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With the advent of new technologies such as IoT (Internet of Things) and Big Data, the increase in users and their different communications have led to a significant increase in energy consumption in network equipment. A new networking technology called SDN (Software Defined Network) is born. It aims to make network management easier. The SDN consists of decoupling the control plane that is the brain, the data plane or the muscles of the network. It allows the programmability of network devices and also the redirection of flows. One or more centralized controllers use algorithms to act remotely on network devices. Because of its operation, this new technology offers opportunities to improve network performance and optimize energy consumption. In this paper, we will use this technology (SDN) to suspend links or routers when they are not used while taking into account the congestion that degrades the quality of service in the network. We have formulated this problem as a linear integer program and proposed algorithms to process it in normal period and peak period. We have used the OMNET ++ simulator to evaluate our algorithms. Thus, our approach showed that 87.5% of ports and 33.33% of links could be shut down to save energy.

Communication networks are progressively evolving in terms of size and performance. There are two types of network equipment: active devices such as routers, switches, etc. (information transmission devices) and passive devices such as cables, fiber optics, etc. (interconnection equipment). Of the two types of equipment, only assets are energy intensive. The evolution of the networks leads to an increase of these equipments in quantity and in performance. The increase of these and their performance increases the consumption of the electrical energy they need for their operation.

A study conducted in 2009 [

The advent of Software Defined Network (SDN) technologies appears to be a good alternative for acting remotely and dynamically on equipment in order to model energy consumption.

In SDN technology, it is a centralized controller that will be responsible for routing packets in the network via SDN protocol (openflow) by programmability by injecting routing rules provided by the application layer (

In this paper, we use this paradigm to act on network devices by enabling or disabling router ports when they are not working. A new strategy has been developed which takes into account the peak periods (dense traffic) and normal (low traffic) minimizing energy while avoiding congestion. The authors of [

Our model is based on that of these authors [

Section 2 will cover previous work. Section 3 describes the mathematical model of our approach. We present in Section 4, the resolution approach. In Section 5, we will evaluate the performance of the model. Section 6 concludes our article.

In this section, we will present some previous work that has addressed the issue of energy consumption in networks. We also formulate some basic assumptions that our future mathematical model must respect.

The consumption of energy has been treated by some researchers [

We orient our work in this way while finding a mathematical model of energy minimization in the SDN network which satisfies the “QoS” in terms of delay of transmission and loss of packets.

• Each port has the same rate of energy consumption.

• Each port can handle multiple services so it can redirect traffic.

• Choose in the graph, the path or paths that seem to offer more energy saving.

Our future mathematical model will be obtained through a set of processes that will involve theories such as graphs; trees etc.

This section will cover the description of our mathematical model.

We formulate our problem as a linear integer program in contributing to the optimization of energy consumption in SDN networks. Let N be a network and n(t) a sub-network of N ( n ( t ) ⊆ N ). We defined a dynamic approach based on two situations of graph theory:

1) The activation and deactivation of the ports of the routers for a given time t. we note the change in energy consumption.

2) We will assume that a router cannot be turned off and therefore must remain awake.

Once switched on, at each given instant t, a link is established between a router i and a router j. It will therefore be a question of maximizing a number of ports to be deactivated in order to have energy savings under “QoS” constraints. In our approach, we will enable or disable router ports using a smart approach.

The number of ports to disable l ( t ) is defined as:

l : [ 0 , + ∞ [ → N t ↦ l (t)

Consider λ max , the total number of ports on a router. This parameter λ max is fixed and depends on the types of routers. If the total number of ports on a router is 8, how much should I disable and how, to hope to save the maximum energy?

Let us consider the function f: the consumption of energy in the sub-networks. We express the model of our approach in mathematical from called objective function of the solution of the problem that is to say (1) and (2).

Which amounts to:

f ( n ( t ) , t ) = ∑ i ∈ n ( t ) f ( i , t , l ( t ) ) + ∑ i , j ∈ n ( t ) f ( k ( i , j , t ) ) (1)

A link is the junction between two routers interfaces. i , j ∈ N having a maximum load capacity of C ( i , j ) packet traffic per second. The links can be in the following state 0 or 1. Let k be the link state variable: 0 state where the router is off and 1 state where the router is on.

The objective function to be minimized becomes:

f ( n ( t ) , t ) = ∑ i ∈ n ( t ) f ( i , l ( t ) , t ) + ∑ i , j ∈ n ( t ) f ( k ( i , j , t ) ) (2)

where f ( i , l ( t ) , t ) is the energy consumption of the router i whose l ( t ) ports were deactivated at time t and f ( k ( i , j , t ) ) represents the energy of the link i, j at time t.

f ( i , t , l ( t ) ) is the function to be explained. Power gain function of router i: “g”. The function g is a linear and increasing function with respect to the number of ports deactivated at time t.

Let g i ( t , l ( t ) ) : the energy gain of the router i such that:

max t l ( t ) ≤ λ max , with g i ( t , l ( t ) ) = a l ( t ) + b

where a > 0 .

if max t l ( t ) ≤ λ max , then f i ( t , l ( t ) ) = C i − ( a l ( t ) + b ) (3)

This is the final expression of our function “energy consumption” of router. Otherwise f i ( t , l ( t ) ) = 0 where C_{i} is the total consumption of the router i and f ( i , t , l ( t ) ) = f i ( t , l ( t ) ) .

We deduce that if all ports are disabled, g i ( t , l ( t ) ) ≈ C i .

We showed above that our function is linear in l ( t ) . It is thus refined in the form of:

f ( n ( t ) , t ) = ∑ i ∈ n ( t ) ( C i − ( a l ( t ) + b ) ) + ∑ i , j ∈ n ( t ) f ( k ( i , j , t ) )

Now every affine function is convex and therefore admits a minimum. Our model then becomes:

min ( f ( n ( t ) , t ) ) = min ( ∑ i ∈ n ( t ) ( C i − ( a l ( t ) + b ) ) + ∑ i , j ∈ n ( t ) f ( k ( i , j , t ) ) ) (4)

With C_{i} = chassis consumption (C_{ch}) + consumption of ports (C_{p}) on. From where:

C i = C c h + C p

The explicit objective function becomes:

min ( f ( n ( t ) , t ) ) = min ( ∑ i ∈ n ( t ) ( ( C c h + C p ) − ( a l ( t ) + b ) ) + ∑ i , j ∈ n ( t ) f ( k ( i , j , t ) ) ) (5)

Under constraint of:

q ( f ( t ) , R ( F ( t ) , n ( t ) , k ( t ) , t ) ≤ Q ( f ( t ) ) , ∀ f ( t ) ∈ F ( t ) and ∑ f ( t ) ≤ C i , j , ∀ f ( t ) ∈ F ( t ) k ∈ { 0 , 1 }

Summary of the ratings:

We have found our mathematical model which minimizes, so a method of resolution proves necessary.

In this part, we proposed a resolution method of our mathematical model.

Solving the problem consists of:

• Solve by integer linear programming f i ( t , l ( t ) ) = C i − ( a l ( t ) + b )

• Solve by the Kruskal algorithm by looking for the maximal tree the function f ( k ( i , j , t ) )

We are going to build a network (lowest total weight covering tree) from which we will obtain our possible energy savings. The ports to be shut down will consist of those of the adjacent routers. For our simulation, we will use a network of 7 routers each with 8 ports and 9 links. All extinctions of adjacent ports cause those of these links (

Our tree covering the lowest total weight becomes (see

Total weight: 12 + 12 + 12 + 4 + 4 + 5 = 49.

Our demand-side extinguishing strategy must select all ports that are not affected by the request and dynamically shut them down.

In our approach, when a router is turned on, it establishes a link with its neighbors and so on in the network.

Our 7-router network has 8 ports each, only one port is turned on and the (n − 1) ports are off with its links. The circuits are to be avoided in the choice of favorable paths (having the lowest weight).

The Modified SPRING Protocol (MSP), is responsible for the extinction of ports and links unsolicited by the request (see Algorithms below).

This

The resolution approach having been found, we will evaluate the performance of our model.

In

Number of routers with 8 ports | Ports off | % Ports off | Number of links | Links off | % Links off |
---|---|---|---|---|---|

7 | 49 | 49/56 = 87.5 | 9 | 3 | 3/9 = 33.33 |

In our model, we explained high (see 4.1) that the extinct ports are those of adjacent routers. Once the port is off, it drives the one of its links. The SDN is a technology based on the programmability of remote equipment via a centralized controller in the network. The SDN controller, thanks to its global view of the network, is responsible for the extinction of the ports and links, if they are not used by means of a modification of the algorithm SPRING.

Our

Our mathematical model in SDN networks minimizes energy consumption. Any router chosen, disabling some ports would give a strong energy saving by this model. Our model is flexible and gives us a double energy saving in ports and links. In the ports, an extinction of 87.5% is possible to make savings and 33.33% in the links to also make savings.

In this article, we found our mathematical model; however, improvements are possible and will be the subject of our future work.

The authors declare no conflicts of interest regarding the publication of this paper.

Kra, L., Gondo, Y., Gooré, B.T. and Asseu, O. (2018) Contribution to the Optimization of the Energy Consumption in SDN Networks. Journal of Sensor Technology, 8, 59-67. https://doi.org/10.4236/jst.2018.83005