GÉANT).

---

🏗️ System Architecture

High-Level Data Flow

flowchart LR
    A[🌐 SFC Request Stream] --> B{Orchestrator}
    C[🔋 Carbon-Intensity Feed] --> B
    D[📡 Topology &<br/>Resource State] --> B
    B --> E[L-CAVO<br/>Lyapunov + Benders]
    B --> F[QL-CAVO<br/>Tabular Q-Learning]
    E --> G[💚 VNF Placement Decision]
    F --> G
    G --> H[📈 Metrics:<br/>CO₂ · Delay · Acceptance]

    classDef green fill:#10B981,stroke:#065F46,color:#fff,stroke-width:2px;
    classDef blue  fill:#3B82F6,stroke:#1E3A8A,color:#fff,stroke-width:2px;
    classDef amber fill:#F59E0B,stroke:#92400E,color:#fff,stroke-width:2px;
    class A,C,D blue;
    class E,F amber;
    class G,H green;

Loading

---

🧠 Proposed Algorithms

🟢 L-CAVO — Lyapunov Carbon-Aware VNF Orchestration

L-CAVO transforms the long-term carbon-minimisation problem into a sequence of per-slot optimisation sub-problems using Lyapunov drift-plus-penalty. A virtual queue Q(t) tracks SFC-rejection debt, and the trade-off parameter V balances carbon savings against acceptance guarantees.

Scoring function:

$$\text{score}(n) \;=\; V \cdot \Delta\text{CO}_2(n) \;+\; 0.5 \cdot \text{delay} \;+\; 0.3 \cdot \text{utilisation} \;+\; 0.05 \cdot Q(t)$$

Tip

As V increases, the algorithm prioritises carbon reduction more aggressively. The theoretical optimality gap decreases as O(1/V).

Algorithm 1 — L-CAVO (paper §VI):

Inputs : V ≥ 0, ε ∈ (0,1), carbon trace {g_z(t)}, topology G
Init   : Q(0) ← 0
for each slot t = 0, 1, …, T−1 do
    1. Observe regional carbon intensities g_z(t) and request set R_t
    2. for each request r ∈ R_t do
           for each VNF k = 1..K_r do
               score(n) ← V·ΔCO₂(n) + 0.5·delay(n) + 0.3·util(n) + 0.05·Q(t)
               n*  ← argmin_n score(n)          subject to CPU, bw, D_max
           Place chain or mark request rejected
    3. rej_t ← |R_t| − admitted_t
    4. Q(t+1) ← max( Q(t) + rej_t − ε·|R_t|, 0 )       ▷ virtual-queue update
end for

Code reference: sc_lc() (lcavo_sim.py:343) and the L-CAVO branch of sim() (lcavo_sim.py:582).

flowchart TD
    S[New time-slot t] --> Q[Read virtual queue Q t]
    Q --> R{SFC requests}
    R -->|For each request| SC[Compute score per node<br/>V · ΔCO₂ + delay + util + Q]
    SC --> BD[Benders decomposition<br/>master + sub-problem]
    BD --> P[Place VNFs greedily<br/>by lowest score]
    P --> UQ[Update Q t+1<br/>by rejection debt]
    UQ --> M[Record metrics]
    M --> S

    classDef start fill:#10B981,stroke:#065F46,color:#fff;
    classDef proc  fill:#3B82F6,stroke:#1E3A8A,color:#fff;
    classDef dec   fill:#F59E0B,stroke:#92400E,color:#fff;
    class S,M start;
    class Q,SC,BD,P,UQ proc;
    class R dec;

Loading

Algorithm 1 — L-CAVO (paper §VI):

Inputs : V ≥ 0, ε ∈ (0,1), carbon trace {g_z(t)}, topology G
Init   : Q(0) ← 0
for each slot t = 0, 1, …, T−1 do
    1. Observe regional carbon intensities g_z(t) and request set R_t
    2. for each request r ∈ R_t do
           for each VNF k = 1..K_r do
               score(n) ← V·ΔCO₂(n) + 0.5·delay(n) + 0.3·util(n) + 0.05·Q(t)
               n*  ← argmin_n score(n)          subject to CPU, bw, D_max
           Place chain, otherwise mark r as rejected
    3. rej_t ← |R_t| − admitted_t
    4. Q(t+1) ← max( Q(t) + rej_t − ε·|R_t|, 0 )       ▷ virtual-queue update
end for

Code reference: sc_lc() (lcavo_sim.py:343) and the L-CAVO branch of sim() (lcavo_sim.py:582).

Benders decomposition (paper §VI-C)

For the per-slot offline benchmark, MILP-OPT is also solved via a lightweight Benders-style refinement that produces a real convergence trace (used by fig22_benders.pdf):

Inputs : current slot's requests R_t, allowed-server set N
Init   : forbidden ← ∅,  UB ← +∞,  LB ← 0
repeat for it = 1..K_max
    Master   : LP relaxation of (x_{r,k,n}, a_r, z_n) over N\forbidden   → LB
    Sub      : integer MILP restricted to servers the LP wants to use   → UB
    gap      : (UB − LB) / UB
    if gap < τ : stop
    Cut      : forbidden ← forbidden ∪ {arg min_n  load_hint(n)}        ▷ Benders cut
end repeat
return best integer placement, iteration log [(it, LB, UB, gap)]

Code reference: milp_benders() (lcavo_sim.py:527) and the fig22 generator (lcavo_sim.py:1063).

🔵 QL-CAVO — Q-Learning Carbon-Aware VNF Orchestration

QL-CAVO uses a tabular Q-learning agent that learns which regions to favour at each time-of-day. The state space encodes (hour, mean_carbon_intensity, queue_length), and actions correspond to region-preference weights.

Important

Training: 300 pre-training episodes on historical carbon profiles, followed by online updates during simulation.

flowchart LR
    OBS[Observe state<br/>hour · CO₂ · queue] --> SEL[ε-greedy action<br/>region weights]
    SEL --> ACT[Greedy placement<br/>under weights]
    ACT --> REW[Reward<br/>= -CO₂ - λ · rejects]
    REW --> UPD[Q-table update<br/>Q ← Q + α · TD]
    UPD --> OBS

    classDef ql fill:#8B5CF6,stroke:#4C1D95,color:#fff,stroke-width:2px;
    class OBS,SEL,ACT,REW,UPD ql;

Loading

Algorithm 2 — QL-CAVO (paper §VII):

Inputs : learning rate α=0.15, discount γ=0.95, ε-greedy schedule 0.25→0.02,
         historical carbon trace, topology G
Init   : Q-table Q[6,4,3,4] ← 0     ▷ (hour × CI × queue) × action
Pre-train (300 episodes on historical trace):
    for each replayed slot t :
        s ← (hour-bucket, CI-bucket, queue-bucket)
        a ← argmax_a Q[s,a]  with prob 1-ε,  else random
        r ← −CI(region_a) / 100
        Q[s,a] ← Q[s,a] + α·( r + γ·max_a' Q[s',a'] − Q[s,a] )
Online (simulation):
    for each slot t :
        s   ← discretise(hour, mean CI, virtual queue)
        a   ← ε-greedy(s)         ▷ pick preferred region
        w   ← weights(a)          ▷ region-preference vector
        place VNFs greedily under w  (sc_ql)
        r   ← −carbon(t)/100 + 0.5·acceptance(t)
        Q[s,a] ← Q[s,a] + α·( r + γ·max_a' Q[s',a'] − Q[s,a] )
        decay ε  (×0.995, floor 0.02)

Code reference: QAgent (lcavo_sim.py:382) and sc_ql() (lcavo_sim.py:437).

---

🚀 Quick Start

1️⃣ Clone & Install

git clone https://github.com/YassirALKarawi/carbon-aware-sfc.git
cd carbon-aware-sfc
pip install -r requirements.txt

2️⃣ Run Simulations

# Quick smoke test (3 seeds, ~5 min)
python lcavo_sim.py --quick

# Full reproduction (30 seeds, ~2 hours)
python lcavo_sim.py --seeds 30

# Generate to a custom output directory
python lcavo_sim.py --output-dir results/full_run

3️⃣ Reproduce Specific Paper Results

# Table III — NSFNET results
python lcavo_sim.py --topology NSFNET --seeds 30

# Table IV — GÉANT results
python lcavo_sim.py --topology GEANT --seeds 30

# Fig. 9 — V-sensitivity analysis
python lcavo_sim.py --topology NSFNET --load Medium --methods L-CAVO

# Fig. 10 — ε-sensitivity analysis
python lcavo_sim.py --topology NSFNET --load Medium --methods L-CAVO --skip-figures

Warning

Full 30-seed reproduction is computationally intensive (~2 h on a modern workstation). Use --quick for a fast end-to-end smoke test before launching the full sweep.

---

⚙️ Configuration

🔧 Parameter	🎚️ Default	📝 Description
--seeds	30	Number of independent simulation runs per scenario
--quick	off	Shortcut for a 3-seed smoke run
--topology	all	Subset of NSFNET,GEANT
--load	all	Subset of Low,Medium,High
--methods	all	Subset of supported algorithms and baselines
--output-dir	results	Root directory for tables/ and figures/
--skip-figures	off	Export CSV tables only (faster)
--no-milp	off	Disable MILP baseline even if PuLP is available

---

📊 Key Results

🌍 Carbon Reduction Performance (NSFNET)

Algorithm	🟢 Low Load	🟡 Medium Load	🔴 High Load
L-CAVO vs EA	~27 %	~26 %	~26 %
QL-CAVO vs EA	~18 %	~17 %	~17 %
Carbon-greedy	~12 %	~11 %	~10 %

🌱 Carbon Reduction vs Energy-Aware Baseline

⏰ Regional Carbon Intensity Profiles

✅ SFC Acceptance Rate

🌐 Cross-Topology Comparison

📈 V-Sensitivity Analysis

⏱️ End-to-End Delay CDF

🧩 Decomposition of Carbon Savings

L-CAVO achieves savings through two complementary mechanisms:

• 🗺️ Spatial steering — placing VNFs in regions with lower instantaneous carbon intensity
• 🕐 Temporal steering — shifting workload toward hours when cleaner energy is available

---

🖼️ Generated Figures

The full simulation produces 19 publication-quality PDF figures.

How to reproduce every figure

A single run of lcavo_sim.py writes all 19 figures under results/figures/. Use the commands below to reproduce them in different fidelity modes (smoke run for review, full run for the paper).

# All 19 figures, paper-grade (30 seeds, ≈ 2 h on a modern workstation)
python lcavo_sim.py --seeds 30

# Same figures, smoke quality (3 seeds, ≈ 5 min) — recommended for review
python lcavo_sim.py --quick

# Reproduce only a subset of scenarios (figures still all generated,
# but with whatever DB entries are available):
python lcavo_sim.py --topology NSFNET --load Medium --methods L-CAVO,QL-CAVO,MILP-OPT

# Tables only, no figures
python lcavo_sim.py --skip-figures

Tip

To download the figures without running the simulation locally, use the "Build figures" GitHub Actions workflow: push to your fork or click Run workflow and download paper-figures from the run's artifacts. The workflow shells out to python lcavo_sim.py --quick.

Per-figure index (paper §VII)

#	📄 Filename	📝 Description	Driver in lcavo_sim.py
7	fig07_carbon_profiles.pdf	Regional carbon intensity over 24 hours	carbon_prof()
8	fig08_reduction_vs_EA.pdf	Carbon reduction vs Energy-aware baseline	scenario sweep
9	fig09_reduction_vs_LA.pdf	Carbon reduction vs Latency-aware baseline	scenario sweep
10	fig10_hourly_carbon.pdf	Hourly carbon emissions by algorithm	NSFNET / Medium
11	fig11_cumulative.pdf	Cumulative carbon over the day	NSFNET / Medium
12	fig12_active_nodes.pdf	Active server count per slot	NSFNET / Medium
13	fig13_power.pdf	Power consumption over time	NSFNET / Medium
14	fig14_delay_cdf.pdf	End-to-end delay CDF	NSFNET / Medium
15	fig15_cross_topo.pdf	Cross-topology carbon comparison	NSFNET + GÉANT
16	fig16_V_sensitivity.pdf	V parameter sensitivity (carbon vs acceptance)	V ∈ {20,50,100,…}
17	fig17_eps_sensitivity.pdf	ε parameter sensitivity	ε ∈ {0.02,…,0.10}
18	fig18_pareto.pdf	Carbon–delay Pareto frontier	V sweep
19	fig19_regional.pdf	Regional VNF placement distribution	per-method rpct
20	fig20_temporal_steering.pdf	Temporal steering toward clean regions	hourly placement
21	fig21_queue.pdf	Virtual queue Q(t) evolution	L-CAVO @ several V
22	fig22_benders.pdf	Real Benders convergence trace per load	milp_benders()
23	fig23_runtime.pdf	Runtime scaling (L-CAVO vs MILP)	per-topology rt
24	fig24_variance.pdf	Sensitivity to carbon-intensity variance σ	sigma ∈ [0.25, 2.0]
25	fig25_opt_gap.pdf	Optimality gap vs V (O(1/V) bound)	V sweep

---

📁 Repository Structure

carbon-aware-sfc/
├── 📜 lcavo_sim.py          # Main simulation engine (all algorithms & figure generation)
├── 📦 requirements.txt      # Python dependencies
├── 📄 LICENSE               # MIT License
├── 📘 README.md             # This file
├── 🖼️  figures/              # Pre-rendered figures used in the README
├── 🧪 tests/                # Unit tests (16 tests, run via pytest)
└── 📊 results/              # Generated outputs (created on first run)
    ├── tables/              #   CSV summary tables
    └── figures/             #   Publication-quality PDF figures

---

📦 Requirements

Package	Version	Purpose
Python	≥ 3.9	Runtime
NumPy	1.26	Numerics
SciPy	1.13	Statistics
Pandas	2.2	Tables & CSV export
NetworkX	≥ 3.1	Topology graphs
Matplotlib	3.9	Publication figures
PuLP	≥ 2.7	MILP baseline (paper uses 2.7; ≥2.8 needed for Python 3.11)

Tip

Optional: Gurobi 11.0 (free academic license) can replace CBC for substantially faster MILP benchmarks.

---

🧪 Testing

# Run the full test suite (16 tests)
pytest -q

# Run a specific suite
pytest tests/test_algorithms.py -v

---

📚 Citation

If you use this code in your research, please cite:

@article{alqaisy2026carbon,
  author  = {Al-Karawi, Yassir},
  title   = {Carbon-Aware Service Function Chain Placement Under
             Time-Varying Grid Intensity: A {Lyapunov}-Optimisation
             and {Q}-Learning Framework},
  journal = {IEEE Trans. Green Commun. Netw.},
  year    = {2026},
  note    = {Submitted}
}

---

📜 License & Attribution

MIT License (simulation code) — see LICENSE for details.
The manuscript is © 2026 the author and may not be redistributed without permission.

---

Made with 💚 at the University of Diyala

⬆ Back to top