which is fully compatible with OSPF. In particular, in [12] the ESIR algorithm is proposed: ESIR .... traffic requirements is not considered at this stage. In particular,.
Implementing Energy-aware Algorithms in Backbone Networks: a Transient Analysis Luca Chiaraviglio, Antonio Cianfrani, Marco Listanti, Luigi Mignano, Marco Polverini DIET Department, University of Roma - La Sapienza, Roma, Italy, email {name.surname}@uniroma1.it Abstract—In this work we study the impact of energy-aware routing algorithms on IP backbone networks, focusing on the routing protocol transients due to network reconfiguration. We first propose the Green Partial Exportation (GPE) algorithm, which is fully compatible with the OSPF protocol and targets the reduction of the number of changed paths in the network; we also realize a green software router by integrating GPE in the Quagga routing suite. Then we define an experimental methodology to evaluate the effects of a green routing strategy on the network behavior, in terms of delay increase and packet loss. Finally, we evaluate our solution on an emulated testbed from a national telecom operator. Our results show a maximum increment of 320 ms for the RTT and a packet loss of 1.45% during the network transients. Moreover, GPE can be safely applied in the network with a time granularity of less than one minute.
I.
I NTRODUCTION
Achieving energy-efficiency for telecommunication devices has become a mandatory goal. Telecom operators are experiencing huge costs connected to the electricity consumption of networking equipments. The electricity bills have been constantly increased in the last years [1], and this trend is expected to grow in the future, due to the increase of traffic, coupled with the constantly growing number of connected devices. IP devices, and in particular linecards, consume a not negligible amount of power (up to 50% of power in a backbone network [2]). Thus, introducing energy-awareness in the IP layer seems a good step toward the sustainability of backbone networks. Among the different solutions proposed in the literature to reduce power consumption (see [3] and [4] for an overview), the exploitation of low power modes for IP devices seems one of the most promising approaches to save energy. When an IP device is put in low power mode, most of its functionalities are not available. For example, the traffic switched by the device is transferred to the other devices that remain at full power. In this way, most of the electronic components on the device can be put in low power, thus saving energy. Solutions proposed so far in the literature investigate the problem by defining set of devices in a low power mode, computed either optimally or by simulation. However, little attention has been put so far to the evaluation of energy aware algorithms in terms of implementation issues. In this paper we focus our attention on the transient times introduced in the network by the energy-aware algorithms. More generally, when an energy saving algorithm is executed as a consequence of a traffic change, many network paths will be modified. During the algorithm execution, the asynchronism of router tables updating among different routers could lead to network paths inconsistency [5]. As a consequence not-
optimal routes could be generated, and eventually loops may occur, causing packet loss in the network. Thus, limiting the network transient introduced by energy-aware algorithms is of mandatory importance for network operators. In this work we focus on this aspect, providing a twofold contribution. We first define the Green Partial Exportation Algorithm (GPE), compatible with the well-known OSPF routing protocol and able to limit the network reconfiguration procedure during the transient time. Then we provide a preliminary experimental methodology for the characterization and the measurement of the transient time in a network. Additionally, we propose an implementation of our solution in the Quagga routing suite, building a green software router ready for deployment in real operator networks, and we measure the routing transients introduced by GPE on an emulated testbed representative of a national telecom operator. To the best of our knowledge, none of the previous works have conducted a similar analysis. The closest paper to our is [6], in which a dynamic management strategy for IP network is implemented based on the idea of changing link weights. The network configurations in terms of weights are centrally computed and then transferred to the nodes by means of a custom-made library based on the SNMP protocol. The evaluation is performed on a network with a limited number of nodes (up to 10), considering the link utilization and the percentage of links in low power. However, the authors do not evaluate the transient behaviour introduced when one configuration is applied in the network, neither the packet loss. A step toward a working testbed for backbone networks is introduced in [7]. However, the presented implementation is tailored to specific vendor devices, and the network size is very small, i.e., only three routers. Moreover, the transients derived from applying the algorithm are not reported. In [8] authors evaluate the impact of their algorithm on the packet delay and losses, but the analysis is only conducted by simulation and not on a testbed. Additionally, in [9] authors have implemented a traffic engineering solution on a 10-nodes network. However, the performance evaluation is only limited to the evaluation of the changes introduced in terms of link bandwidth and not in terms of transients indicators. Finally, in [10] authors have proposed a prototype of an energy-efficient router based on the aggregation of multiple devices with green capabilities. Our paper is complementary to this work, since here we focus on the evaluation of an energy-aware algorithm on a backbone network. The rest of the paper is organized as follows. The GPE description is reported in Sec. II. The implementation of our green router is reported in Sec. III, while the transient time characterization is discussed in Sec. IV. Performance
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evaluation obtained on a emulated network is reported in Sec. V. Finally, conclusions are drawn in Sec. VI. II.
G REEN PARTIAL E XPORTATION A LGORITHM
The algorithm we propose targets the reduction of power by putting in low power state IP links of a network running the OSPF protocol.The problem can be sketched as follows. Given: i) the topology, expressed in terms of nodes (i.e., routers) and links, ii) the traffic matrix, measured at a given time, iii) the link power consumption. Find: the set of links in low power mode. Subject to: i) connectivity and maximum link utilization constraints.1 The problem can be formulated with a Mixed Integer Linear Programming formulation [11], and solved with different heuristic techniques (see [3] for an overview). In this work, we start from [12] in order to define a new heuristic which is fully compatible with OSPF. In particular, in [12] the ESIR algorithm is proposed: ESIR is based on the exportation procedure, which is a mechanism that allows to share the same routing tree for adjacent nodes. Unfortunately, this approach suffers of two problems: i) it does not allow to put in low power links bidirectionally, which limits its application in real networks, and ii) it works with a loose granularity, since it requires the modification of a whole routing tree, while just a subset of paths should be changed in order to put in low power a link. To overcome these issues, in this work we have redefined the exportation mechanism, modifying the concept of sharing the same routing among two nodes. In particular, we exploit the intuition that a node can import only a subset of paths from one (or more) of its neighbors. In the following, we formalize the routing path sharing approach, called Partial Exportation (PExp). Next, we define the heuristic to find the Partial Exportations (PExps) allowing to put in low power the maximum number of links. Let G(R, L) be the graph representing the network topology, where R is the set of routers and L is the set of undirected links. In Fig. 1.a we report a simple network scenario composed of 5 routers and 6 undirected links, used to simply explain our proposal. We suppose that the network routing is managed by means of the Open Shortest Path First (OSPF) routing protocol, then each router computes the Shortest Path toward each destination; in Fig. 1.b we show the shortest paths computed by router A. We call P = {Psd , ∀s, d ∈ R} the set of all shortest paths in the network. Considering that the IP forwarding at each router is based on the detection of a next hop for each destination, we define the set Kij : the set of 1 We assume that when the links are put in low power the traffic is protected from physical link failures by means of the underlying optical layer.
destinations reached by router i using j as next hop. For each router it is possible to detect a number of set Kij equal to the number of adjacent nodes. Referring to the simple network scenario reported in Fig. 1.b and focusing on router A, we have that KAC = {C}, KAB = {B, E} and KAD = {D}. In this context, we indicate as enij a local process that forces router i to use the router n as next hop for all destinations belonging to the set Kij . In other words enij modifies a subset of network paths in i, i.e., the ones having j as next-hop. This local process represents a PExp. The outcome of enij is to exclude link lij from packet forwarding performed at router i; for this reason we define lij as the target link for the PExp enij . For instance, in Fig. 1.c the effects of eB AC on A are shown: i) new paths for destinations in KAC (i.e., router C) having B as next hop, are computed; ii) the link lAC is not more used to forward packets. The new path from A to C is composed of two parts: the hop from A to the new next hop B, and the IP path from B to the destination C. The set of all available PExps for a given network can be computed considering that a generic PExp enij must satisfy the following three conditions: i) nodes i and j are adjacent; ii) nodes i and n are adjacent; iii) for each destination node in Kij , node i does not belong to the path Pnd . The former two conditions are obvious, requiring the adjacency relationship among routers involved by the PExp; the last condition assures that the execution of a PExp avoids the generation of routing loops. We refer V to the set of all possible PExp as E = {enij |(lij ∈ L, lin ∈ L) i ∈ / Pnd ∀d ∈ Kij }. The scope of our work is to detect a set of PExps able to minimize the network power consumption. Before defining a specific strategy for the energy minimization problem, it is important to analyze the consequences of multiple PExps execution. In particular the outcome of multiple PExps execution must lead to valid routing paths, i.e., no loops have to be generated. To guarantee the correctness of routing, we introduce the compatibility property. A similar analysis has been already proposed in [12], where the more general exportation mechanism is considered. In particular, it has been proved that an exportation can be performed if and only if such exportation does not modify the new paths of an already performed exportation. Considering that the PExp operation is obtained from the general exportation mechanism defining more restrictive conditions, the same compatibility condition holds. In the following we provide a formal definition of the compatibility property in the case of PExps. For each PExp enij , it is possible to detect the set of new modified paths Pi,j = {Pid , ∀d ∈ Kij }. The compatibility new property is satisfied if paths in Pi,j will be not modified by further PExps. In order to better formalize the previous rule
Given the set E and simplifying the notation used to identify each PExp, it is possible to represent the compatibility relationships of a specific exportation ei introducing the incidence vector vei : the generic k-element of vei , i.e., vei (k) is equal to 1 if ei and ek are compatible, otherwise it is equal to 0. By definition, compatibility is a symmetric property, i.e., vei (k) = vek (i). As already stated before, a weak point of the work in [12] is to focus on directed links. Due to hardware-related constraints, a link can be put in low power state only if both link directions are not used to forward traffic; in other word the only execution of enij does not allow to put in low power the link lij . The execution of two different PExps, one from i to j and another one from j to i, is required to enable low power state on a network link. To cope with this problem, we introduce the concept of move m{ei , ej }, which is simply a set of two PExps, ei and ej , acting on the two directions of the same link. The compatibility relationship can be easily extend to moves: two moves m1 = {e1 , e2 } and m2 = {e3 , e4 } are compatible if all PExps composing the two moves are compatible each other. In particular, the following formula can be used to calculate the compatibility between the two moves:
vm1 (m2 ) = vm2 (m1 ) = ve1 (e3 )·ve1 (e4 )·ve2 (e3 )·ve2 (e4 ) (1) The set of all the compatibility vectors associated to each move gives rise to a square and symmetric matrix that can be thought as the adjacency matrix of a new graph. We refer to it as compatibility graph G (M, C), where each node m ∈ M is a move, and an edge c ∈ C among two nodes represents the compatibility relationship between the two moves. Starting from the set of available moves and from the compatibility graph, it is possible to define a simplified version of the energy minimization problem; the link congestion due to traffic requirements is not considered at this stage. In particular, considering that each move is able to put in low power mode a single link and assuming that each link consumes the same amount of power, the energy minimization problem is equivalent to the problem of detecting the largest set of compatible moves; the extension to the case of links with different power values is straightforward, since it requires the introduction of a weight for each link in C. The problem of finding the largest set of compatible moves is equivalent to finding the largest clique in a graph [13], a well known problem
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for each PExp, we move from the set of modified paths to the set of critical links, defined as the set of links crossed by a modified path. For instance, referring to Fig. 1.c, the set of critical links associated to eB AC is represented by the links composing the new path from A to C, i.e., {lAB , lBE , lEC }. From the PExp definition, a PExp enij modifies only the paths crossing the target link, i.e., lij . Therefore, the compatibility property among PExps can be easily checked considering the target links and critical links. To summarize two PExps a and b are compatible each other, if the set of critical links of a does not include the target link of b and vice versa. Referring D to Fig. 1, the two PExp eB AC and eEC are not compatible because the link lEC is a critical link for eB AC .
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of graph theory. It has been proved that the problem is NPhard, therefore an heuristic algorithm is needed. The algorithm we propose here is called Green Partial Exportation (GPE). The scope of GPE is to detect a set of compatible moves S that are also able to satisfy traffic requirements avoiding links congestion. The idea of the algorithm is to scan the available moves starting from the ones having the highest degree in G. At each step of the algorithm the following steps are performed: i) the move m with the highest degree in the compatibility graph is selected, ii) the traffic-related constraints are checked; iii) the nodes that are not adjacent to m are removed from the compatibility graph. This process is repeated until no more moves can be added to S. III.
G REEN S OFTWARE ROUTER I MPLEMENTATION
In this section, we present the implementation of the green software router running GPE. In particular, our algorithm is fully compatible with the OSPF protocol, so we are able to provide a router prototype and to test it on a realistic scenario. The prototype is a Software Router, a general purpose PC equipped with open-source software: we used the Quagga [14] software, which is a Unix package that provides TCP/IP based routing services with routing protocols support. Quagga is composed of different processes, called daemons. In particular, each routing process is managed by a separate daemon. The OSPF demon is called ospfd. All the routing processes are coordinated by a specific demon, called zebra, whose functionalities include the update of the Kernel routing table. We consider a centralized network scenario where a Central Elaboration Unit (CEU) is responsible for energy saving activation, while the network routers are able to execute the PExps. More in detail, the CEU is responsible to: i) estimate the traffic matrix (TM), ii) locally run the GPE algorithm and compute the set of PExps, iii) notify the PExps to the involved routers. In our case, i) and ii) are performed offline, in the sense that the traffic variation over time is assumed to be known, and for each TM we compute a set of PExps. The communication among the CEU and an involved router, to pass the set of PExps, can be performed in two different ways: i) defining a new dedicated OSPF control message; or ii) implementing a new configuration command, available on the Command Line Interface (CLI) of the router, into ospfd code for the execution of a specific PExp. In this work we realized the latter option, that requires the establishment of a remote TCP connection
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from the CEU to an involved router each time PExps have to be enabled on that router. The generic OSPF router must be able to execute a PExp; to do that we have modified the ospfd daemon. As reported in Fig. 2, the new PExp module is introduced and it is activated by the reception of the new OSPF control message or by the execution of the new CLI configuration command. Moreover, in order to implement the powering off/on procedure, we have implemented an interface with the Green Abstraction Layer (GAL) proposed in [15]; the GAL acts as an abstraction layer for the HW and the physical resources, providing a set of standard functions to manage the device power state. Thus, rather than working with HW specific APIs, we adopt the functions provided by GAL. The interaction with GAL allows to enable the low power state or the reactivation of a linecard. The final outcome of the procedure is that a subset of the kernel routing table lines are updated by the zebra daemon as a consequence of the PExp procedure. IV.
T HE TRANSIENT TIME CHARACTERIZATION
The implementation of the PExp procedure on OSPF devices makes possible to evaluate the impact of our energy aware solution on the network behavior. In particular, we focus on the network transient time, i.e., the time passing from the activation of the energy saving solution to the availability of new ”green” paths. This time is very important since it allows to evaluate the feasibility of a specific solution and also to set the minimum time interval for the execution of two consecutive instances of the algorithm. The characterization of the transient time for a single device, during a routing update event, has been already studied in the past [16], referring to it as convergence time: the time required by a router to execute the paths computation algorithm, to modify its routing table, and to forward the traffic on new paths. To the best of our knowledge a similar analysis for the whole network is not provided in literature. The transient event can be defined as the composition of the following events: i) the execution of GPE on the CEU to compute the PExps to be notified; ii) the sending of OSPF control messages from the CEU to all involved routers; iii) the execution of PExps, performed independently on each router; iv) the modification of the routing table and the following traffic switching on new paths, performed independently on each router. If we focus on a single router, the previous operations are performed sequentially. If we extend our analysis to the whole network, the previous events could overlap; this is mainly due to the asynchronism of the last three operations. In general, each router receives the OSPF control message in a different time instant, due to the sequential generation of messages by the CEU and to the different times required by the messages to reach each router. Moreover the time required to execute the PExp operations, to modify the routing table and to switch the traffic on new paths, depends on the hardware features of the routers, and in general cannot be considered equal among the devices. The most remarkable side effect of this asynchronism is network paths inconsistency during the transition time. The
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paths inconsistency can have different consequences: from the generation of sub-optimal routes, leading to delay increase, to the creation of network loops, causing packet loss in the network. Thus, it is very important to define a way to measure the transient time, in order to introduce a new performance evaluation of an energy-aware algorithm. As explained before it is not possible to foresee the exact time each event occurs during the transient phase, so a precise formula for the transient time computation cannot be detected. Therefore the best way to characterize it is to perform direct measurements on real or emulated networks. The methodology we propose here consists in focusing on specific network paths, and to follow their evolution during the algorithm execution. Paths evolution is monitored by means of ICMP packets, exploiting the ping utility. In particular, when a ping command is launched on a source router, a sequence of ICMP echo request packets is generated toward a specific destination router; the resulting ICMP reply packets are received from the source router. This packets exchange allows to monitor three path performance indexes: i) the Round Trip Time, ii) the hop count (managing the TTL field), and iii) the number of probes lost (considering the ICMP sequence number). To summarize, the transient time measurement consists in the following steps: i) launching the ping command on a source router toward a destination router; ii) enabling GPE on the CEU; iii) collecting the measurement statistics at the source node. The obtained results allow to characterize the transient time, as detailed in the next section. V.
P ERFORMANCE E VALUATION
Network Scenario We adopt a realistic backbone scenario provided by Orange - France Telecom (FT) [17]. The topology, is composed of 38 nodes and 72 bidirectional links, as reported in Fig. 3. Due to the lack of space, here we report a brief summary of the scenario. We refer the reader to [17] for a detailed explanation. In brief, the operator has provided: i) the complete traffic matrix (TM), together with its temporal variation over a working day (the time granularity for each TM is nearly 5 minutes) reported in Fig. 4, ii) the link weights, assuming a single path between each source and each destination, iii) link capacities, with a minimum link granularity of 40G, iv) link propagation delays based on node distance.
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Emulator Description We implemented our solution with the Netkit emulator [18] in order to overcome the issue of building an experimental testbed with a large number of real devices. In fact, Netkit is able to create instances of virtual machines, each one equipped with the basic functionalities of Unix. We modified the Netkit code in order to create virtual machines equipped with the modified version of Quagga supporting PExp. Then, we implemented a set of scripts to automatically build the network topology, the OSPF configuration files, and the list of interfaces for each virtual machine. Moreover, we implemented also the CEU node, able to run GPE for computing the network configuration for each traffic matrix. Test Methodology Since we are interested in evaluating the impact of GPE on the transients in the network, we proceed in the following way, as already described in Section IV: before a configuration is applied, we run a ping command from a node to all the other nodes, with a granularity of 30 ms between probes.2 The ping is then run for a period of time long enough to capture all the transients introduced. By processing its output, we are able to assess the impact of transient times needed to configure the network from one traffic matrix to the following one. Note that, in this work, we focus only on the routing protocol transients. However, there are also other factors that might influence the transient time introduced in the network. For example, the linecards wake up time may be not marginal. However in [19] authors have proven that a maximum delay of 127.27 ms may be introduced if efficient design is taken into account. This time is not considered in this work, as we are interested in measuring the transients introduced by the routing changes. However, this effect can be introduced in the emulator and we leave it for future work. Results We first check the validity of the results obtained with the testbed. Fig. 5 reports the number of links put in low power versus time considering the simulator and the testbed implementation. As expected, there is a perfect match between the two trends, with a higher number of links put in low power during night w.r.t. the day. Moreover, we report also the results of the ESIR algorithm [12]. As expected, GPE is 2 We verified that 30 ms is the minimum time granularity allowed by the emulator in order to run the ping command from a single node to all the other nodes.
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more efficient than ESIR, being able to put in low power the links bidirectionally and also with a fine granularity thanks to the PExp mechanism. Finally, the figure reports also the GPE average shortest path length, showing that the path length tends to increase during the night due to the higher number of links put in low power. To give more insight, Fig.6 reports the performance of GPE and ESIR in terms of percentage of changed paths for each traffic matrix. As expected, the percentage of changed paths follows a typical day night trend. More in depth, during the night the percentage of changed path is higher compared to the day as a consequence of the higher number of links put in low power. Interestingly, GPE changes at most 5% of the paths, while ESIR almost 50%. Thus, we can see that GPE is very effective in reducing the amount of changed paths while increasing the number of links put in low power w.r.t. ESIR. This result highlights the capability of GPE in limiting its impact on network reconfiguration and, as a consequence, in reducing transient-related events. In the following, we then consider the impact of applying a single traffic matrix on the emulator running GPE. We initially assume that the propagation delays are not present, in order to evaluate the transients coming solely from the changes in the routing tables. In particular, we select the off-peak matrix
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which includes the highest number of links put in low power, and we repeatedly apply it for 20 times (recall that all the links are put at full power between one run and the following one). We first select a set of test nodes, namely Ts = {6, 12, 14, 18} to collect the measurements. All these nodes are taken from different sections of the network, which roughly represent the periphery (these nodes are also colored in dark blue in Fig. 3). From each node in Ts we start to run the ping command and then we apply the network configuration. The ping command stops roughly after 800 ping probes for each s-d pair (we have verified that this number of probes is sufficiently high to catch all the transients in the network). The experiment is then repeated for 20 times. For each run, we select the maximum RTT from each source to each destination, and we collect the number of ping lost. Fig. 7 reports the measured RTT values over the runs to all the destinations. Bar reports average values (i.e., the average of the maximum RTT for a given source-destination pair). Error-bars report the confidence intervals, assuming a 99% of confidence. Interestingly, the transient time is quite limited, being bounded at maximum by 320 ms, thus proving the effectiveness of our solution. Note that the maximum RTT in normal conditions, i.e., all links put at full power, is always below 1 ms (not reported in the figures for clarity) due to the fact that in this case link propagation delays are not considered. Moreover, the transient time depends on the destination selected. For example, considering the results with source node 6, we can see that the maximum RTT tends to increase for those nodes that are ”far” in terms of hops from 6, e.g., 15 and 9. In this case, the paths going to these nodes are changed by more than one partial exportation, and therefore finding a new route requires more time. Finally, observe also the high variability affecting the measured RTT; this is due to the fact that the commands for the partial exportations are not executed at the same time to the nodes, and therefore their application is not deterministic. Similar considerations hold also for source nodes 12, 14 and 18. We then consider the number of ping lost during the transient times, reported in Fig. 8. The figure reports the results obtained assuming again Ts as test set. Astonishingly, the number of lost packets is very limited, being at maximum always lower than 10 for each source and each destination,
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representing only 1.25% over the total number of packets sent during the measurement window. Moreover, observe that there is a strong correlation between the number of ping lost and the measured RTT (reported in Fig. 7): the more the s-d pair is ”far” in the topology, the higher will be the maximum RTT and also the number of ping lost. We then extend our analysis by considering the full day variation. For each traffic matrix, we collected the maximum RTT and the number of ping lost for each node, and then compute average values over all the nodes, as reported in Fig. 9. Interestingly, both the RTT and the number of ping lost are quite limited over the full time period, proving again the efficacy of our algorithm. These results show that the application of GPE generates a delay of 300 ms on average in the network, coupled with a limited number of ping lost (in the worst case 1.45% of ping probes are lost on average in the network). In the final part of our analysis, we evaluate the temporal evolution of the RTT for a specific traffic flow during the network reconfiguration, when also the link propagation delays are considered. Fig. 10 reports the RTT versus time considering the traffic flow originated from node 6 and directed to node 23, when passing from the peak to the off-peak traffic matrices. At time t = 20 s the GPE commands are sent from the CEU to the nodes (the vertical blue lines mark the starting time and the ending time for launching the GPE commands). At the beginning of the analysis, the flow is routed on directed link 6-23, the RTT is around 30 ms and it is also almost stable; at the end of the network reconfiguration, i.e., t ≥ 55 s, the direct link 6-23 is put in low power, the new path followed by the flow is composed of 4 nodes (6-22-7-23) and the RTT
under the GreenNet FIRB Future in Research project. Moreover, we would like to thank Massimo Rimondini for the fruitful discussions on the Netkit emulator.
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RTT variation from node 6 and node 23.
is around 90 ms.3 It is very interesting to analyze the RTT behavior during the transient phase, since many events can be detected: i) first of all, it is clearly visible that t = 45 s represents the time instant in which the path modification takes place; ii) the whole GPE configuration procedure, i.e., the connections establishment and the relative PExps enabling among CEU and involved routers, requires about 30 seconds; iii) the network reconfiguration begins as soon as the first GPE configuration commands are executed, as suggested by RTT spikes after t = 20 s; iv) from the path modification time instant, the transient is exhausted in less than 10 seconds. The total time from launching the GPE commands to stabilization of transients takes less than one minute. This number provides also the minimum interval for applying GPE in the network, a value which is in line with the daily temporal variation of traffic. Finally, note that in this case no packets are lost, thus showing the efficacy of our solution. VI.
C ONCLUSIONS AND F UTURE W ORK
We have studied the impact on the routing transients by applying GPE, an energy-aware algorithm which is fully compatible with OSPF. We have implemented GPE on a green SW router, and we have considered an emulated testbed from a national telecom operator. We have then measured the increment in the RTT and the number of ping lost as a consequence of the application of GPE in the network. Our results confirms the efficacy of our approach: during transients, the maximum RTT is at most equal to 320 ms, and the percentage of lost packets is at most 1.45%. Moreover, the results show that GPE can be applied if the interval repetition is in the order of dozens of seconds, which for example occurs in the case of daily traffic variations. As next step, we plan to publicly release our solution to the community, and to install our green software routers on real devices. In this way, we will be able to evaluate the transient times considering both the time required to apply the exportations and the time needed to put at full power a linecard in sleep mode. VII.
ACKNOWLEDGEMENT
The research leading to these results has received funding from the Italian Ministry of University and Research (MIUR) 3 Minor variations are a consequence of the elaboration times needed to traverse node 22 and 7
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