Machine Learning-Based Multipath Routing for Software Defined Networks

Abstract

Network softwarization has recently been enabled via the software-defined networking (SDN) paradigm, which separates the data plane from control plane allowing for a flexible and centralized control of networks. This separation facilitates implementation of machine learning techniques for network management and optimization. In this work, a machine learning-based multipath routing (MLMR) framework is proposed for software-defined networks with quality-of-service (QoS) constraints and flow rules space constraints. The QoS-aware multipath routing problem in SDN is modeled as multicommodity network flow problem with side constraints, that is known to be NP-hard. The proposed framework utilizes network status estimates, and their corresponding routing configurations available at the network central controller to learn a mapping function between them. Once the mapping function is learned, it is applied on live-inputs of network status and routing requests to predict a multipath routing solutions in real-time. Performance evaluations of the MLMR framework on real traces of network traffic verify its accuracy and resilience to noise in training data. Furthermore, the MLMR framework demonstrates more than 98.99% improvement in computational efficiency.

Appendices

Appendix 1: Column Generation-Based Approach

We give a brief description of the column generation-based approach presented in [16] to solve the MCNF with side constraints. The CRP is expressed in arc-flows rather than path-flows. Then, a subset of paths that satisfy the side constraints, i.e., feasible paths, is considered for each flow. Denote the set of feasible paths $\bar{\mathcal {P}}_f = \{ p | p \in \mathcal {P}_f, \sum _{l \in \mathcal {L}} \delta _{pl} \omega _{fl} \le u_f\}, ~ \forall f \in \mathcal {F}$. Incorporating the side constraints into the set of feasible paths, allows formulating the problem as a linear program which is given by [16],

$$ \begin{aligned} \text{CRP-LP:} \quad {{\mathop {\min}}}_{\theta_{p},\delta_{pl}}&\sum_{f \in \mathcal {F}} \sum_{p \in \bar{\mathcal {P}}_{f}} \theta_{p} d_{f} \eta_{p} + \sum_{f \in \mathcal {F}} \mathfrak {M} ~\mathfrak {s}_{f} \end{aligned} $$

(16)

$$\begin{aligned} \hbox {s.t.}&\sum _{f \in \mathcal {F}} \sum _{p \in \bar{\mathcal {P}}_f} \delta _{pl} \theta _{p} d_f \le g_l,~\forall l \in \mathcal {L} \end{aligned}$$

(17)

$$\begin{aligned}&\sum _{p \in \bar{\mathcal {P}}_f} \theta _{p} d_f + \mathfrak {s}_f=d_f,\quad \quad ~~~\forall f \in \mathcal {F} \end{aligned}$$

(18)

$$\begin{aligned}&\theta _{p} d_f \ge 0~~\quad \forall p \in \bar{\mathcal {P}}_f, \forall f \in \mathcal {F} \end{aligned}$$

(19)

$$\begin{aligned}&\mathfrak {s}_f \ge 0~~\forall f \in \mathcal {F}. \end{aligned}$$

(20)

Here, $\mathfrak {s}_f$ is an artificial variable associated with demand f constraint. Moreover, each variable has a cost coefficient $\mathfrak {M}$. The theoretical difficulty of CRP is now hidden in $\bar{\mathcal {P}}_f$, i.e., the generation of paths.

Let $\mathfrak {\pi }_l$ and $\kappa _f$, be dual variables associated with (17) and (18), respectively. Then, the CRP-LP problem can be decomposed into F subproblems, i.e., a problem for each flow, and the following column-generation-based approach is applied. In each iteration, the Procedure 1 provides upper and lower bounds. Therefore, it can be stopped when they are sufficiently close to each other.

A label correcting algorithm is used to solve each of the subproblems [16]. The algorithm allows creation of multiple labels, each with a cost and weight at each node. The labels are sorted in a priority queue in accordance with their cost value. In each iteration, a label is chosen and updated. Let s, t, lim, Q and n(i) be the source, the destination, the weight limit, the priority queue, and the number of labels at node i, respectively. Then, a formal description of the multi-labeling algorithm is given in Algorithm 1. Let $\omega _{ij}$ be a weight coefficient of the link connecting nodes i and j for a given flow f; hence, it is equivalent to the a weight coefficient $\omega _{fl}$. Similarly, let $\bar{c}_{ij}$ be the link reduced costs corresponding to $\bar{c}_{fl}$ of the link l connecting nodes i and j.

Appendix 2: Complexity Analysis

In order to be able to compare the computational time of both MLMR framework and CGbA, the number of flows F can be written in terms of number of forwarding elements N. Assume that there are flows from each forwarding element to all other elements; hence, the number of flows $F=N^2$. Let h be the number of layers in the proposed DNN. Then, the maximum number of neurons in any of the layers of the proposed DNN is $KN^2$. Therefore, the runtime of h matrix multiplications is $\mathcal {O}\left( h (KN^2)^3\right)$, i.e., $\mathcal {O}(K^3 N^6)$, where $K<< N$ and h is constant.

The CGbA consists of five major steps outlined in Procedure 1. The Floyd-Warshall algorithm can be used to identify the shortest feasible paths between every pair of nodes in first step. Then, the runtime of the first and second step is $\mathcal {O}\left( N^3 \right)$. The CRP-LP is solved in step three for each flow $f \in \mathcal {F}$. Given that the runtime of the label correcting algorithm is $\mathcal {O}\left( lim^2N^2\right)$, where lim is bounded by N and $F=N^2$, the third step runtime is $\mathcal {O}(N^6)$ [16]. In step four and five, the maximum number of columns that can be added for all flows is $N^2(K-1)$ and the runtime of solving the subproblem is $\mathcal {O}( N^4)$. Thus, the runtime of steps three, four and five is $\mathcal {O}\left( N^2(K-1)[N^6+N^4]\right)$. Hence, the overall time of CGbA is $\mathcal {O}\left( N^8(K-1)\right)$.

The empirical and asymptotic computational analysis demonstrate superiority of the proposed MLMR framework to the CGbA.