On the performance of online and offline green path establishment techniques
 Alejandro RuizRivera^{1},
 KwanWu Chin^{1}Email author,
 Sieteng Soh^{2} and
 Raad Raad^{1}
https://doi.org/10.1186/s136380150417z
© RuizRivera et al. 2015
Received: 4 May 2015
Accepted: 21 June 2015
Published: 16 July 2015
Abstract
To date, significant effort has gone into designing green traffic engineering (TE) techniques that consolidate traffic onto the minimal number of links/switches/routers during offpeak periods. However, little works exist that aim to green MultiProtocol Label Switching (MPLS) capable networks. Critically, no work has studied the performance of green label switched paths (LSPs) establishment methods in terms of energy savings and acceptance rates. Henceforth, we add to the current stateoftheart by studying green online and offline (LSP) establishment methods. Online methods rely only on past and current LSP requests while offline ones act as a theoretical benchmark whereby they also have available to them future LSP requests. We introduce a novel metric that takes into account both energy savings and acceptance rates. We also identify a new simpler heuristic that minimizes energy use by routing source–destination demands over paths that contain established links and require the fewest number of new links. Our evaluation of two offline and four online LSP establishment methods over the Abilene and AT&T topologies with random LSP setup requests show that energy savings beyond 20 % are achievable with LSP acceptance rates above 90 %.
Keywords
1 Introduction
The Climate Group Organization [1] reports that the Information and Communication Technology (ICT) industry accounts for up to 2 % of global carbon gas emissions. This is expected to increase further with the continued popularity of a number of services and technologies such as Internet protocol TV (IPTV) [2], Voice over IP (VoIP) [3], the Internet of Things (IoT) [4], and cloud computing [5]. In fact, global IP traffic is estimated to have a compound growth rate of 21 % from 2013 to 2018 [6], surpassing the zettabyte (1000 exabytes) threshold in 2016. As a result, analysis such as [7] forecasts that the global carbon footprint of telecommunication network devices will grow by 5 % each year between 2002 and 2020 due to the steady rise in electricity demand. The authors of [8] indicate that the United States of America (USA) alone uses 24 TWh per year, costing around $24 billion annually.
In their seminal work, Gupta et al. [9] highlighted the need to reduce the energy consumption of the Internet. Their work inspired a number of research directions with the common aim of reducing the energy expenditure of routers/switches. In general, these works can be categorized as (i) sleeping [10], which aims to place subcomponents of devices or devices themselves to sleep, (ii) link adaptation [11], which scales the energy consumption according to varying link utilization, (iii) proxying [8], which reduces network chatters by way of a proxy, and lastly (iv) traffic engineering (TE) [12–16], whereby traffic is routed across the minimal number of links and routers. We note that in general energy efficiency is a contemporary research issue that is of considerable interest to researchers. For example, a number of works have studied green TE approaches that consider application and data center characteristics; e.g., [17–20]. Another is designing energy aware protocols for nextgeneration networks such as Internet of Things [21, 22], vehicular networks [23, 24], and wireless sensor/mesh networks [25, 26].
The methods investigated in this paper belong to the TE category. We focus on Multiprotocol Label Switching (MPLS) networks. In particular, green label switched paths (LSPs) methods that use the fewest number of links. We note that establishing label switched paths (LSPs) to meet one or more QoS constraints or/and to maximize the number of admitted LSPs is a wellresearched problem; see Section 2. However, there are only few works that are energy aware; see Section 2.
 1.
It compares the LSP acceptance rates of existing online and offline energy aware algorithms for establishing LSPs. We study (i) offline approaches, where the complete set of LSP setup requests is known in advance, and (ii) online approaches, where we only know the current and past LSP setup requests. In fact, this is the first study that compares all these approaches over the same topologies. Moreover, we propose an Integer Linear Program (ILP) formulation for the offline version of the problem.
 2.
This paper presents and studies the performance of two offline and four online heuristics: i) Offline Most Overlapped (OfflineMO) [27], a technique that aims to use paths that share the most links with past or/and future LSP requests, ii) Offline with Ratio (OfflineR), which is similar to OfflineMO but favors paths that require fewer number of new links, iii) Online Most Overlapped (OnlineMO), which is similar to its offline counterpart, is an algorithm that uses paths that share the most links with already established links, iv) Online with Ratio (OnlineR), which is similar to OnlineMO but prefers paths that involve the minimal number of new links, v) Online Minimum Hops (OnlineMinH) [28], an approach that gives priority to paths with a small number of hops, and vi) Online Random LSP (OnlineRLSP) [29] which selects paths randomly.
 3.
The paper also introduces and uses a ratio, called ρ, of the percentage of shut down links (PSL) and LSP acceptance requests (LAR) to quantify how well a method performs in terms of energy savings and its ability to accept new LSP requests. This metric ρ allows us to evaluate whether a solution that is able to accept a larger number of LSP requests also has significant energy savings. Extensive experiments involving wellknown topologies such as Abilene and AT&T using varying traffic loads confirm that LSP acceptance rates above 90 % are feasible with 20 % of links shut down.
The rest of the paper is structured as follows. Section 2 surveys related works. Section 3 outlines a formal definition of the problem. Section 4 introduces the proposed heuristics. Section 5 describes our research methodology and presents and discusses the evaluation results. Our conclusions are presented in Section 6.
2 Related work
This section is divided into two parts. The first part presents different green routing techniques. It then briefly describes works that aim to optimize the establishment of LSPs in conventional (nonenergy sensitive) MPLS networks.
2.1 Green approaches
Current IP networks are designed to handle the worstcase scenario in terms of failures and traffic demands [10]; thus, not surprisingly, they are overprovisioned to handle peak traffic demands. On the contrary, many works have shown traffic to exhibit diurnal patterns [30]. Moreover, the utilization of backbone networks can be less than 30 % [8]. Consequently, given these observations, a number of researchers have proposed to power off network elements.
2.1.1 2.1.1 LSP establishment methods
We start by reviewing works that deal with energyefficient LSP establishment methods.
In [28], the authors propose an online routing algorithm, called Energy Efficient MultiConstrained Routing Algorithm (E^{2}MCRA), that aims to maximize LSP acceptance rates and minimize the number of active nodes and links while also considering additive QoS constraints. Its key ideas are to route a LSP request over paths with the minimum number of hops and instead of exhaustively exploring all paths, the algorithm searches only subgraphs induced by active routers and links. In [27], the authors exploit preinstalled backup paths used to protect against failed links on a primary LSP. The proposed algorithm, called GBP, achieves energy saving by rerouting traffic from protected links onto these backup paths. In addition, long backup paths are avoided. Protected links are then shut down. References [31, 32] use an ILP to minimize the number of active links/routers during a given period of time while satisfying all traffic demands in every interval. The ILP’s objective function considers the following factors: i) energy consumed by an active chassis, ii) energy consumed by line cards when powered on, and iii) the energy consumed by a chassis when transitioning from the off to on state. Coiro et al. in [33, 34] present Distributed and Adaptive Interface Switchoff for Internet Energy Saving (DAISIES), an online algorithm that continuously monitors the load of each link and calculates a new set of link weights. Its aim is to reduce the number of links carrying traffic. The new link weights are then used by Dijkstra’s algorithm to generate a new network topology, and links that are not part of this topology are switched off.
As we will elaborate in Section 5, the performance of E^{2}MCRA is similar to that of an online heuristic that prefers to route an LSP over active links; see Section 5.3. Advantageously, the heuristic does not involve the expensive LookAhead and DFS phases of E^{2}MCRA. In addition, one of the heuristics we investigated shares a key similarity to GBP whereby it avoids the use of long paths and aims to route over existing paths without having to establish new links.
2.1.2 2.1.2 Green TE
To date, there are a number of green TE approaches. However, they do not consider LSPs. We briefly summarize a few key works. A modification of the Open Short Path First (OSPF) algorithm [35] is presented by Cianfrani et al. in [36]. They propose EnergyAware Routing (EAR), whereby links that are not part of the shortest path tree (SPT) calculated by each router are switched off. In a different work, the authors of [12] formulated a mixed integer linear programming (MILP) problem to maximize the total power savings while minimizing the overall maximum link utilization (MLU). The main ideas are to select candidate paths with the minimum number of hops, shorter than the network diameter, or meet endtoend delay constraints. In [37], the authors consider the problem of scheduling deadline constrained flows and their routing in a data center. Specifically, they formulated a convex optimization problem where the decision variables are to determine the transmission rate of a flow and its route such that a network’s total energy expenditure is minimized. A key constraint is that the rate assigned to a flow must ensure all its data is transmitted within a given deadline.
In [38], routers are ranked according to one of the following criteria: i) random ii) degree iii) number of flows, or iv) number of active neighbors. They propose heuristics that either select the highest ranked router to be shut down or one with the highest power consumption. Wang et al. [39] aim to eliminate packet loss that occurs when consolidating traffic. They focus on IP networks that implement the Fast Reroute (FRR) NotVia technique [40], where for a given source–destination pair, there are multiple precomputed paths that are used upon a failure.
In a different work, Bianzino et al. [13] propose an algorithm called Green Distributed Algorithm (GrIDA) that switches off links according to a link’s current load and power consumption. Lin et al. [41] consider the QoS of flows when switching off network elements. On the other hand, the Green Distributed Routing Protocol for Sleep Coordination (GDRPPS) algorithm of [42] divides core routers into two sets: traditional routers (TRs) and power saving routers (PSRs). TRs are not allowed to sleep whereas PSRs are routers running GDRPPS and, therefore, go to sleep whenever the traffic load is low. Before powering down, a PSR first checks whether the network remains connected if it shuts down. If so, it informs a coordinator it will enter sleep mode.
Athanasiou et al. [15] propose EnergyAware Traffic Engineering (ETE), a distributed and offline algorithm that loadbalances traffic while minimizing energy consumption and MLU. ETE is composed of the following algorithms: i) Load Balancing (LB). Each ingress node finds the amount of traffic destined to a given egress node that needs to be routed through each of its links in order to maximize link utilization; ii) Energy Saving (ES). Each ingress node takes an input traffic information from LB and uses it to calculate the minimum number of links required to carry said traffic. The authors of [43] propose heuristics to determine the network configuration that consumes the least amount of energy within a search space that contains all possible combination of nodes and active/sleeping links. To reduce the search space, the proposed heuristics generate all patterns for a given topology, where a pattern is a subgraph of the original topology induced by a subset of sleeping links. In a different approach, the authors of [44] present Energy Aware TE (EATe), whereby traffic is spread across multiple paths. Cuomo et al. [45] introduce a topology aware algorithm called Energy Saving based on Algebraic CONnectivity (ESACON). This algorithm relies on the algebraic connectivity of a network. In particular, they rely on the fact that algebraic connectivity is a good indicator of a graph’s robustness to node and link failures [46]. Finally, the authors of [47] present Energy Profile Aware Routing (EPAR), an energy aware TE approach that uses network equipment energy profiles (EPs) and builds on the Energy Aware Routing (EAR) algorithm proposed in [9]. EPAR accounts for the different EPs of devices and routes traffic along paths with energyefficient components.
To the best of our knowledge, existing works thus far either do not consider LSPs, and for those that do, they have not considered the relationship between LSP acceptance rates and energy savings. This is critical because a given rule used to establish LSPs may yield a low acceptance rate; i.e., it blocks future LSPs from being admitted despite having large energy savings. In this regard, only [28] has considered both energy consumption and acceptance rate jointly. However, they only compared their proposed method to one other green LSP establishment approach and did not study the relationship between the remaining number of active links and the acceptance of future LSP requests. We on the other hand consider six heuristics. Critically, we compare online against offline approaches and evaluate them using a novel metric that succinctly quantifies the advantage of an LSP establishment method in terms of energy saved and acceptance rate. Moreover, we present a new and simple heuristic that has comparable performance to the one presented in [28].
2.2 Nongreen LSP establishment approaches
As noted in Section 1, there are many studies on increasing LSP acceptance rates by minimizing interference between LSPs. In addition, these studies also address the problem of establishing LSPs that satisfy one or more QoS constraints. Critically, the majority of these studies do not aim to conserve energy. In [48], Hong et al. propose Multiple Constraintbased Shortest Path First (MCSPF), which is based on the widely used Constraint Shortest Path First (CSPF) [49] algorithm. MCSPF aims to select LSPs that satisfy bandwidth and endtoend delay constraints while maximizing LSP acceptance rates. In [50], the authors present a modification to the WangCrowcroft (WC) algorithm [51] in an effort to increase LSP acceptance rates by taking into account the order of arriving LSP requests. The resulting WangCrowcroft with Sorting (WCS) algorithm improves upon WC by reordering LSP requests according to their bandwidth and delay requirements. De Oliveira et al. [52] propose Stochastic Performance Comparison Routing Algorithm (SPeCRA), an algorithm that adaptively selects the best LSP establishment method, in terms of LSP acceptance rates, among a given set of candidate methods.
QoS routing approaches are discussed in [53, 54], namely, the WidestShortest Path (WSP), ShortestWidest Path (SWP), and ShortestDistance Path (SDP) algorithms. These algorithms establish LSPs between a given (s,d) pair by selecting paths that have sufficient bandwidth to satisfy the demand requested by the source s. WSP only considers the shortest path. If there are multiple equally good paths, WSP selects the one with the maximum bandwidth. SWP selects the path that contains the maximum available bandwidth. Lastly, SDP selects a path with the least cost, where cost is defined as the reciprocal of the available path bandwidth. The MPLS Adaptive Traffic Engineering (MATE) algorithm proposed by Elwalid et al. [55] aims to reduce network congestion by adaptively load balancing traffic across paths. The algorithm routes traffic using preestablished LSPs according to metrics such as packet delay, packet loss, or network utilization. In [56], the authors apply evolutionaryfuzzy strategy to predict the utilization level of links. This then allows routers to select a path for flows that are likely to accept the flow; i.e., their goal is to minimize the expected blocking probability.
In general, the aforementioned works optimize the allocation of LSPs based on different QoS constraints such as bandwidth, packet loss, and endtoend delay, e.g., [48]. The order of LSP setup requests is also important when establishing paths [50]. Past works such as [52] have also shown the importance of minimizing interference in order to increase LSP acceptance rates. A key gap is that these methods have not taken energy consumption into account when selecting the optimum LSPs. Indeed, existing works assume the existence of redundant paths and nodes [55]. Green LSP establishment methods, however, have an opposite aim, whereby they seek the minimal number of nodes or links. Hence, this paper adds to the existing literature by analyzing and studying existing as well as new green LSP establishment methods and provides a comparison of their acceptance rates.
3 Problem description
Before defining the problem formally, we first introduce a number of notations. We model the network as a directed graph G(V,E), with V being the set of V nodes, and E representing the set containing E edges. We denote the link between nodes i and j as e _{ ij } or (i,j). Each link has capacity c _{ ij } and utilization u _{ ij }. Let Q be the set of LSP establishment requests that arrive at the set of ingress routers I⊂V. Each LSP establishment request q∈Q is a tuple < s,d,b w>, where s and d denote the source and destination of a request, and b w>0 is the corresponding requested bandwidth. We also define a function B(q) that returns the bandwidth of request q. Let P _{ q } be the set of all simple paths that can be used to serve LSP request q∈Q. Specifically, \(P_{q}=\{{p_{q}^{1}}, {p_{q}^{2}}, \ldots p_{q}^{P_{q}} \}\) is a set of candidate paths for q sorted in increasing path length order. Each path \({p_{q}^{k}}\) in P _{ q } contains a set of \({p_{q}^{k}}\) links, meaning \({p_{q}^{k}}\subseteq E\). We define the set of paths that use link (i,j) as \(P_{\textit {ij}}=\{ {p_{q}^{k}}\;\; e_{\textit {ij}}\in {p_{q}^{k}}\}\), for all q∈Q and k=1,2,…,P _{ q }. Hence, the total traffic over a given link (i,j) is \(B_{\textit {ij}} = \sum _{p\in P_{\textit {ij}}} B(p)\) and its link utilization is u _{ ij }=B _{ ij }/c _{ ij }.
The problem at hand is as follows: given i) a MPLS network consisting of label switching routers (LSRs) and directional links with fixed capacity, ii) traffic demands described as a set of tuples < s,d,b w>, which may be given a priori, i.e., offline, or in a realtime manner, i.e., online, the problem at hand is to minimize the overall energy consumption of the MPLS network by finding a set of LSPs that satisfy the given traffic demand of each request using the minimal number of links/routers. It is worth noting that in the online version of the described problem, the establishment of current LSPs affects the utilization of links/routers and hence may affect the acceptance of future LSP requests. The challenge is therefore to assign LSPs such that energy usage is reduced, while accommodating future traffic demands.
where the function B(χ) returns the bw value associated with the path/request corresponding to decision variable χ. As an example, consider Fig. 2 with demands q= < a,d,10> and r= < c,b,20>. The capacity constraint for link (a,b) is therefore \({X^{1}_{q}}\times 10 + {X^{2}_{r}}\times 20 \le 100\), with c _{ ab }=100.
where ≽ represents the ≥ operator executed component wise on the set \(\bar {T_{\textit {ij}}}\) or \(\bar {F(v)}\); referring to Fig. 2, link e _{ ab } with decision variable X _{ ab } will have the following constraints: \(X_{\textit {ab}}\ge {X^{1}_{q}}\) and \(X_{\textit {ab}}\ge {X^{2}_{r}}\). That is, the decision variable X _{ ab } is set to 1 only if \({X^{1}_{q}}\) or \({X^{2}_{r}}\) or both are set to 1.
Given that each router and link consumes a given amount of energy, minimizing the number of active routers and links would reduce the total energy consumed by a network. The objective function can also be adapted to include the specific power consumption of a NIC. We leave this as a future work.
The aforementioned offline version of the problem is solvable only for small networks due to the number of binary variables that grow exponentially with network size and demands. In particular, there could be an exponential number of paths that can be used for a given demand q. In fact, the offline version of our problem corresponds to the wellknown multicommodity minimumcost flow (CMCF) problem and is therefore NPcomplete; please refer to [57] for details. Henceforth, in the next section, we present different heuristics to address both online and offline versions of the formulated problem.
4 Heuristics
LSP setup requests and k paths shared by all implemented algorithms
L S P _{ q }  s  d  bw  k shortest paths  

1  R3  R1  14  [ R3,R1]  [ R3,R2,R1]  [ R3,R4,R2,R1] 
2  R4  R2  41  [ R4,R2]  [ R4,R3,R2]  [ R4,R3,R1,R2] 
3  R2  R4  40  [ R2,R4]  [ R2,R3,R4]  [ R2,R1,R3,R4] 
In the following sections, we will describe the following heuristics in detail:

Offline Most Overlapped (OfflineMO): aims to use paths that share the most links with past or future LSP requests.

Offline with Ratio (OfflineR): same as OfflineMO but favoring paths that require the fewest number of new links.

Online Most Overlapped (OnlineMO): aims to use paths that share the most links with already established LSPs.

Online with Ratio (OnlineR): same as OnlineMO but prefers paths that involve the minimal number of new links.

Online Minimum Hops (OnlineMinH): gives priority to paths with a small number of hops.

Online Random LSP (OnlineRLSP): selects paths randomly.
We remark that OnlineMinH and OnlineRLSP have been considered in [28, 29], respectively. However, all other heuristics are new. Moreover, as noted in Section 2, no works have compared all these heuristics comprehensively. As we will show in Section 5, OnlineR has the best performance in terms of energy saved and LSP acceptance rate.
4.1 Offline approaches
Algorithm ?? presents a general overview of how offline heuristics are applied to each LSP request q∈Q. By definition, all these heuristics know in advance all LSP setup requests in Q, and their respective k shortest paths P _{ q }. This means they can determine the best links to use or avoid by looking at past, current, and future LSP requests. Hence, the results obtained via offline heuristics constitute the best possible performance for any online heuristics. For the reader’s convenience, Algorithm ?? also defines the variables used by the different H e u r i s t i c(.) functions.
For each arriving LSP request, q= < s,d,b w >, the set of all shortest (s,d) paths is generated. H e u r i s t i c(.) then processes all the (s,d) paths and returns a candidate path to serve the LSP request. If H e u r i s t i c(.) returns multiple paths, the algorithm selects the one with the fewest number of hops; if there is a tie, the first path is selected. If all the links on the selected candidate path are able to meet the required bandwidth demand, the path is assigned to (s,d). The algorithm then subtracts the requested demand from the available bandwidth, see line9, of each link on the established LSP and each of these links are marked as active permanently. On the contrary, if the selected candidate path is not able to serve the requested demand, H e u r i s t i c(.) evaluates the remaining paths of q. If no paths with sufficient bandwidth is found, it rejects LSP request q and moves to the next one.
4.1.1 4.1.1 OfflineMO
The goal is to select paths that share the most links. OfflineMO compares each \({p^{k}_{q}}\) of a given request q with the candidate paths of other requests in Q. For each \({p^{k}_{q}}\), where k=1,2,..,P _{ q }, the function H e u r i s t i c(.) finds and stores the number of matching links in a variable s c o r e≥0 that gives the total number of its links that are in common with paths for other requests.
OfflineMO selects \({p^{k}_{q}}\) that has the maximum score value. The links within the chosen \({p^{k}_{q}}\) are then added into links_used. If a given \({p^{k}_{q}}\) has insufficient bandwidth, which depends on the MLU of the different links composing that path, it is removed from P _{ q }.
OfflineMO example. L S P _{1} has a request <R3, R1, 14 Mb >, and three candidate paths: [ R3,R1],[ R3,R2,R1],[ R3,R4,R2,R1]
L S P _{ q }  \({p^{1}_{q}}\) links  \({p^{2}_{q}}\) links  \({p^{3}_{q}}\) links  

2  R4−R2  R4−R3  R3−R2  R4−R3  R3−R1  R1−R2 
\({p^{3}_{1}}\)  \({p^{2}_{1}}\)  \({p^{1}_{1}}\)  
3  R2−R4  R2−R3  R3−R4  R2−R1  R1−R3  R3−R4 
\({p^{3}_{1}}\)  \({p^{2}_{1}}\)  \({p^{3}_{1}}\)  
\({p^{3}_{1}}\) 
From Table 2, we can see the score for each of the P _{ q } paths for L S P _{1}. For example, for \({p^{1}_{1}}\), i.e., [ R3,R1], its score is 1, given that \({p^{1}_{1}}\) appears one time. The score for [ R3,R2,R1] is 2, and the score for [ R3,R4,R2,R1] is 4. This means the H e u r i s t i c(.) function for L S P _{1} returns [ R3,R4,R2,R1] as the path that has the highest overlap and, therefore, is chosen by OfflineMO.
4.1.2 4.1.2 OfflineR
Similar to OfflineMO, OfflineR aims to use paths that have as many common links as possible to other paths and, additionally, gives preference to the ones that require the fewest number of new links to be set up. Note, new links are defined as those that are not carrying any traffic, i.e., not in links_used. In order to do this, we reuse the score variable from the OfflineMO algorithm and introduce the variable R a t i o _{off} for each of the \({p^{k}_{q}}\) paths of a given request q. The said variable is defined as score/new_links_number, where new_links_number stores the number of new links that would have to be established if path \({p^{k}_{q}}\) is selected. The function H e u r i s t i c(.) calculates the R a t i o _{off} for each of the \({p^{k}_{q}}\) paths and selects one with the maximum R a t i o _{off} value. In the special case when new_links_number is equal to 0, i.e., all the links in a given \({p^{k}_{q}}\) path already exist, the variable is set to 1. This is to avoid division by 0.
OfflineR example. L S P _{1} has a request <R3, R1, 14 Mb >, and L S P _{2}, <R4, R2, 41 Mb >, and three candidate paths: [ R3,R1], [ R3,R2,R1], [ R3,R4,R2,R1], and [ R4,R2], [ R4,R3,R2], [ R4,R3,R1,R2], respectively
L S P _{ q }  links_used  k paths  score  new_links_number  R a t i o _{off}  Selected path k 

1  {}  [ R3,R1]  1  1  1  [ R3,R4,R2,R1] 
[ R3,R2,R1]  2  2  1  
[ R3,R4,R2,R1]  4  3  1.33  
2  R3−R4  [ R4,R2]  1  0  1  [ R4,R2] 
R4−R2  [ R4,R3,R2]  0  2  0  
R2−R1  [ R4,R3,R1,R2]  1  3  0.33 
4.2 Online approaches
Algorithm ?? presents the pseudocode for our online heuristics. Note that this pseudocode is similar to the pseudocode presented in Algorithm ??. The difference is that by definition, online approaches only have knowledge of the current and past LSP requests.
4.2.1 4.2.1 OnlineMO
Following a similar criterion to its offline counterpart, OnlineMO selects \({p^{k}_{q}}\) with links that overlap the most with existing links. H e u r i s t i c s(.) calculates for each \({p^{k}_{q}}\) the number of links in common with already established links and stores this in the num_used_link variable. The \({p^{k}_{q}}\) path with the maximum number of links in common is selected as the candidate LSP. The variable num_used_link indicates path \({p^{k}_{q}}\) contains at least one link that is already established and, therefore, can be reused.
OnlineMO example. L S P _{1}<R3,R1,14 Mb> and L S P _{2}<R4,R2,41 Mb>
L S P _{ q }  links_used  k paths  num_used_link  Selected path k 

1  {}  [ R3,R1]  0  [ R3,R1] 
[ R3,R2,R1]  0  
[ R3,R4,R2,R1]  0  
2  R3−R1  [ R4,R2]  0  [ R4,R3,R1,R2] 
[ R4,R3,R2]  0  
[ R4,R3,R1,R2]  1 
4.2.2 4.2.2 OnlineR
This heuristics is similar to its offline counterpart; i.e., OfflineR. The objective here is to reduce energy consumption by utilizing established links and, additionally, favoring paths that require the fewest new links.
Note that this approach is similar to that of [27]. Specifically, for the routing of a given (s,d) pair demand, the technique in [27] uses an existing shortest backup path. It aims to minimize the establishment of new links. In contrast, OnlineR does not only consider backup paths of a given (s,d) pair paths but considers the shortest paths used to route demands for other (s,d) pairs. This helps reduce the need to establish new links.
We reuse the term num_used_links from the OnlineMO algorithm and new_links_number from OfflineR and introduce the term R a t i o _{on} as the ratio num_used_links/new_links_number. For each \({p^{k}_{q}}\) paths of the current request q, H e u r i s t i c(.) calculates its R a t i o _{on} and then selects as the candidate LSP \({p^{k}_{q}}\) whose R a t i o _{on} is maximum. In the special case when new_links_number is equal to zero, i.e., all the links in a given \({p^{k}_{q}}\) path have already been established, the variable is set to 1. This is to avoid division by 0.
OnlineR example. L S P _{1}<R3,R1,14 Mb> and L S P _{2}<R4,R2,41 Mb>
L S P _{ q }  links_used  k paths  num_used_link  new_links_number  R a t i o _{on}  Selected path k 

1  {}  [ R3,R1]  0  1  0  [ R3,R1] 
[ R3,R2,R1]  0  2  0  
[ R3,R4,R2,R1]  0  3  0  
2  R3−R1  [ R4,R2]  0  1  0  [ R4,R3,R1,R2] 
[ R4,R3,R2]  0  2  0  
[ R4,R3,R1,R2]  1  2  0.5 
As an example, any of the paths in L S P _{1}, i.e., [ R3,R1], [ R3,R2,R1], and [ R3,R4,R2,R1], will require all their links to be setup. Therefore, their num_used_links value will be zero, and their ratio will also be zero. H e u r i s t i c(.) will break the tie by selecting the shortest path [ R3,R1].
We now turn our attention to L S P _{2}. Its paths, i.e., [ R4,R2], [ R4,R3,R2], and [ R4,R3,R1,R2], will have a num_used_links value of 0, 0, and 1, respectively. The value of new_links_number for each of candidate path of L S P _{2} can be found by counting the links that are not included in the Links used column. Specifically, the corresponding new_links_number value for [ R4,R2], [ R4,R3,R2], and [ R4,R3,R1,R2] is 1, 2, and 2, respectively. Given the value of num_used_links and new_links_number, R a t i o _{on} can be calculated and H e u r i s t i c(.) returns the candidate path with highest value. In this case, path [ R4,R3,R1,R2] is selected.
4.2.3 4.2.3 OnlineMinH
This heuristic, which is also reported in [28], chooses as a candidate LSP, the \({p^{k}_{q}}\) path of the current request q with the minimum number of hops. We skip its example due to its simplicity.
4.2.4 4.2.4 OnlineRLSP
The H e u r i s t i c(.) for OnlineRLSP randomly selects one of the \({p^{k}_{q}}\) paths in the set P _{ q } for the current request q. Note that random path selection is essentially similar to EqualCost Multipath (ECMP), as used by CSPF [29].
5 Evaluation
The performance of the aforementioned heuristics is evaluated using two popular topologies: Abilene and AT&T North America [59, 60]. The Abilene network consists of 11 nodes and 28 directional links, whereas the AT&T network consists of 25 nodes and 112 directional links.
We conducted our simulations in MATLAB [61]. The three components of a LSP request < s,d,b w> are generated randomly as follows: i) s and d are sets to an integer from the range [ 1,V], where s≠d, ii) bw is a value in [ 1,B W _{Max}]. LSP requests are generated in advance in both online and offline scenarios. We assume that when all links are active, all these LSP requests can be admitted.
Algorithm ?? describes the procedure used for all simulations. Please note steps 4 and 7. These steps show the calculations performed by H e u r i s t i c(.) for a given set of LSP requests Q. In particular, for all requests q in Q, H e u r i s t i c(.) needs to explore P _{ q } shortest paths; each of them with a maximum length of V hops. Therefore, our algorithms have a running time complexity of O(P _{ q }QV.
In order to measure the goodness of a solution, we define a new metric ρ=P S L/(100−L A R). Recall that PSL is the percentage of shutdown links and LAR is the LSP acceptance rate. Consider two green LSP methods: L S P _{ A } and L S P _{ B }. Assume both can shut down the same number of links. For instance, P S L _{ A }=P S L _{ B }=40 %. However, let us assume they have an LSP acceptance rate of L A R _{ A }=90 % and L A R _{ B }=80 %, respectively. Therefore, we have ρ _{ A }=4 and ρ _{ B }=2. Given that ρ _{ A }>ρ _{ B }, we conclude that L S P _{ A } is better than L S P _{ B }. Consider a second example. Let us assume that P S L _{ A }=30 % and P S L _{ B }=40 %, and both have the same LAR, say L A R _{ A }=L A R _{ B }=70 %. Therefore, ρ _{ A }=1 and ρ _{ B }=1.3, and ρ _{ B }>ρ _{ A }. In this case, L S P _{ B } is better because it is able to shut down a larger number of links while keeping the same LSP acceptance rate. Please note that when a green approach attains LAR = 100 %, its ρ will go to infinity. In this case, we set ρ to PSL.
We conducted 30 simulation runs for each of the heuristics discussed in Section 4 using the following number of arriving LSP requests (Q): 50, 300, 500, 700, 1000, and 2000. In order to simulate different network loads, for each Q value, we set B W _{Max} to 50, 200, 400, 600, and 1000 Mb/s. Finally, we compute ρ for each of the evaluated approaches.
In the following sections, note that low network load refers to scenarios with no more than 300 LSP requests and their max requested bandwidth is less than or equal to 200 Mb. Conversely, we use the term high network load for scenarios where the number of LSP requests is at least 1000 and their max requested bandwidth is greater than or equal to 600 Mb.
5.1 Offline approaches
For AT&T, if the network load is low with Q=50, OfflineR has an average link utilization of 2.9 % against 3.23 % for OfflineMO. In high network load scenarios, i.e., Q=2000, the average link utilization of OfflineR reaches 56.13 % versus 62.71 % for OfflineMO; this indicates an increase of 1935.5 and 1941.4 %, respectively. These results are also consistent for Abilene. Under low network load, i.e., Q=50, OfflineR has an average link utilization of 12.64 % and OfflineMO 18.18 %; when the network load is increased to Q=2000, the average link utilization rises to 86.01 and 93.15 %, respectively, which means a rate of increase of 680.45 % for OfflineR and 512 % for OfflineMO. The average link utilization of Abilene is consistently 2.1 times that of AT&T under the same network load. This is because Abilene has fewer links, or smaller network capacity. This difference in link utilization has a direct impact on the final number of active links.
Overall acceptance rate of offline heuristics over AT&T and Abilene
Offline  

AT&T  Abilene  
Max req. bw (Mb)  OfflineR  OfflineMO  OfflineR  OfflineMO 
50  1.0  1.0  1.0  0.99 
200  0.99  0.99  0.88  0.81 
400  0.96  0.94  0.71  0.62 
600  0.91  0.89  0.59  0.52 
1000  0.82  0.79  0.47  0.42 
Average  0.94  0.92  0.73  0.67 
Figure 5 shows the LSP acceptance rate for this scenario is above 40 %. This is in spite of the average link utilization being above 80 % as observed in Fig. 3.
With respect to Abilene, Fig. 6 shows that both approaches present a similar performance with an average LSP acceptance rate of 73 % for OfflineR and 67 % for OfflineMO. However, given that the network utilization of Abilene increases more rapidly than AT&T, the observed LSP acceptance rate also decreases significantly; as an example, consider the case when the number of LSP requests is 2000 and the max requested bandwidth is 400; for AT&T, the LSP acceptance rate is above 70 % for both approaches, whereas for Abilene, the acceptance rate is below 40 %.
5.2 Online approaches
In the case of Abilene, OnlineMinH also produces the lowest average link utilization at 56.48 %. Surprisingly, the second best performer at 65.2 % is OnlineRLSP that selects LSPs randomly. However, the utilization of OnlineRLSP is very close to that of other approaches. As expected, when the network load increases, link utilization also increases. In particular, OnlineMinH shows an increase of 53.44 % and 74.68 % for AT&T and Abilene respectively when going from the lowest to the highest possible network loads.
Online heuristics that exhibit the largest LSP acceptance rates for AT&T and Abilene
Online  

AT&T  Abilene  
Max req. bw (Mb)  OnlineMinH  OnlineRLSP  OnlineMinH  OnlineRLSP 
50  1.0  1.0  1.0  1.0 
200  0.99  1.0  0.89  0.86 
400  0.96  0.96  0.74  0.67 
600  0.92  0.92  0.63  0.55 
1000  0.83  0.82  0.49  0.45 
Average  0.94  0.94  0.75  0.71 
OnlineMinH and OnlineRLSP exhibit the best performance for both topologies. Overall, OnlineMinH has a slightly better performance than OnlineRLSP. Specifically, for AT&T, OnlineMinH and OnlineRLSP present the same overall LSP acceptance rate of 94 %. For Abilene, OnlineMinH, shows an average LSP acceptance rate of 75 % against 71 % for OnlineRLSP.
These LSP acceptance rates are due to OnlineMinH attaining the lowest average link utilization for both topologies, see Figs. 7 and 8.
Note that the total average LSP acceptance rate for the online approaches, 83.5 %, is larger than the total average LSP acceptance rate for the offline approaches, 81.5 %. These total average LSP acceptance rates are obtained by computing the mean of the average values presented in Tables 6 and 7, respectively. The main goal of offline approaches when establishing LSPs is to minimize the overall energy consumption of the network even if this implies a decrease in LSP acceptance rates. On the other hand, OnlineMinH and OnlineRLSP do not consider energy savings as the main factor when establishing LSPs and their main objective is to accept as many future LSP requests as possible. Consequently, they have higher LSP acceptance rates. This tradeoff between energy savings and LSP acceptance rates will be discussed in more detail in Section 5.3 when we compare the tested heuristics according to their ρ ratio.
5.3 Discussion
Comparison of the performance of online approaches and OfflineR according to their ρ ratio for AT&T
Heuristic  Percentage of shut  Percentage of links  Overall LSP  ρ 

down links (%)  shut down by OfflineR  acceptance rate (%)  
OfflineR  22.1  100  94  3.7 
OnlineMO  21.6  97.7  92  2.7 
OnlineR  19.3  87.3  92  2.4 
OnlineMinH  17.0  76.9  94  2.8 
OnlineRLSP  5.7  12.2  94  0.95 
Comparison of the performance of online approaches and OfflineR according to their ρ ratio for Abilene
Heuristic  Percentage of shut  Percentage of links  Overall LSP  ρ 

down links (%)  shut down by OfflineR  acceptance rate (%)  
OfflineR  8.6  100  73  0.31 
OnlineR  2.9  33.4  67  0.08 
OnlineMO  2.14  24.9  67  0.06 
OnlineMinH  2.13  24.8  75  0.09 
OnlineRLSP  0.12  1.4  71  0.004 
It is interesting to see that OnlineMinH and OnlineRLSP are among the approaches with the worst performance in regard to the overall percentage of shut down links, with 17 and 5.7 %, for AT&T, and 2.13 and 0.12 %, for Abilene, respectively. At the same time, these two approaches have the highest LSP acceptance rate. OnlineMinH has an overall LSP acceptance rate of 94 and 75 % for AT&T and Abilene, respectively. The corresponding values for OnlineRLSP are 94 and 71 % for AT&T and Abilene, respectively. On the other hand, OnlineMO and OnlineR show the lowest LSP acceptance rate; both recorded a percentage of 92 % for AT&T and 67 % for Abilene, respectively. However, these two approaches are the ones that were able to shut down the largest percentage of links. For AT&T, the percentage of shut down links when using these approaches is 21.6 and 19.3 %, respectively. When tested over Abilene, OnlineR exhibits a slightly better performance than OnlineMO; i.e., 2.9 versus 2.1 %, respectively. As expected, there is a clear tradeoff between LSP acceptance rates and the number of active links. The larger the LSP acceptance rate, the fewer the number of links a green technique is able to shut down. The good performance of OnlineMO and OnlineR is due to their low overall link utilization; see Figs. 7 and 8.
Table 8 also shows that for AT&T, the percentage of shut down links for the best online approach, OnlineMO, is around 97.7 % of the percentage of shut down links observed for OfflineR. OnlineMO selects paths that require the fewest number of new links, which decreases the overall percentage of active links. On the other hand, OnlineRLSP randomly selects paths without considering energy consumption. This results in OnlineRLSP exhibiting the smallest percentage of shut down links among the studied approaches, with only 12.2 % of the recorded percentage of OfflineR. For Abilene, Table 9 indicates that OnlineR and OnlineRLSP exhibit the best and worst performance, respectively. Specifically, OnlineR is able to shut down 24.9 % of the links shut down by OfflineR, whereas, OnlineRLSP only shuts down 1.4 % of the links shut down by OfflineR.
6 Conclusions
In this paper, we have analyzed the problem of reducing the energy consumption of an MPLS network using online and offline path establishment methods. We believe this to be the first extensive work that studies green LSP establishment solutions. We study six heuristics over the same topologies. Notably, we compare online and offline heuristics in terms of energy savings and LSP acceptance rates. On the Abilene and AT&T topologies, results indicate that during offpeak periods, LSP acceptance rates above 90 % are possible with 20 % of links shut down to conserve energy.
As a future work, we plan to extend the work in [62] to maximize the number of accepted connections and channel assignment in a green network. We remark that although we assume a MPLS network, the online and offline heuristics may be applicable to other networks. This is because a LSP can be interpreted as a path or connection from a source node. For example, establishing paths in wireless sensor networks in an online or offline manner [63] with the goal of minimizing the number of involved sensor nodes so that other nodes can conserve their energy. Another possible direction is to consider multicast; e.g., [64]. The problem then is to construct a tree using the minimal number of nodes that supports all arriving demands. Lastly, implications on security will have to be considered; see [65, 66].
Declarations
Acknowledgements
Author Alejandro RuizRivera acknowledges and thanks the support of Catholic Education network (CEnet) and its staff.
Authors’ Affiliations
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