Definition and Evaluation of Cold Migration Policies for the Minimization of the Energy Consumption in NFV Architectures

Abstract

In the Network Function Virtualization (NFV) paradigm any service is represented by a Service Function Chain (SFC) that is a set of Virtual Network Functions (VNF) to be executed according to a given order. The running of VNFs needs the instantiation of VNF Instances (VNFIs) that are software modules executed on Virtual Machines. In this paper we cope with the migration problem of the VNFIs needed in the low traffic periods to switch off servers and consequently to save energy consumption. The consolidation has also negative effects as the energy consumption needed for moving the memories associated to the VNFI to be migrated. We focus on cold migration in redundant architecture in which virtual machines are suspended before performing migration and energy consumption required for transfer of virtual machine memory is the main concern. We propose migration policies that determine when and how to migrate VNFI in response to changes to SFC request intensity and location. The objective is to minimize the total energy consumption given by the sum of the consolidation and migration energies. The obtained results show how the policies allows for a lower energy consumption with respect to the traditional policies that consolidate resources as much as possible.

Appendix A Application of the Markov Decision Process (MDP) Theory for the Determination of the Global Policy

The proposed approach is based on choosing the solution in an a-priori determined and “good” possible solutions set. The assignment of the VNF nodes and links of the graph ${G}^{VNFI}=({V}^{VNFI},{E}^{VNFI})$ to server nodes and physical network paths respectively is defined as mapping. The global policy $\mathcal {D}^{glo}$ consists in choosing the mapping ${\varGamma }_h$ to be applied in each traffic state $T_h$ $(h=0,1,\cdots ,N-1)$ so as to minimize the objective function expressed by (1). The proposed simplified approach consists in selecting the mappings $\varGamma _h$ $(h=0,1\cdots ,N-1)$ applied in the traffic states $T_h$ $(h=0,1,\cdots ,N-1)$ by a set $\varTheta$; the choice of these mappings is accomplished by applying optimality criteria based on minimization of power consumption, minimization of reconfiguration costs,$\cdots$; not all of the mappings in $\varTheta$ can be applied in any state $T_h$ but only the admissible ones that do not lead to overcome the link bandwidth and the node processing resources. We denote with $\theta _{h,l}$ $(l=1,\cdots ,n_h)$ the $n_h$ mappings belonging to $\varTheta$ and admissible for the traffic condition $T_h$ ($h=0,\cdots ,N-1$); the state diagram reported in Fig. 6 represents the set of admissible mappings for each traffic state; it is organized in N levels where the $h-th$ ($h=0,1,\cdots ,N-1$) level is composed by the $n_h$ bi-dimensional states $(T_h,\theta _{h,l})$ $(l=1,\cdots ,n_h)$. The objective is to determine a policy that establishes which mapping to apply when traffic changes happens. Formally a policy is characterized by the set of integer values $\mathcal {D}=\{d_{h,l} \ \ h=0,1\cdots ,N-1; l=1,2,\cdots ,n_h\}$ where $d_{h,l}$ establishes that from the state $(T_h,\theta _{h,l})$, the mapping $\theta _{(h+1)\bmod N,d_{h,l}}$ has to be applied when the new traffic condition $T_{(h+1)\bmod N}$ occurs. Our objective is to determine the policy $\mathcal {D}^{glo}$ that minimizes the total cost in a cycle-stationarity period. We can determine the policy $\mathcal {D}^{glo}$ by finding the optimal policy in a Discrete Time Markov Decision Process (DTMDP) [8, 11] whose Markov chain is characterized by the states of Fig. 6. The state and transition costs [8, 11] in the DTMDP are as follows. Each state $(T_h,\theta _{h,l})$ is characterized by the consolidation energy cost $E^c_{(\theta _{h,l})}$ that is the energy consumed in the stationary interval $T_h$ when the mapping $\theta _{h,l}$ is applied. Furthermore a transition from the state $(T_h,\theta _{h,l})$ to the state $(T_{(h+1)\bmod N},\theta _{(h+1)\bmod N,k})$ is characterized by the migration energy cost $E^m_{(\theta _{h,l},\theta _{(h+1)\bmod N,k})}$ that is the energy consumed to move the virtual machines involved in migration process.

The number of possible alternatives [8, 11] in the state $(T_h,\theta _{h,l})$ is equal to $n_{(h+1)\bmod N}$ that is the number of mappings applicable when the traffic state transition from $T_h$ to $T_{(h+1)\bmod N}$ occurs. The integer variable $d_{h,l}$ ($d_{h,l}\in [1..n_{(h+1)\bmod N}]$) codes the alternative chosen in the state $(T_h,\theta _{h,l})$ that involves the use of the mapping $\theta _{(h+1)\bmod N,d_{h,l}}$. When $d_{h,l}$ has been specified for $h\in [0..N-1]$ and $l\in [1..n_h]$, a mapping policy has been determined. The optimal mapping policy $\mathcal {D}^{glo}$ = $\{d_{h,l}^{glo} \ \ h=0,1\cdots ,N-1; l=1,2,\cdots ,n_h\}$ is the one that minimizes the expected total cost. To determine it we apply the policy iteration method [8, 11] that needs the evaluation versus the alternative $d_{h,l}$ of both the transition probabilities $p_{h,l}^{j,k,d_{h,l}}$ from the state $(T_h,\theta _{h,l})$ to the state $(T_j,\theta _{j,k})$ and the cost $q_{h,l}^{d_{h,l}}$ to be expected in the next transition out of the state $(T_h,\theta _{h,l})$. The transition probabilities $p_{h,l}^{j,k,d_{h,l}}$ are reported in Fig. 6 for the alternatives $d_{h,l}$ = 1, $d_{h,l}$ = k and $d_{h,l}$ = $n_{(h+1)\bmod N}$. We can notice as the choice of the alternative $d_{h,l}$ involves only a transition with probability 1 from the state $(T_h,\theta _{h,l})$ to the state $(T_{(h+1)\bmod N},\theta _{(h+1)\bmod N,d_{h,l}})$. Thus we can simply write:

$$\begin{aligned} p_{h,l}^{j,k,d_{h,l}} = \left\{ \begin{array}{lcl} 1 &{} &{} if \ \ \ j=(h+1)\bmod N, \ \ \ k=d_{h,l} \\ 0 &{} &{} otherwise \\ \end{array} \right. \end{aligned}$$

(10)

For the evaluation of $q_{h,l}^{d_{h,l}}$ we observe that if the choice of the alternative $d_{h,l}$ in the state $(T_h,\theta _{h,l})$ leads not to change the applied mapping, that is $\theta _{(h+1)\bmod N,d_{h,l}}\equiv \theta _{h,l}$, the migration energy costs are not involved and only the energy consumption cost $E^c_{(\theta _{h,l})}$ of applying the mapping $\theta _{h,l}$ has to be considered. Otherwise when a mapping change occurs, also the migration energy cost $E^m_{(\theta _{h,l},\theta _{(h+1)\bmod N,d_{h,l}})}$ from the mapping $\theta _{h,l}$ to the mapping $\theta _{(h+1)\bmod N,d_{h,l}}$ has to be added. Hence we can write:

$$\begin{aligned} q_{h,l}^{d_{h,l}}= \left\{ \begin{array}{lcl} E^c_{(\theta _{h,l})} \ \ if \ \ \theta _{(h+1)\bmod N,d_{h,l}}\equiv \theta _{h,l} \\ E^c_{(\theta _{h,l})+E^m_R(\theta _{h,l},\theta _{(h+1)\bmod N,d_{h,l}})} \ \ otherwise \end{array} \right. \end{aligned}$$

(11)

Once established the transition probabilities $p_{h,l}^{j,k,d_{h,l}}$ and the cost $q_{h,l}^{d_{h,l}}$ as a function of the alternative $d_{h,l}$ we can find the policy $\mathcal {D}^{glo}$ = $\{d_{h,l}^{glo}, \ \ h=0,1\cdots ,N-1; l=1,2,\cdots ,n_h\}$ by applying the policy-iteration method [8, 11].

Fig. 6.

Bi-dimensional Discrete Time Markov Chain in which each state is characterized by some possible alternatives; the choice of an alternative in each state determines a mapping policy.