DeeP-TE: Data-Enabled Predictive Traffic Engineering

• DeeP-TE is a framework that directly learns input-output mappings from historical routing data using Hankel matrix techniques without explicit traffic matrix estimation.
• It minimizes network congestion and limits frequent routing changes by solving a convex optimization problem that incorporates linear autoregressive predictions and persistent data excitation.
• Numerical experiments on real topologies show near-optimal delay performance (within 8% of an oracle) and a 75% reduction in routing changes compared to baseline methods.

Data-Enabled Predictive Traffic Engineering (DeeP-TE) is a framework for adaptive network routing that updates routing configurations over time-varying traffic without ever explicitly measuring or inferring the full traffic matrix. In the 2025 formulation, it leverages the behavioral theory of linear systems and data-enabled predictive control (DeePC) to generate routing updates directly from historical routing decisions and link-load measurements, with the objective of minimizing network congestion while controlling performance degradation caused by frequent route changes. Numerical experiments on real network topologies with real traffic matrices report close-to-optimal control effectiveness together with significantly lower routing variations than baseline methods (Yin et al., 19 Aug 2025).

1. Formal problem statement

DeeP-TE models the network as a directed graph $G=(V,E)$ with $n_l=|E|$ links, each of capacity $C_{\ell_i}$, and $n_w=|V|(|V|-1)$ origin-destination demands. Demand $d$ at time $s$ has volume $w_d(s)$. For each demand $d$ there are $n_{p,d}$ precomputed paths, and $n_p=\sum_d n_{p,d}$ denotes the total number of path variables. The routing configuration at sample $n_l=|E|$0 is

$n_l=|E|$1

with $n_l=|E|$2 and $n_l=|E|$3.

The link-load vector $n_l=|E|$4 obeys the static path-load relation

$n_l=|E|$5

where $n_l=|E|$6 and $n_l=|E|$7 is the incidence matrix of paths for OD $n_l=|E|$8. Routing updates occur every control interval $n_l=|E|$9 spanning $C_{\ell_i}$0 sampling slots, with $C_{\ell_i}$1. Within each control interval $C_{\ell_i}$2, the routing is held constant as $C_{\ell_i}$3 for $C_{\ell_i}$4.

The design is driven by two competing goals. The first is to minimize cumulative link delay,

$C_{\ell_i}$5

where $C_{\ell_i}$6 is a convex increasing delay-utilization function. The second is to limit large routing changes between intervals, measured by $C_{\ell_i}$7. The resulting optimal-control formulation over $C_{\ell_i}$8 intervals is

$C_{\ell_i}$9

Because $n_w=|V|(|V|-1)$0 is never directly measured, the formulation rules out a model-based solution in the usual traffic-matrix sense. This is the central problem setting that motivates DeeP-TE (Yin et al., 19 Aug 2025).

2. Behavioral-system foundation and DeePC construction

The core predictive mechanism is DeePC. For a discrete signal $n_w=|V|(|V|-1)$1 and an integer $n_w=|V|(|V|-1)$2, the $n_w=|V|(|V|-1)$3-row Hankel matrix is defined as

$n_w=|V|(|V|-1)$4

Willems’ fundamental lemma is the key representational result. If the past routing record $n_w=|V|(|V|-1)$5 is persistently exciting of order at least $n_w=|V|(|V|-1)$6, then any other trajectory of length $n_w=|V|(|V|-1)$7 can be represented as a linear combination of columns of the Hankel matrix built from $n_w=|V|(|V|-1)$8. In the stateless mapping $n_w=|V|(|V|-1)$9, the system order is $d$0 and the minimal data length is $d$1, where $d$2 is the number of independent routing variables.

Partitioning the Hankel matrix $d$3 into two block rows $d$4 for routing and $d$5 for loads yields the relation

$d$6

For any candidate routing vector $d$7, solving the least-squares system for $d$8 yields the predicted load vector $d$9. Thus prediction is performed directly in the input-output space, without identification of explicit model matrices.

To extend this to a receding horizon of $s$0 intervals, the formulation predicts piece-wise-constant traffic matrices $s$1 via a simple linear autoregressive model trained offline on past $s$2. For each horizon step $s$3, DeeP-TE forms dummy loads $s$4 that would result if $s$5 were applied to past $s$6, $s$7, through small Hankel solves, and then combines them via linearity:

$s$8

where $s$9 are the AR-model coefficients.

The resulting data-driven predictive control problem is

$w_d(s)$0

subject to the Past-Hankel constraints for dummy-load predictions, the reconstruction equation for $w_d(s)$1, and the flow-split constraints on $w_d(s)$2. Here $w_d(s)$3 discounts future cost, $w_d(s)$4, and $w_d(s)$5 regularizes $w_d(s)$6 for noise robustness (Yin et al., 19 Aug 2025).

3. Algorithmic workflow and implementation details

The implementation is organized in discrete control intervals $w_d(s)$7 of duration $w_d(s)$8.

Step 0 (Offline): precompute top-$w_d(s)$9 shortest paths for each OD and assemble $d$0; train an AR-model $d$1 of order $d$2 on historic $d$3 data.

Step 1 (Data collection): within interval $d$4, at each sample $d$5, record $d$6. To ensure persistent excitation, randomly perturb a small fraction, for example $d$7, of elephant-flow splits each sample.

Step 2 (Prediction): compute past mean traffic $d$8 if available or approximate it; form Hankel blocks $d$9 and $n_{p,d}$0 from collected data; then, for $n_{p,d}$1 and $n_{p,d}$2, solve

$n_{p,d}$3

to obtain dummy loads $n_{p,d}$4.

Step 3 (Optimization): solve the convex program

$n_{p,d}$5

subject to the Hankel constraints and split-sum constraints.

Step 4 (Implementation): apply $n_{p,d}$6 for the next control interval and return to Step 1.

The reported experimental parameter choices are $n_{p,d}$7 min, $n_{p,d}$8 min with $n_{p,d}$9, horizon $n_p=\sum_d n_{p,d}$0, autoregressive order $n_p=\sum_d n_{p,d}$1, and discount factor $n_p=\sum_d n_{p,d}$2, together with $n_p=\sum_d n_{p,d}$3 and $n_p=\sum_d n_{p,d}$4 (Yin et al., 19 Aug 2025).

A notable practical feature is that control actions are generated directly from historical routing data and the corresponding link-rate data. This means that the operational loop is defined over observable routing and load records rather than over an explicitly estimated traffic-matrix state.

4. Experimental evaluation and reported performance

The reported evaluation uses three real topologies from SNDlib—France with 21 nodes and 41 links, Geant with 22 nodes and 36 links, and TA1 with 24 nodes and 55 links—together with 20 independently generated 3-day traffic series at 5 min granularity. These traces mix a few large elephant inter-DC flows with many small flows, and each series is split into 30 min control intervals (Yin et al., 19 Aug 2025).

The baselines are: OPT, an omniscient oracle that knows the true $n_p=\sum_d n_{p,d}$5 every 5 min and re-optimizes to minimize $n_p=\sum_d n_{p,d}$6; CONST, the static optimum over the first two days’ mean traffic matrix; and TG-5 min / 30 min, Tomogravity estimation every 5 min or 30 min followed by MPLS-style path-split optimization. Performance is evaluated with two metrics:

$n_p=\sum_d n_{p,d}$7

and

$n_p=\sum_d n_{p,d}$8

The paper reports the following averages across 60 series:

Method	$n_p=\sum_d n_{p,d}$9	$n_l=|E|$00
OPT	1.00	2.5
CONST	1.25	0.00
TG-5 min	1.45	8.2
TG-30 min	1.38	3.1
DeeP-TE	1.08	0.8

These results support two specific claims. First, DeeP-TE achieves within $n_l=|E|$01 of the oracle delay. Second, it incurs on average only $n_l=|E|$02 $n_l=|E|$03-units of routing change per 30 min, which is reported as a $n_l=|E|$04 reduction in routing change compared with the 30 min TG baseline. Figure 1 is described as a box-plot of PR versus log RC showing DeeP-TE near the lower-left corner, indicating the simultaneous attainment of good delay and low rerouting (Yin et al., 19 Aug 2025).

5. Mechanism, significance, and conceptual distinctions

The stated explanation for the reported behavior is that DeeP-TE directly learns the input-output mapping from past routing perturbations to link-load responses. By doing so, it avoids any intermediate traffic-matrix inversion and therefore remains robust to under-determined tomography errors. The paper further states that aggregating only the elephant flows and collapsing routing splits link-wise reduces the decision dimension from thousands down to a few dozen, making the Hankel-based prediction accurate with only a handful of well-designed perturbations (Yin et al., 19 Aug 2025).

This yields an important conceptual distinction within predictive traffic engineering. DeeP-TE, in the 2025 sense, is not built around an explicit demand-estimation stage. A common assumption in WAN traffic engineering is that adaptive routing must first solve a traffic-matrix measurement or inference problem and only then optimize routes. DeeP-TE is formulated precisely to avoid that dependency. A plausible implication is that the framework shifts the central systems problem from tomography accuracy to excitation design, Hankel conditioning, and receding-horizon optimization.

It is also distinct from neural-network routing approaches. In the related line summarized as “A Deep Learning Perspective on Network Routing,” traffic engineering under demand uncertainty is posed as stochastic optimization over a decision function $n_l=|E|$05, typically parameterized by a neural network $n_l=|E|$06, with maximum-link-utilization as the primary objective. In experiments on Abilene, GEANT, and a Microsoft production WAN, that approach reports median MLU within $n_l=|E|$07 of oracle and online inference times of $n_l=|E|$08–$n_l=|E|$09 s, but its architecture and learning procedure are fundamentally different from the Hankel- and DeePC-based construction of DeeP-TE (Perry et al., 2023).

6. Assumptions, limitations, and research directions

The 2025 formulation makes several assumptions explicit. The mapping $n_l=|E|$10 is linear in $n_l=|E|$11 for fixed $n_l=|E|$12, and the predictive model treats slow $n_l=|E|$13-variations via linear autoregression and low-order basis functions; the paper states that large nonlinear or abrupt traffic shifts may degrade performance. It also assumes that traffic cyclo-stationarity within the control interval can be captured by a small set of basis functions, and it identifies data excitation as a practical requirement: perturbations that are too small lead to ill-conditioned Hankel solves, while perturbations that are too large risk service disruption (Yin et al., 19 Aug 2025).

The paper lists several potential extensions: data-enabled robust MPC with uncertainty bounds, hybrid schemes in which some OD flows are directly measured or estimated while the rest are handled by DeeP-TE, nonlinear extensions via kernel-based DeePC or subspace-dynamic extensions for higher-fidelity traffic models, and integration with reinforcement learning to adapt the magnitude and choice of perturbations. These directions remain consistent with the framework’s central premise of predicting control-relevant behavior directly from data rather than from a full parametric model.

Methodologically adjacent work in data-enabled predictive control illustrates how these extensions might develop. “Distributed data-driven predictive control for cooperatively smoothing mixed traffic flow” formulates a cooperative DeeP-LCC problem with Hankel-based local predictors, linear coupling constraints, and an ADMM implementation that exchanges only two $n_l=|E|$14-vectors per link per iteration while keeping raw Hankel data local. “Physics-Augmented Data-EnablEd Predictive Control for Eco-driving of Mixed Traffic Considering Diverse Human Behaviors” augments DeePC with physical residual constraints and online Hankel updates. These works address mixed vehicular traffic rather than packet-routing traffic engineering, but they show that distributed decomposition, physics augmentation, and online data specialization are compatible with the broader DeePC paradigm. This suggests plausible future variants of DeeP-TE with distributed optimization, hybrid physical constraints, or adaptive Hankel maintenance at larger operational scale (Wang et al., 2022, Li et al., 2023).