Modeling The Interaction between TCP and Rate Adaptation at Links

Transcription

1 Modeling The Interaction between TCP and Rate Adaptation at Link Faheem Khuhawar, Marco Mellia, Michela Meo Dip. di Elettronica e Telecomunicazioni, Politecnico di Torino, Italy. {firtname.latname}@polito.it Abtract In thi paper, we model and invetigate the interaction between the TCP protocol and rate adaptation at intermediate router. Rate adaptation aim at aving energy by controlling the offered capacity of link and adapting it to the amount of traffic. However, when TCP i ued at the tranport layer, the control loop of rate adaptation and one of the TCP congetion control mechanim might interact and diturb each other, compromiing throughput and Quality of Service (QoS). Our invetigation i lead through mathematical modeling coniting in depicting the behavior of TCP and of rate adaption through a et of Delay Differential Equation (DDE). The model i validated againt imulation reult and it i hown to be accurate. The reult of the enitivity analyi of the ytem performance to control parameter how that rate adaptation can be effective but a careful parameter etting i needed to avoid undeired diruptive interaction among controller at different level, that impair QoS. I. INTRODUCTION In lat decade, Information and Communication Technology (ICT) ha been oberved a an evident energy conumer and number of initiative are taken to reduce energy conumption and improve energy efficiency [1]. Furthermore, the riing trend of the amount of traffic, due to the diffuion of video and data ervice, a well a the more and more widepread ue of communication device in general, and dramatic improvement in technologie to make them more efficient have everely increaed the energy demand. Hence, in all field of ICT and for all technologie, robut countermeaure are required to cope with the rapid growing trend of energy conumption. In the context of wired network, recently the interet in aving energy conumption ha brought the emergence of new propoal and tandard. For intance, the IEEE Energy Efficient Ethernet 802.3az tandard aim at improving efficiency of the traditional Ethernet protocol, that require that the tranmitter and the receiver remain continuouly active even if there i no data to end, leading to wate of energy (about 0.5 for 1GBae-T and 5 for GBae-T), by entering low conuming leep mode when there i no traffic. The adoption of the new tandard allow to ave an amount of energy that, in the bet cae, i.e., when the tranmiion conit of large burt and gap, become roughly proportional to link utilization; however, limited advantage are achieved when the tranmiion conit of mall packet with relatively mall and regular inter-packet gap. Thu, ome work try to overcome thi problem, and aim at more efficient energy proportionality, a [2] propoe to end cumulative Acknowledgement (ACK), i.e., ue delay parameter to end ACK together after certain time or ue larger frame ize. In [3], it i propoed to end packet a a burt by collecting the packet (packet coalecing) in queue with a certain limit and end them at once on the link. Another quite promiing approach to ave energy and to make the device energy conumption more proportional to the offered load, conit in rate adaptation. Leveraging on the fact that le energy i needed when low tranmiion rate are ued intead of high rate, the idea conit in adjuting the data tranmiion rate or capacity according to traffic dynamic: when traffic i high, the maximum capacity i ued, but when traffic i low, low tranmiion rate, that conume le energy, are ued. For intance, [4] propoe to ue dicrete tranmiion rate according to traffic intenity. hile [5] take another approach, that i to adapt the data rate according to link utilization. In thi paper, we focu on thi kind of approach. Thu, the objective of our rate controller i to maximize the energy aving without compromiing the QoS. The rate adaptation mechanim implemented in the router might, however, negatively interact with other mechanim implemented at upper level. In particular, we conider here the poible interaction between the rate adaptation control loop and TCP congetion control loop [6]. The cenario i quite important, being TCP the tranport protocol that carrie mot of the traffic. The control loop defined in the congetion avoidance phae of TCP baically, i) increae the amount of traffic injected in the network when there eem to be enough bandwih and, ii) perform multiplicative decreae of the amount of injected traffic upon lo indication. On it ide, the rate adaptation cheme ha a control loop that i controlled by the amount of traffic injected in the network, a een by the queue ize. Hence, the data rate are adapted baed on the offered load. Thu, if not properly tuned, the two control loop might negatively interact. For example, a rate reduction of the rate adaptation algorithm might induce TCP to reduce injected traffic; in it turn, thi TCP traffic reduction indicate that load decreae and might trigger further rate reduction in the router. Thi interaction might lead, finally, to bad performance and impair end-uer Quality of Experience (QoE). Aim of thi work i to know how thee two control loop (rate adaptation loop and congetion control loop) interplay with each other. To invetigate the interplay of the two control loop, we propoe in thi paper a fluid model analyi. Hence, a queue

2 TABLE I PARAMETERS AND VARIABLES Decription Symbol Value Unit TCP congetion window 0 : 0 packet Queue length Q 0 : 0 packet Etimated queue length Q 0 : 0 packet Capacity C 0 : packet/ec Initial capacity C 0 packet/ec Capacity controller threhold 5:25 packet Lo controller threhold 20 packet Propagation delay R o 0.02 econd Delay of lo indication τ 0.03 : 0.04 econd Round Trip Time RT T R o + Q/C econd Control interval (model) δ m 1/ econd Control interval (imulator) δ 1/0 econd Lo caling factor K l 1/80 Capacity caling factor 1 : 5000 Smoothing factor α 0:1 Lo rate L 0:1 length driven rate adaptation cheme i conidered and analyzed through mathematical modeling uing a fluid model baed framework. Several experiment are then conducted through imulation to validate the reult obtained from the model. The paper i organized a follow. In ection II, we tart by decribing the model through the et of differential equation along with the two propoed rate adaptation model. Later, time evolution of parameter obtained by olving the ytem of differential equation along with it imulation reult to validate the model are dicued in ection III. Steady tate analyi of the model and the impact of tuning the parameter value are highlighted in ection IV. Latly, comparion of reult obtained from both the model plu concluion drawn are mentioned. II. FLUID MODEL The etting up of rate adaptation cheme require the modeling of TCP behavior. Hence, a et of coupled Delay Differential Equation (DDE) are derived to decribe the baic TCP evolution. e build upon the differential equation propoed in [7] that depict the well known TCP congetion control mechanim. The olution of the model provide the evolution in time of TCP a well a network parameter uch a window ize, queue length and capacity. The framework ue the fluid baed model, wherein the parameter evolve a a continuou proce. Table I report the lit of variable ued in thi paper. A. TCP Model The TCP model focue on the evolution of the congetion window ize, that we denote by (t). e conider only the congetion avoidance mechanim of TCP, ince thi i the one that mainly determine the performance of long-lived TCP flow and we neglect the low tart phae. Furthermore, ince we conider, a typical, a low lo regime, the timeout behavior i alo neglected. The evolution of the congetion window ize in congetion avoidance baically conit of two part; the additive increae by one egment of MSS (Maximum Segment Size) every RTT and multiplicative decreae in cae of lo indication. In our cae, loe of type Triple Duplicate (TD) ACK are conidered. The TCP ender receive the lo indication (TD ACK) after roughly one RTT. Thi delay parameter i denoted in our model by the ymbol τ. Thu, a lo indication received at time t mean that a lo actually occurred in the router at time t τ. Similar to [7], we conider a cenario in which a Random Early Detection (RED) queue management algorithm i ued in the router, thu, loe occur according to the RED mechanim that depend on the queue length. Further decription about RED queue management algorithm can be found in [8]. An extention of the model to other queue management cheme i left for future work. Let the lo rate at time t be denoted by L(t). Given TCP delay in detecting loe, at time t TCP perceive a lo rate equal to L(t τ). The number of loe i thu given by the product of the lo rate time the throughput, that, in it turn, i given by ratio between the congetion window ize and the round trip time; the number of loe i thu equal to L(t τ) (t τ ) RT T (t τ ). Under the fluid model baed framework, the RED queuing policy can be modeled by making loe proportional to queue length, according to the following, L(t) =K l (Q(t τ) ) for 0 L(t) 1 (1) where L(t) repreent the lo rate, and K l i the lo rate caling factor that define the growth of the drop probability function in the RED queue. i the lo threhold, thereafter the RED queue tart to drop packet. Similarly, Q(t τ) repreent the current queue length at time t τ, i.e., when the tranmitter ee the lo. The evolution of the round trip time take the following form, RT T (t) =R o + Q(t) (2) C(t) where R o i the propagation delay (that i contant) and the correpond to the queuing delay meaured in fraction Q(t) C(t) econd. Similarly, RT T (t τ) =R o + Q(t τ ) C(t τ ). Putting the above mechanim together, the TCP congetion avoidance behavior can be modeled by the following DDE, d (t) = 1 RT T (t) (t) 2 d (t) ( ) (t τ) L(t τ) RT T (t τ) where the derivative repreent the change of window ize meaured in packet. The differential equation that decribe the queue length evolution can be written a the difference between the arrival rate of packet at the queue, repreented by the term (t) RT T (t) and the rate at which the packet are erved, repreented by (3)

3 the capacity C(t), dq(t) = (t τ) RT T (t τ) C(t) for 0 Q(t) Q max (4) The differential equation i bounded between 0 and Q max,o that the erving of packet occur when the queue length i greater than zero. B. Rate Adaptation e decribe here the model of the rate adaptation algorithm, i.e., of the trategy with which the tranmiion rate i adapted to the queue length. In particular, we focu on two lightly different controller: in the firt one, the rate i adapted to the intantaneou queue length, in the econd one a weighted average of the queue length i ued a control parameter. 1) Rate Controller I: The idea i to deign a rate controller that adapt the tranmiion rate according to queue length evolution. In other word, the ervice rate or capacity C(t) increae/decreae if the intantaneou queue length grow above/below a certain threhold. Baed on the value of threhold parameter, the controller ha the ability to aggreively operate at maximum capacity (low value of ) i.e., minimal energy aving while maintaining high QoS; or aggreively reduce energy conumption at the expene of poibly compromiing QoS (high value of ). The rate controller can be modeled by, dc(t) = K c (Q(t) ) for C min C(t) C max (5) where repreent the capacity caling factor and the queue length threhold, with the rate controller being bounded between minimum and maximum capacity contraint. 2) Rate Controller II: In thi cae, the rate controller adapt the rate to an average queue length, and, in particular to the Exponentially eighted Moving Average (EMA) queue length intead of the intantaneou queue length. The purpoe i to poibly make the controller more table by adapting the rate more lowly to queue length variation. The EMA mooth the variation of the queue length through a moothing factor, α, with 0 < α < 1. A queue length ampling interval equal to δ m i ued. The value of δ m i choen to be fixed and it i et to 1 /C max, which mean the value i updated on almot every packet tranmiion. Hence, the equation decribing the evolution of EMA queue length a hown in [7] i a follow, d Q(t) = log(1 α) δ m Q(t) log(1 α) δ m Q(t) (6) where Q(t) repreent the average queue length. Therefore, the rate controller baed on etimated queue length can be decribed with the following equation, dc(t) = ( Q(t) ) for C min C(t) C max (7) III. MODEL VALIDATION In thi ection we firt decribe the kind of reult that can be obtained by the model and provide a firt analyi of them; we then validate the analytical model by comparion againt imulation reult. A. Time Evaluation The et of coupled delay differential equation (3), (4), (5), i.e., the ytem of differential equation, are olved numerically in order to get the evolution in time of the mentioned parameter. To derive a firt et of reult, we et the model parameter a follow. The initial tarting capacity repreented with C 0 to packet /ec; operating within the range of C min = 0 to C max = packet /ec. The capacity threhold parameter i et to = 5 packet. Similarly, the lo threhold i fixed to =20packet. The queue length i bounded in the region of Q min =0to Q max = 0 packet. The lo caling factor K l = 1 /80, which i equivalent to RED drop bound going from 20 to 0 packet with packet dicard probability function of value 1, when the queue length i equal to the maximum, Q max. The propagation delay i fixed to R o =0.021 econd and the lo delay indication factor to τ =0.036 econd. Figure 1 illutrate an example of the evolution of the parameter baed on rate controller I. Oberve the fact that the capacity, after ome tranient period, achieve, a deired, the maximum poible value. The congetion window ize, a well a the queue length, continuouly vary in time and it ocillate, a i expected from long-lived TCP flow in congetion avoidance. The evolution of parameter baed on rate controller II i pretty much the ame for low value of, wherea the evolution of capacity i much moother for higher value of with repect to rate controller I, ee Section IV for detailed dicuion. B. Simulation Reult 1) Deign Parameter: To validate the rate adaptation model, a imple network topology i imulated through a dicrete event imulator developed in OMNeT++. The conidered cenario i hown in Fig. 2, conit of two node, namely client and erver, that communicate with each other uing the TCP protocol (TCP Reno flavor along with default TCP configuration). The communication happen in eion and, during a eion, the client end a FTP requet for a file to the erver and wait for the reply to complete before ending a new requet. The connection get cloed if either imulation time limit i reached or if number of requet get complete. In our cae, connection get cloed due to imulation time limit contraint, which i et to 500 econd. Simulation parameter are choen a thoe ued earlier for the analytical model. Thu, the node are connected with the link capacity of packet/ec (packet ize of 1452 byte) and propagation delay of 0.02 econd. The downlink i repreented with the path from erver to client that i heavily loaded with the long-lived TCP flow, wherea the uplink path i lightly loaded a it contain only ACK. All the node utilize RED queue mechanim with

4 Capacity Evolution (Controller I with Mean= for =5, =1) along the path implement the rate adaptation algorithm at queue a detailed below Client Router Server PER Fig. 1. indow Size (packet) Queue Length (packet) Queue Length (packet) Congetion indow Evolution (Mean=29.59 for R o =0.024, τ= ) Queue Length Evolution (Mean=8.70 for =20, K l =0.0125) EMA Queue Length Evolution (Mean=13.76 for α=0.002, δ m =0.001) Lo Rate Evolution (Mean= ) Example of evolution of the parameter baed on the fluid model. lower and upper bound limit of 20 and 0 packet and linear growth of the packet dicard probability from 0 to 1. The router delay = 0.02 max. data-rate = bp Fig. 2. The imulation topology. 2) Rate Controller I: To validate the fluid model baed rate controller I preented in Section II-B1, we have implemented the equivalent rate control mechanim on the router uing the OMNeT++ imulator. The implementation of rate control mechanim on link layer i mathematically decribed a the following, C(t) =C(t)+(Q(t) )δ (8) The parameter are choen imilar to mathematical model decribed earlier. Furthermore, the capacity i bounded in the region of C min = 0 to C max = packet /ec with the initial tarting capacity et to C 0 = packet /ec. Theδ in the imulator i the time interval wherein the controller check the queue condition and update the rate. To get optimal reult, the value of δ hould be le than the value of RTT. e have choen δ to be mall enough to react adequately toward the change in queue length. Thi action can be compenated if the value of K c i choen to be high enough. Indeed, the product of δ i equivalent to the decribed in the fluid model. Since the differential equation olution neglect a number of TCP mechanim (low tart phae, timeout, and o on), while the imulator ha a detailed decription of the TCP protocol, we expect to ee ome different behavior, epecially during the initial tranient phae due to low tart. Alo the fact that the differential equation model provide olution a continuou increment, while the imulator work in dicrete tep, i going to make the reult from the two approache different. Figure 3 illutrate the behavior of rate controller evolution implemented uing OMNeT++ imulator for different value of δ along with it comparion with fluid model baed rate controller. The comparion of reult how that the fluid model i very accurate, depite the different approache a dicued above, and follow the trail of capacity evolution obtained through imulation. 3) Rate Controller II: e repeat the experiment decribed in previou ection with the ame parameter but for the rate controller, which now evolve baed on EMA queue length. The evolution of etimated queue length i computed uing the following formula, Q(t) =(1 α) Q(t)+αQ(t) (9)

5 Fig. 3. Capacity Evolution (Controller I with R o =0.02, τ=0.04, δ =0.0001, =5) =1 (Fluid Model) K =K c c δ =1 (Simulator) K =5 (Fluid Model) c K =K c c δ =5 (Simulator) K =0 (Fluid Model) c K =K c c δ =0 (Simulator) Capacity controller baed on intantaneou queue length. The parameter α repreent the moothing factor ranging between 0 and 1, where the value α =1repreent the cae of no averaging, i.e., of intantaneou queue length. Hence, (8) become, C(t) =C(t)+( Q(t) )δ () Figure 4 how the behavior of rate controller baed on EMA queue length and it comparion with fluid model baed rate controller. The imulation reult how that the model doe quite well in capturing the dynamic of capacity evolution for different value of. Fig. 4. Capacity Evolution (Controller II with R o =0.02, τ=0.04, δ =0.0001, =5) =1 (Fluid Model) K =K c c δ =1 (Simulator) K =5 (Fluid Model) c K =K c c δ =5 (Simulator) K =0 (Fluid Model) c K =K c c δ =0 (Simulator) Capacity controller baed on average etimated queue length. IV. INTERACTION BETEEN TCP AND RATE ADAPTATION A. Steady State Analyi The teady tate analyi of the fluid model allow u to analyze the fundamental relationhip between the parameter of the model. To analyze the teady tate of the deigned rate adaptation cheme decribed in Section II-B1, we derive the equilibrium condition of the et of differential equation, (3), (4), (5) and oberve it equilibrium tate. At the teady tate auming <, when the derivative are null, we have, 2 = L, C = RT T, Q = (11) From thee expreion, we oberve that, a expected and a typical of TCP behavior, the window ize depend on the invere of the quare root of the lo rate and adapt to the capacity through the RTT. Interetingly, the mean queue length ettle to the value of, that i the control threhold of capacity. Conidering that the capacity i bounded within C min and C max parameter, we have the following teady tate equation for capacity, which baically how two regime: ( ) min RT T,C max, < C = ( ) (12) max RT T,C min, > Thee expreion ugget that if the control of capacity kick in before the control of TCP, that occur through loe ( < ), the capacity tabilize to the maximum one C max, given the teady tate capacity (C = RT T >C max). However, given (C min <C= RT T <C max), the teady tate capacity ettle within the range of C min and C max, i.e., capacity i caled according to intantaneou offered load. If intead, loe occur when capacity controller ha not yet entered into play ( > ), the TCP control loop hrink the window and the TCP performance, without actually letting RT T the capacity to grow. Thi eventually mean the ratio become maller and therefore, the capacity regime i forced to tabilize at the minimum bound C min, given the teady tate (C = RT T <C min). A fundamental guideline to the deign of the interaction between the rate adaptation and the TCP control loop i thu to make TCP control loop act when capacity control i already effective. In term of parameter etting, thi mean making be maller than. Extending the teady tate analyi baed to rate controller II i imple, and the concluion are imilar to thoe dicued above. The only difference i that intead of queue length (Q) ettling around the, the rate controller adjut it capacity in uch a way that the etimated queue length ( Q) ettle around the value of. B. Parameter Senitivity e report in thi ection the impact of parameter on the capacity evolution conidering the cae where the controller i baed on intantaneou queue length, namely rate controller I. Senitivity analyi baed on rate controller II i omitted, a the concluion drawn baed on rate controller II are imilar to the one obtained from rate controller I. Note that the value of parameter etting for each imulation experiment are indicated in the title of the correponding figure. Impact of : The parameter i the threhold for the rate adaptation capacity controller to cale the capacity. The value of i choen to be le than, o that before loe occur, capacity i allowed to increae and poibly avoid loe; a choice of larger than would make loe act on the congetion control of TCP before capacity i increaed and would, thu, end up forcing the capacity to it minimum C min a een in Section IV-A. The teady tate analyi ugget that the capacity controller trie to adjut capacity uch that the mean queue length i kept around the value of. The maller the value of i, the more aggreive

6 the capacity controller i in puhing capacity to it maximum C max. Thi i confirmed by the reult of the experiment that are reported in Figure 5, repreenting the impact of on capacity evolution. Clearly, mall value of lead to a more reactive control that make the capacity grow to the maximum in a hort time. Oberve alo the cae previouly mentioned with >, that converge the capacity to it minimum. Capacity Evolution ( =1, =20, K l =1/80, R o =0.02, τ=0.04) =5 = = =19 =25 Fig. 5. Influence of. Impact of : The capacity caling parameter ymbolize how aggreive the capacity controller i toward the change in queue length. Figure 6 illutrate the impact of on the evolution of the capacity, i.e., on the performance of the controller. For low value of, the rate controller i low in reacting and reache maximum capacity in long time (order of 0 econd). Large value of are therefore needed to avoid that the TCP performance deteriorate. Moreover for high value of, the controller react much fater but it rik to follow too cloely the variation of the queue length, a indicated by the large ocillation that can be een in the zoomed mall picture in the ame figure. Capacity Evolution ( =5, =20, K l =1/80, R o =0.02, τ=0.04) =0 =50 = =5 =2 =1 Fig. 6. Influence of. Impact of τ: The parameter τ repreent the amount of time need by the ource to react to a lo indication. Uually, the time to react to loe in TCP i about the RTT, ince loe are detected through the flow of ACK. However, here, we vary τ to check how the time delay between the occurrence of loe and TCP reaction interact with the rate adaptation mechanim. e, thu, perform ome experiment in which we let τ vary and collect the reult in Fig. 7, that illutrate the impact of τ on the evolution of capacity. hen τ i large, it mean that TCP react with a large delay to ome loe and then it become le aggreive in growing the congetion window. Thi implie that many loe occur in the meanwhile and TCP end up reducing ignificantly the window ize. Thi, in turn, mean mall queue length and mall capacity. Notice indeed that for large τ (i.e., for large RTT), the ytem i not able to reach C max. Capacity Evolution ( =1, =5, =20, K l =1/80, R o =0.02) τ=0.01 τ=0.02 τ=0.03 τ=0.04 τ=0.05 Fig. 7. Influence of τ. Impact of : The parameter repreent the value of the queue ize at which loe tart to occur. In term of control, ince loe act a input to the congetion control loop of TCP, repreent the value of the queue at which the congetion control kick in. The impact of the parameter i hown in Fig. 8, that report the capacity evolution for different value of.high value of reult in high value of the TCP window ize, which eventually reult in long queue. A previouly dicued, when the value of i large the capacity controller can act on the capacity and reach the maximum before loe occur, i.e., before TCP control loop enter into play. The capacity controller become more aggreive for higher value of, a the difference between Q(t) and in (5) get higher. Thi mean that large value of mean a more reactive controller, a hown in the figure. Overall the reult are imilar to the choice of een in Fig. 5. Capacity Evolution ( =1, =5, K l =1/80, Ro=0.02, τ=0.04) =25 =20 = = Fig. 8. Influence of. Impact of K l : Analogou to, the parameter K l i the lo caling factor that repreent the reactivity of the lo control. Higher value of K l reult in higher loe, and lower TCP window ize. Small window ize, in it turn, implie mall queue length and mall capacity. For the ake of brevity, the figure i omitted here.

7 Impact of R o : The propagation delay R o make the control loop of TCP be more or le cloely coupled with the queue with it own control loop in the rate adaptation. Large value of R o make the TCP congetion control react lowly to the queue tate and thi end up inducing ocillation to the queue length and tranmiion rate. Reult are imilar to the one oberved for the variation of τ. C. Average Capacity To further invetigate the interplay between rate adaptation and TCP control loop, we focu on the average value of capacity taken from each imulation run of econd duration. The meaure i accounting the initial tranient growth a well a the teady tate of capacity. e conider the rate controller I and let the parameter vary between 5 to 25 while keeping the loe contant ( =20and K l =1/80). Again, the rate controller evolve baed on the ame value of C min = 0, C max =, andc 0 =. Reult are reported in Fig. 9 for different value of ; to emphaize the relationhip between and, we report on the x-axi the value. e oberve that the capacity reache C min for >, wherea the region with > 0 repreent to thoe cae in which the capacity controller react to the change in queue length before the congetion controller kick in. It i intereting to oberve that the value eem to have a tronger impact on reult than the value of, uggeting that the undertanding of interplay between TCP and rate adaptation control loop i extremely important; carefully controlling the interaction between the two control allow to achieve larger capacity, while acting on the rate adaptation alone might be uele. Fig. 9. Average Capacity (Controller I for K l =1/80, =20, R o =0.02, τ=0.04) =1 =3 =5 =7 = Behavior of average tranient plu teady tate capacity. The reult how that the rate controller baed on etimated queue length yield to moother and more table reult with repect to the rate controller baed on intantaneou queue length. hile thi i quite intuitive, it i important to emphaize that thi moother behavior i achieved at the cot of larger average queue length and larger amount of loe, that might, in general, in their turn deteriorate the QoS (higher delay variance, poibility of multiple loe and therefore difficultie in reacting to loe, and o forth). However, the difference are not that large in abolute term. Finally, for very large value of, the controller I uffer from much larger ocillation than controller II (ee alo Fig. 6). Thi reult in decreae of average capacity. Queue Length (packet) Lo Rate Average Capacity ( =5, R o =0.02, τ=0.04) Controller I Controller II Average Queue Length (α=0.002, δ m =0.001) Fig.. 3 x 3 Average Lo Rate (K l =1/80, =20) Controller I Controller II Controller I Controller II Comparion of average capacity, queue length, lo rate. V. COMPARISON BETEEN THE CONTROLLERS e make in thi ection a direct comparion between the performance of the two propoed rate adaptation controller. To do o, we run the analytical model for 500 econd and we take the average value of variou parameter, uch a the capacity, queue length and lo rate; the computed average include the tranient phae a well a the teady tate phae. Figure how the comparion of the reult for the two controller, for a wide range of value of. VI. CONCLUSION In thi paper, we have propoed a mathematical model to analyze the interaction between TCP congetion control and rate adaptation cheme implemented at the router to ave energy. The model are baed on differential equation and imulation experiment have validated the model a being accurate and uitable to predict the ytem performance. The model accurately approximate TCP behavior depite the fact

8 that a number of TCP mechanim, like timeout and low tart, were diregarded. Reult indicate that the interaction between the rate controller and TCP i quite critical, and improper etting of the parameter might lead to bad performance. It might indeed happen that low rate are ued in the router, with correponding low throughput for the connection. Fine tuning of the rate controller parameter i needed. hen properly tuned, the controller can be table, leading to high capacity when needed with good reulting performance for TCP, confirming that rate adaptation can reduce energy conumption while maintaining high QoS, but at the cot of careful mechanim deign. ACKNOLEDGMENTS The reearch leading to thee reult ha received funding from the European Union Seventh Framework Programme (FP7/7-2013) under grant agreement n (Network of Excellence TREND). REFERENCES [1] R. Bolla, R. Bruchi, F. Davoli, and F. Cucchietti, Energy Efficiency in the Future Internet: A Survey of Exiting Approache and Trend in Energy-Aware Fixed Network Infratructure, Communication Survey Tutorial, IEEE, vol. 13, no. 2, pp , [Online]. Available: [2] P. Reviriego, A. Sanchez-Macian, and J. A. Maetro, On the Impact of the TCP Acknowledgement Frequency on Energy Efficient Ethernet Performance, in Proceeding of the IFIP TC 6th international conference on Networking, er. NETORKING 11. Berlin, Heidelberg: Springer-Verlag, 2011, pp [Online]. Available: [3] K. Chritenen, P. Reviriego, B. Nordman, M. Bennett, M. Motowfi, and J. Maetro, IEEE 802.3az: The Road to Energy Efficient Ethernet, Communication Magazine, IEEE, vol. 48, no. 11, pp , november 20. [4] S. Nedevchi, L. Popa, G. Iannaccone, S. Ratnaamy, and D. etherall, Reducing Network Energy Conumption via Sleeping and Rate- Adaptation, in Proceeding of the 5th USENIX Sympoium on Networked Sytem Deign and Implementation, er. NSDI 08. Berkeley, CA, USA: USENIX Aociation, 8, pp [Online]. Available: [5] C. Gunaratne, K. Chritenen, B. Nordman, and S. Suen, Reducing the Energy Conumption of Ethernet with Adaptive Link Rate (ALR), Computer, IEEE Tranaction on, vol. 57, no. 4, pp , April 8. [6] M. Allman, V. Paxon, and E. Blanton, TCP Congetion Control, IETF RFC 5681, Tech. Rep., Sept. 9. [Online]. Available: [7] V. Mira,.-B. Gong, and D. Towley, Fluid-baed Analyi of a Network of AQM Router Supporting TCP Flow with an Application to RED, in IN PROCEEDINGS OF ACM SIGCOMM, 0, pp [8] S. Floyd and V. Jacobon, Random Early Detection Gateway for Congetion Avoidance, IEEE/ACM Tran. Netw., vol. 1, no. 4, pp , Aug [Online]. Available: