TCP Symbiosis: Congestion Control Mechanisms of TCP based on Lotka-Volterra Competition Model

TCP Symbiosis: Congestion Control Mechanisms of TCP base on Lotka-Volterra Competition Moel Go Hasegawa Cybermeia Center Osaka University 1-3, Machikaneyama-cho, Toyonaka, Osaka 56-43, JAPAN Email: hasegawa@cmc.osaka-u.ac.jp Masayuki Murata Grauate School of Infomation Science an Technology Osaka University 1-3, Yamaaoka, Suita, Osaka 56-871, JAPAN Email: murata@ist.osaka-u.ac.jp Abstract In this paper, we propose TCP Symbiosis, which has a robust, self-aaptive an scalable congestion control mechanism for TCP. Our metho is quite ifferent from existing approaches. We change the winow size of a TCP connection in response to information of the physical an available banwiths of the en-to-en network path. The banwith information is obtaine by an inline network measurement technique we have previously evelope. Using the banwith information we can resolve the inherent problems in existing AIMD/MIMD-base algorithms such as perioic packet loss an unfairness cause by the ifference in RTT. We borrow algorithms from biophysics to upate the winow size: the logistic growth moel an the Lotka-Volterra competition moel. This is because these moels escribe changes in the population size of a species that epens on the living environment. The population of a species can be viewe as the winow size of a TCP connection an the living environment as the banwith of the bottleneck link. The greatest avantage of using these moels is that we can refer to previous iscussions an results for various characteristics of the mathematical moels, incluing scalability, convergence, fairness an stability in these moels. Through mathematical analysis an extensive simulation experiments, we compare the propose mechanism with traitional, HighSpee TCP, Scalable TCP an, an exhibit its effectiveness in terms of scalability to the network banwith an elay, convergence time, fairness among competing connections, an stability. I. Introuction With increases in the heterogeneity an the complexity of the Internet, many problems have emerge in s congestion control mechanism [1-3] for example. The primary reasons for these problems are that the congestion signals are only inicate by packet loss an that uses fixe Aitive-Increase-Multiplicative-Decrease AIMD parameter values to increase an ecrease winow size, whereas those parameters shoul be change accoring to the network conitions. Although many solutions have been propose for there problems [4-6], most of them inherit the funamental congestion control mechanism of : the AIMD mechanism triggere by the etection of packet losses in the network. The congestion control mechanism improves the throughput by ajusting the increasing an ecreasing parameters statically an/or ynamically. However, most previous stuies have focuse on changing the AIMD parameters to accommoate particular network environments. Since these methos employ a hoc moifications for a certain network situation, their performance when applie to other network environments is unclear. Because winow size inicates the maximum amount of packets that TCP can transmit for one Roun Trip Time RTT, an aequate winow size for a TCP connection is equal to the prouct of the available banwith an the rountrip propagation elay between the sener an receiver hosts. measures the RTTs of the network path between sener an receiver hosts by checking the eparture times of the ata packets an the arrival times of the corresponing AC packets. However, oes not have an effective mechanism to recognize the available banwith. This explains the funamental problem: cannot converge its winow size to an aequate value when the network environment varies. In a sense, traitional can be consiere to be a tool that measures available banwith because of its ability to ajust the congestion winow size to achieve a transmission rate appropriate to the available banwith. However, it is ineffective because it only increases the winow size until packet loss occurs. In other wors, inuces packet loss in orer to obtain information about the available banwith-elay prouct of the network. That is, even when the congestion control mechanism of TCP works perfectly, the TCP sener experiences packet losses in the network at some intervals. Since all moifie versions of TCP using the AIMD policy, incluing the generalize AIMD algorithm [7] an its variants, contain this essential problem, they cannot avoi packet losses in the network even if they behave ieally. There are some TCP variants, incluing TCP Vegas [8] an [6], that utilize the RTT values for the congestion inication, base on the fact that the RTTs for a TCP connection usually increase before packet losses occur when the network is congeste. However, such RTT-base approaches cannot be applie to high-spee networks ue to an inherent problem, i.e., changes in RTT values of the en-toen network path becomes invisible as the network banwith becomes large. We believe, therefore, that if a TCP sener recognizes the banwith information of the network path quickly an aequately, it can create a better mechanism for congestion control in TCP. Although numerous measurement tools that measure the physical an available banwiths of network paths have been propose in the literature [9-14], we cannot irectly employ these existing methos in TCP mechanisms, primarily because these methos utilize a lot of test probe packets. Moreover, these methos also require too much time to obtain one measurement result. Accoringly, we have propose a metho calle Inline measurement TCP ImTCP that avois these

problems in [15, 16]. It oes not inject extra traffic into the network, an instea it estimates the physical/available banwiths of the network path from ata/ac packets transmitte by an active TCP connection in an inline fashion. Furthermore, since the ImTCP sener obtains banwith information every 1 4 RTTs, it is well able to follow the traffic fluctuation of the unerlying IP network. We believe that, by irectly measuring banwith information, the congestion control in TCP becomes truly scalable to the banwith elay prouct of the network. AIMD- an MIMD-base mechanisms such as HighSpee TCP H [4] an Scalable TCP [5] are more scalable than, but they have serious problems in parameter tuning. Since no knowlege of the banwith information is obtaine, the control parameters are configure base on implicit/explicit assumptions about the network environment. For example, in [4], the recommene control parameters are to fill the network link with 1 Gbps banwith, 1 msec RTT, an a packet loss rate of 1 7. One of the avantages of the propose mechanism is that it is not necessary to configure the control parameters accoring to the network environment. In aition, because ImTCP is implemente at the bottom of the TCP layer, this measurement mechanism can be inclue in various types of TCP congestion control mechanisms. In this work, we propose a new congestion control mechanism for TCP, which we call TCP Symbiosis, that utilizes the information of physical an available banwiths obtaine from an inline measurement technique. The propose mechanism oes not use a hoc algorithms such as TCP Vegas an instea employs existing algorithms, which enable us to mathematically iscuss an guarantee their behavior even though posing a simplification of the target system. More importantly, it becomes possible to give a reasonable explanation for our control parameter selections within TCP, instea of conucting intensive computer simulations an/or choosing parameters in an a hoc fashion. We have esigne a winow size control algorithm whose purpose is to quickly ajust the winow size to an aequate value base on banwith information in orer to fairly istribute banwith among competing connections. For this, we borrowe algorithms from the logistic growth moel an the Lotka-Volterra competition moel [17], both of which are use in biophysics to escribe changes in the population of species. The biophysics moels were chosen base on their intrinsic stability an robustness, which is achieve even when they behave without any interaction in an autonomous an istribute fashion. This is the case for the congestion control of TCP: each TCP connection behaves inepenently, but still we want to improve the banwith utilization an the throughput of the connection. When applying the logistic growth an Lotka-Volterra competition moels to the congestion control algorithm of our TCP, the population of a species can be viewe as the winow size of a TCP connection, the carrying capacity of the environment as the physical banwith, an interspecific competition among species as banwith sharing among competing TCP connections. In the present paper, an analytic investigation of the propose algorithm is performe base on previously reporte iscussions an results regaring various biophysical characteristics of the mathematical moels, incluing scalability, convergence, fairness an stability. Enowing TCP with these characteristics is the primary objective of the present stuy. Furthermore, a performance analysis for the situation where the traitional an TCP Symbiosys share the bottleneck is present to show the fairness property of the propose mechanism against the existing TCP version. We also present extensive simulation results in orer to evaluate the propose mechanism an show that, compare with traitional an other TCP variants for high-spee networks, the propose mechanism utilizes network banwith effectively, quickly, an fairly. II. Lotka-Volterra Moel an Application to TCP Congestion Control Mechanisms In this paper, we inten to buil a robust self-aaptive congestion control mechanism for TCP. In this sense, the propose metho is quite ifferent from existing approaches. The concept of the winow upating algorithm of the propose metho is borrowe from a biological system, which is often pointe out to be robust [18], because in many biological systems, the actions of the entity e.g., living organism are not etermine base on the results of irect interactions among entities, but rather on information obtaine through the environment, which is a funamental necessary conition for the system to be robust. The concept is often calle stigmergy in the literature see, e.g., [19]. With respect to the current case, the winow increase/ecrease strategy is etermine base on the physical an available banwith, rather than on the packet loss or RTTs, which are irect consequences of the activities of the TCP connections. A. Brief Introuction to the Lotka-Volterra Moel 1 Logistic Moel The logistic equation is a formula that represents the evolution of the population of a single species over time. Generally, the per capita birth rate of a species increases as the population of the species becomes larger. However, since there are various restrictions on living environments, the environment has a carrying capacity total population size, which is usually etermine by the available sustaining resources. The logistic equation escribes such changes in the population of a species as follows [17]: t N = ɛ 1 N N 1 where t is time, N is the population of the species, is the carrying capacity total population size of the environment, an ɛ is the intrinsic growth rate of the species <ɛ. Lotka-Volterra Competition Moel The Lotka-Volterra competition moel is a well known moel for examining the population growth of two or more species that are engage in interspecific competition. In the moel, Equation 1 is moifie to inclue the effects of both interspecific competition an intraspecific competition. The basic twospecies Lotka-Volterra competition moel with both species N 1 an N having logistic growth in the absence of the other is comprise of the following equations [17]: 1 N 1 + γ 1 N N 1 t N 1 = ɛ 1 t N = ɛ 1 1 N + γ 1 N 1 N 3

Number of Species 1 1 8 6 4 4 6 8 1 Species #1 Species # Fig. 1. Changes in population of two species with the Lotka-Volterra competition moel where N i, i, an ɛ i are the population of the species, the carrying capacity of the environment, an the intrinsic growth rate of the species i, respectively. In aition, γ ij is the ratio of the competition coefficient of species i with respect of species j. In this moel, the population of species 1 an oes not always converge to a value larger than, an in some cases one species becomes extinct, epening on the values of γ 1 an γ 1. Commonly, the following equations are sufficient conitions for the two species to survive in the environment [17]: γ 1 < 1, γ 1 < 4 1 Assuming that the two species have the same characteristics, they have the same values: = 1 =, ɛ = ɛ 1 = ɛ, an γ = γ 1 = γ. Then, Equations an 3 can be written as follows: t N 1 = ɛ 1 N 1 + γ N N 1 5 t N = ɛ 1 N + γ N 1 N 6 In aition, Equation 4 can be written as γ<1. Figure 1 shows the population changes in the two species using Equations 5 an 6, where = 1, ɛ = 1.95 an γ =.9, an species joins the environment 1 secons after species 1. From the figure, we can observe from this figure that the population of the two species converges quickly to the same value. We can easily exten Equations 5 an 6 for n species as follows: t N i = ɛ 1 N i + γ n j=1,i j N j N i 7 Note that survival an convergence conitions are ientical, i.e., γ < 1. Even when two or more species exist, each inepenently utilizes Equation 7 to obtain N i, an the population of the species can converge to the value equally share among competing species. We consier that the changing population trens of species epicte in Figure 1 is ieal for controlling the transmission spee of TCP. That is, by using Equation 7 for the congestion control algorithm of TCP, rapi an stable link utilization can be realize, whereas each TCP connection can behave inepenently as an autonomous istribute system. However, this moel cannot be irectly applie to the congestion control algorithm of TCP because the moel must obtain N j. This is iscusse in the next subsection. B. Application to Winow Size Control Algorithm To convert Equation 7 to a winow increase/ecrease algorithm, we consier N i as the transmission rate of TCP sener i an as the physical banwith of the bottleneck link. Furthermore, when applying Equation 7 to the congestion control algorithm for connection i, it is necessary for connection i to know the ata transmission rates of all other connections that share the same bottleneck link. This assumption is quite unrealistic with respect to the current Internet. Therefore, we use the sum of the ata transmission rates of all of the other connections using the physical an available banwiths as follows: n N j = A i j=1,i j where A i is the available banwith for connections i. Thus, Equation 7 becomes: t N i = ɛ 1 N i + γ A i N i 8 Here we assume that all connections share the same bottleneck link in the equation. Note that when each TCP connection has a ifferent physical banwith, the propose mechanism share the bottleneck link banwith in a reasonable manner, which we will iscuss in Subsection IV-E. The propose mechanism requires moifications only with respect to sener-sie TCP, an no change in receiver-sie TCP is require. A TCP sener controls its ata transmission rate by changing its winow size. To retain the essential characteristics of TCP an ecrease the implementation overhea, we employ winow-base congestion control in the propose TCP by converting Equation 8 to obtain an increasing algorithm of winow size in TCP. The winow size of connection i, w i,is calculate from N i, the transmission rate, using the following equation: w i = N i τ i where τ i is the minimum value of the RTTs of connection i, which is assume to equal the propagation elay without a queuing elay in the intermeiate routers between sener an receiver hosts. Next, Equation 8 can be rewritten as follows: t w i = ɛ 1 w i + γ A i τ i τ i Finally, we integrate { Equation 9 } as follows: w w i t = ie ɛt 1 γ 1 A i { } e ɛt w i 1 γ 1 A i 1 w i 9 { γ A i}τ i 1 +{ γ Ai}τi In Equation 1, when we set the initial value of the winow size w i an the current time to t =, we can irectly obtain winow size w i t for any time t. We use the above equation for the control algorithm of the winow size of TCP connections. Equation 1 requires measurement of the physical an available banwiths of a network path. Therefore, we utilize the inline network measurement technique in ImTCP [15, 16]. In [15, 16], the authors propose ImTCP, which is an inline network measurement technique for the physical an available banwiths of network paths between TCP sener an receiver hosts. ImTCP can continuously measure banwith by using ata an AC packets of a TCP connection uner ata transmission. That is, the TCP sener transmits ata packets at intervals etermine by an inline measurement algorithm an checks the arrival interval times of the corresponing AC packets to estimate banwith. Since ImTCP performs the measurement without transmitting aitional probe packets over the network, the effect on other network traffic is negligible. ImTCP can also quickly upate the latest changes

in banwiths by frequently performing measurements one result per 1 4 RTTs as long as TCP transmits ata packets. The authors have also propose an implementation esign of ImTCP, in which the measurement program is locate at the bottom of the TCP layer. The propose implementation esign maintains the transmission/arrival intervals of TCP ata/ac packets by introucing a FIFO buffer between the TCP an IP layers. Note that the measurement algorithm has limite effect on TCP s congestion control algorithm [15], meaning that the measurement algorithm can be applie to any TCP variant incluing our metho propose in this paper. Note that the inline network measurement algorithm can estimate both of the physical an available banwiths base on the assumption that the narrowest link on the physical banwith of the en-to-en network path becomes the tightest link on the available banwith. Accoring to the algorithm in [16], when such an assumption is not satisfie, that is, when the narrowest link an the tightest link are ifferent in the path, the physical banwith cannot be measure exactly, whereas the available banwith can be obtaine successfully. However, in that case, since the physical banwith is likely to be unerestimate, this measurement error oes not cause a serious problem for the propose congestion control mechanism, because unerestimation of the physical banwith oes not result in injecting too many packets into the network. III. Characteristics of Propose Mechanism In this section, we analyze various characteristics of the propose mechanism, such as scalability, convergence, parameter setting issues an fairness against. This analysis illustrates that the propose mechanism essentially solves the problems inherent in. A. Convergence Time an Scalability In this subsection, we assume that the physical banwith an available banwith A are constant, which means that the utilization of the bottleneck link are stable. In the propose mechanism, the winow size then converges to a certain value in the propose mechanism. The converge winow size, which is enote as w, can be obtaine by setting w/t = in Equation 9: w = {1 γ + γa}τ 11 where τ is the roun-trip propagation elay the TCP connection. In what follows, we consier the time which is require to increase the winow size from w to ρ w <ρ<1, w <ρw. In the propose mechanism, using Equation 1, the time T becomes as follows: 1 ρ T= ɛ { 1 γ w } w 1 A ln 1 ρ w 1 ρ ɛ1 γ ln w w 1 ρ w 1 ρ = ɛ1 γ ln 1 γ + γaτ w 1 1 ρ w because A is satisfie. Note that ɛ an γ are fixe parameters of the propose mechanism. The issue of setting these parameters will be iscusse in the next subsection. This equation inicates that time T of the propose mechanism increases logarithmically with respect to link banwith an propagation elay τ. In the case of, we can easily calculate T reno, the time necessary to increase winow size from w to w,as follows: T reno =w w τ =[{1 γ + γa}τ w ] τ 13 where τ is the average value of the RTTs of the TCP connection. Here, we ignore the effect of the elaye AC option [] an focus only on the congestion avoiance phase of. In the case of H, which is essentially base on the AIMD policy as in the case of, T hstcp is given by: T hstcp w w τ = {1 γ + γa}τ w τ 14 a max a max where a max is a parameter of H that inicates the maximum winow size increase uring one RTT equivalent to aw in [4]. Equations 13 an 14 inicate that the time require to increase the winow size is proportional to physical banwith an propagation elay τ. This illustrates that the time require to fully utilize the banwith-elay prouct of the network path is proportional to the banwith-elay prouct. H was esigne as a new congestion control mechanism to resolve problems inherent in for high-spee an long elay networks. However, since the winow size control algorithm of H is essentially base on the AIMD policy, this algorithm suffers from poor scalability to the banwith-elay prouct. has a winow size control algorithm base on Multiplicative Increase Multiplicative Decrease MIMD policy an escribes logarithmic increases in time with respect to increases in link banwith [5]. We calculate its convergence time T stcp as follows: ln w τ = 1 a ln {1 γ + γa}τ τ 15 T stcp = 1 a w w where a is an parameter that inicates the increase in winow size when receiving one AC packet. In [5], a =.1 [packet] is the efault value. This equation inicates that has goo scalability to network banwith: however, has poor scalability to propagation elay. has the same equilibrium properties as TCP Vegas, an the winow size is upate at intervals base on the RTT [6]. This means that oes not have goo scalability to the propagation elay of the en-to-en network path, as will be shown in Section IV. B. Stability an Fairness In this Subsection, we utilize the microeconomics analogy as in [1] an its followers to iscuss the stability an fairness property of the propose congestion control mechanism. We consier a single link with the following link cost function: Cx = 1 px 16 for possible constant p, which implicitly represents the parameter of Active Queue Management AQM at the link buffer. x is the total traffic arrival rate to the link. By the efinition of the available banwith, we have; A i = w k 17 τ k k i By using the above equation, we can re-write Equation 9 as follows: t w i = ɛ 1 γ w i γ w k w i τ i τ k k

the Propose Mechanism Winow Size τ + B 1 ρ τ + B 1 ρ τ + B ρτ 1 cycle Sum of the winow size of an the propose mechanism Winow size of Winow size of the propose mechanism Throughput Ratio 1 8 6 4 Buffer = 1/4 BDP Buffer = 1/ BDP Buffer = 1 BDP Buffer = BDP Buffer = 4 BDP Ratio=1 Physical Banwith = [Mbps] Minimum Roun-trip Propagation Delay = τ[msec] Size of the Output Buffer of the Bottleneck Link = B [packets] ρτ Time T 1 3 4 5 6 7 8 Fig.. Moel use for fairness analysis Fig. 3. Changes in the winow sizes of Fig. 4. an the propose mechanism Ratio of throughput for various buffer sizes We efine the sening rate of connection i as x i = w i /τ i, an assume τ i is constant. Then we can erive the ynamics of x i as follows: t x i = ɛγx i p p γ 1 γx i p x k 18 k We here introuce the following function U i x: U i x = p 1 γ 1 γx x Then we can obtain the following eqation from Equation 18: t x i = ɛγx i p U ix i C x k k From this equation, we can regar the propose mechanism as the source with the utility function U i x an link cost function Cx uner the prevailing assumptions. We first note that U i x is inepenent of the RTT τ i, which means that there is no RTT bias in the propose mechanism. We confirm this characteristics in Section IV. The next remark is that U i x epens on the parameters physical capacity of the link, p parameter pof link cost, an γ. For, since we assume that each TCP connection obtains the value of physical capacity by using ImTCP, we can say that the propose mechanism provies fair performance when the same value of is obtaine by competing connections. The effect of ifferent values of is iscusse in Subsection IV- E. For γ, which is the control parameter of the propose mechanism, we show the setting guieline of γ in the next Subsection, an show that the value of γ woul affect on the buffering behavior of the bottleneck link, not on the behavior of each connections. This means that the source of the propose mechanism shoul use the ientical value for γ, which oes not affect on the fairness property. For p, on the other han, it means that we have a problem in the propose mechanism that its behavior epens on the AQM parameter. Moifying the algorithm to remove this epenency is one of the future research topic of this work. We also note that since U i x = p1 γ/γ an γ<1, the utility function U i x is strictly concave. This guarantees that the social welfare problem as follows has a unique solution: SY STEM maximize i U ix i C k x k over x i, for all i This characteristics clearly shows the stability of the propose congestion control mechanism. C. Parameter Settings The congestion control algorithm of the propose mechanism has two parameters, γ an ɛ. In this subsection, we iscuss the effect of these parameters an present some guielines for configuring γ an ɛ. 1 γ Setting The parameter γ inicates the egree of the influence of the other competing connections that share the same bottleneck link. To converge winow size to a positive value espite the physical banwith i of each connection, it is necessary to satisfy the conition <γ<1. Furthermore, base on Equations 11 an 1, we nee to consier the trae-off between convergence spee an the final number of packets accumulate within the buffer at the bottleneck link. That is, although smaller γ leas to faster convergence spee, it increases the queue size of the bottleneck router buffer when the winow size is converge. Using Equation 11 we can easily obtain the sum of the winow size of n TCP connections as follows: n n w i = τ 19 1+n 1γ i=1 where we assume that the physical banwith an the elay τ of each connection are ientical. From Equation 19 queue size Q at the bottleneck link is given by: n 11 γ Q = τ 1+n 1γ This equation shows that Q increases as n becomes larger. However, as n goes to infinity, we can obtain the following equation: lim Q = 1 γ τ 1 n γ That is, there exists an upper boun of the queue size with respect to an increase in the number of concurrent TCP connections. Therefore, if the bottleneck link has a large enough buffer, the propose mechanism will inuce no packet losses regarless of the number of TCP connections. TCP Reno, H, an, on the other han, increase their winow size until they fully utilize the buffer at the bottleneck link, an as a result, they cannot avoi perioic packet losses. ɛ Setting ɛ etermines convergence spee, as shown in Equation 9. Generally, when we convert Equation 1 into a iscrete equation, the population of the species oes not converge with ɛ [17]. In contrast, the winow size upating

algorithm propose in Subsection II-B converts Equation 1 into a iscrete equation in such a way that it oes not cause oscillation. Therefore, in the propose algorithm, there is no limitation on ɛ, which means that as ɛ becomes larger, the winow size converges faster. However, an excessively large value of ɛ causes the TCP sener to transmit numerous packets in bursty fashion, which may reuce the network performance. D. Competition with In this subsection, we investigate the fairness property of the propose mechanism with respect to competing connections. For this purpose, we compare the throughput of two TCP connections which an the propose mechanism share a bottleneck link, by analyzing changes in congestion winow sizes. Figure epicts the network moel for analysis, where is the physical banwith, τ is the minimum roun-trip propagation elay, not incluing the queuing elay, an B is the size of the output buffer aopting a TailDrop scheme, of the bottleneck link. As explaine above, the propose mechanism converges its winow size to a certain value whereas continues to increase its winow size until a packet loss occurs. Hence, even when both TCP connections compete at the bottleneck link banwith, perioic packet loss occurs at the buffer. We, therefore, assume that both TCP connections experience packet loss when the buffer becomes fully utilize. Therefore, the winow size of the two TCP connections changes cyclically, triggere by packet loss. Figure 3 escribes such changes in the winow size. Here, we efine one cycle as the perio between two packet losses an enote the length of the cycle as T. We assume that the receive socket buffer of each TCP connection is large enough not to limit the congestion winow size evolution. In this analysis, we assume that the sener of the propose mechanism can obtain precise physical banwith information. From Figure 3, by using ρ <ρ<1, the winow size of the propose mechanism just before packet loss occurs is represente as ρτ. Since the sum of the winow size of both connections is τ + B when the buffer becomes full, the winow size of connection at that time can be escribe as 1 ρτ + B. Then, the winow size of the propose mechanism immeiately after packet loss occurs becomes ecrease to ρτ/, an that of becomes 1 ρτ + B/. Since increases its winow size by one packet every RTT, T, which is the uration time of one cycle, can be calculate as follows: 1 ρτ + B T = τ where τ is the average value of the RTTs of the TCP connection. the winow size of the propose mechanism can be obtaine from Equation 1 by substituting for A as follows: we ɛt τ wt = we ɛt 3 1 + τ From Equations 1 an 3, we can calculate T, which is equal to the time require for the winow size to increase from ρτ/ to ρτ, as follows: T = 1 ρ ɛ ln 1 ρ τ ρτ/ ρτ/ = 1 ρ ɛ ln 4 1 ρ From Equations an 4, we obtain the following equation: 1 ρτ + B τ = 1 ρ ɛ ln 5 1 ρ Note that the ratio of the throughput of the connection to that of the propose mechanism is equal to the ratio of areas enclose by the the x axis an each line, inicating changes in the winow size, as epicte in Figure 3. The area for, S reno, is given by: S reno = 3 4 {1 ρ τ + B} τ On the other han, the area for the propose mechanism, enote as S propose, is calculate as follows: T S propose = wtt = τ ɛ ln ρ 1 ρ Finally, the average ratio of the throughput of to that of the proposal mechanism is given by: λ = S 3 reno 4 {1 ρ τ + B} = 6 S propose τ ɛ ρ ln1 ρ Note that ρ is given by solving Equation 5. From Equations 5 an 6, we can unerstan the relationship between the variables ɛ, an B an the ratio of throughput λ. Next, we show some numerical examples of the throughput ratio. Here we ignore the queuing elay an assume τ = τ. Figure 4 shows changes in the throughput ratio with respect to ɛ, where we set = 1 [Mbps] an τ = 5 [msec]. The five lines represent the results when the buffer size B is 1/4, 1/, 1,, an 4 times the banwithelay prouct BDP of the bottleneck link, respectively. In Figure 5, we show the results when we set τ = 5 [msec] an B to 41 [packets] equal to BDP when = 1 [Mbps], where the five lines escribe the results when = 1, 5, 1, 5, an 1 [Mbps]. These results show that ɛ, which realizes fairness between an the propose mechanism, rastically changes when we moify an/or B. Furthermore, in some situations, especially when the buffer size is large compare with the banwith-elay prouct, fairness cannot be realize by configuring ɛ. One reason is that the propose mechanism converges its winow size to τ, whereas continues increasing its winow size until the buffer has been fully use. The primary reason of this unfairness is the characteristics of ImTCP [15, 16] which we eploye in the propose mechanism for banwith measurement: ImTCP estimates an available banwith of the en-to-en network path, not a fair shair of the bottleneck link banwith. In other wors, if there exists an inline measurement algorithm which can estimate a fair banwith share of the network, we can employ it to our propose congestion control mechanism. From another point of view, the congestion control algorithm of the propose mechanism is essentially more conservative than. In contrast, has an aggressive winow size control algorithm. Therefore, the unfairness between the propose mechanism an cannot be avoie when they co-exist in the network. A similar iscussion can also be foun in the literature regaring TCP Vegas [, 3], an we believe this is the primary reason that TCP Vegas was not successfully eploye in the Internet. In the case of an its variants using AIMD/MIMD

Fig. 5. Throughput Ratio 6 5 4 3 1 1 3 4 5 6 7 8 = 1 Mbps = 5 Mbps = 1 Mbps = 5 Mbps = 1 Mbps Ratio=1 Ratio of throughput for various physical banwiths policies, the winow size just after packet loss occurs epens on the bottleneck link buffer size. That is, the throughput of these connections is improve as the buffer size increases. However, as buffer size becomes larger, the packets within the buffer also become larger, which means that the queuing elay is also increase. IV. Simulation Results In this section, we present simulation results by which to evaluate the performance of the congestion control mechanism propose in Section II. A. Simulation Settings We use ns- [4] for the simulation experiments. Traitional, HighSpee TCP H, Scalable TCP, an are chosen for performance comparison. We set ɛ = 1.95 an γ =.9 for the propose mechanism accoring to the iscussion in Subsections II-A an III-C. Note that we have confirme that changes in these parameters have a limite effect on the performance of the propose mechanism, especially on the transient behavior, an that the characteristics of the propose mechanism shown below oes not change. The parameters in H an are set to the value escribe in [4] an [5], respectively, an SAC option [5] is set to be enable for both protocols. has the parameter α, which shoul be change accoring to the link banwith. Accoring to the guielines in [6] we set α = 1,, 5, 1,, 5, an 1 for link banwiths = 1,, 5, 1,, 5, an 1 [Mbps], respectively. The network moel use in the simulation is epicte in Figure 6. The moel consists of sener/receiver hosts, two routers, an links between the hosts an routers. N tcp TCP connections are establishe between TCP sener i an TCP receiver i. To create backgroun traffic, we injecte UDP packets at a rate of r up into the network, where the packet size istribution follows the traffic observation results in the Internet [7]. That is, N tcp TCP connections an an UDP flow share a bottleneck link between the two routers. The banwith of the bottleneck link is enote as BW, an the propagation elay is τ. The banwith an the propagation elay of the access link for TCP sener i are bw i an τ i, respectively. We eploye the TailDrop scheme at the router buffer, an the buffer size is set to be equivalent to the banwith-elay prouct between sener an receiver hosts. B. Basic Behavior First, we confirm the funamental behavior of the propose mechanism with one TCP connection. Figure 7 shows the changes in winow size of, H,, FAST TCP, an the propose mechanism, where we set N tcp =1, BW = 1 [Mbps], τ = 5 [msec], bw 1 = [Mbps], an τ 1 = 5 [msec]. In this case, we o not inject UDP traffic into the network. The result shows that, H, an connections experience perioic packet loss ue to buffer overflow, because these connections continue increasing the winow size until packet loss occurs. On the other han, since the winow sizes of an the propose mechanism converge quickly to an ieal value, no packet loss occurs. The spee of winow size increase is much higher for an the propose mechanism than for H an, meaning that an the propose mechanism can more effectively utilize the link banwith. Furthermore, Figure 8 escribes the results for the case in which BW = 1 [Gbps] an bw 1 = [Gbps]. Base on these results, we observe that an H increase their winow size slowly. However, the spee of the winow size increase of the other mechanisms remains fast regarless of the link banwith. Note also that H an, which rapily increase their winow size, cause more packet losses than. In the case of Figure 7, the SAC mechanism works well, an the sener host avois timeouts. However, as shown in Figure 8, many retransmission timeouts occur because the SAC mechanism cannot recover all of the lost packets as the link capacity becomes large. C. Scalability to Network Banwith an Delay We next investigate the scalability to the link banwith of the propose mechanism by checking the convergence time, efine as the time require for the TCP connection to utilize 99% of the link banwith. We set N tcp =1,τ 1 = 5 [msec], τ = 5 [msec], an τ u = 5 [msec]. Figure 9 shows changes in the convergence time when we change BW from 1 [Mbps] to 1 [Gbps], where r up is set to. BW [Mbps] an bw 1 is set to be equal to BW. In the figure, the average values an the 95% confience intervals for 1 simulation experiments are shown. From this figure, we can see that the connection requires a great eal of time to fully utilize the link banwith since the increasing spee of the winow size is fixe at a small value, regarless of the link banwith. H ramatically reuces the convergence time, but the larger the link banwith becomes, the greater the convergence time that is require in orer to fill the bottleneck link banwith. This means that H is funamentally unable to resolve the scalability problem of. In the case of an, the convergence time remains constant regarless of the link banwith, which is also confirme in [5] an [6]. The propose mechanism retains an approximately constant convergence time regarless of the link banwith, which shows goo scalability to network banwith. We also note that the convergence time of the propose mechanism is a slightly worse than that of, especially in Figure 9. This is because of the choice of the control parameters in both mechanisms. In other wors, with a ifferent set of the control parameters for an the propose mechanism, the opposite results may be obtaine. In aition, since the congestion control mechanism of FAST TCP is base on that of TCP Vegas, it is consiere that has the same ifficluty in parameter setting as TCP Vegas escribe in [8]. Anyway, the most important

N TCP BW [Mbps] τu [msec] bw i [Mbps] τi [msec] UDP Traffic r UDP [Mbps] BW [Mbps] τ[msec] TCP Connections BW [Mbps] τu [msec] bw i [Mbps] 5 [msec] Winow Size [packets] 18 16 H 14 Propose 1 1 8 6 4 4 6 8 1 Winow Size [packets] 18 16 14 1 1 8 6 4 4 6 8 1 H Propose Fig. 6. Network topology in simulation experiments Fig. 7. Changes in winow size BW=1 [Mbps] Fig. 8. Change in winow size BW=1 [Gbps] characteristics observe in Figures 9 an 1 is scalability to the banwith-elay prouct of the network, which means that the convergence time changes as the banwith an/or elay become large. Moreover, we investigate the scalability to the propagation elay of the propose mechanism. We set N tcp = 1, BW = 1 [Mbps], bw 1 = [Mbps], τ 1 = 5 [msec], an r up = [Mbps]. Figure 1 shows the changes in the convergence time when we change τ from 1 [msec] to 5 [msec]. This figure shows that the connection requires quite a long time to fully utilize the link banwith because it only increases its winow size by one packet per RTT. The convergence time of H an is less than that of. However, the greater the increase in propagation elay, the larger the convergence time becomes. has goo scalability to link banwith as escribe in Figure 9, but the convergence time increases when the elay becomes larger because H,, an increase their winow size when receiving AC packets, which epens on RTT. The propose mechanism maintains the best scalability to the network elay, because, as shown in Subsection III-A, the convergence time increases logarithmically with increases in the elay or banwith. D. Aaptability an Fairness We also investigate the aaptability an fairness of the propose mechanism by checking the effect of changes in the number of TCP connections. We set N tcp = 5, BW = 1 [Mbps], τ = 5 [msec], bw i = 1 [Mbps] 1 i 5, an τ i = 5 [msec]. We o not inject UDP traffic into the network. TCP connections 1 5 join the network at, 1, 3, 5, an 7 [sec] an stop sening ata packets at 9, 95, 1, 15, an 11 [sec], respectively. Figure 11 shows changes in winow size for the five TCP connections with respect to the time for H,,, an the propose mechanism. Figure 11a shows that H control their winow size with the AIMD policy an realize fairness among connections by inucing perioic packet losses. From Figure 11b, we can see that cannot realize fairness among connections because its winow size control algorithm is base on the MIMD policy. In Figure 11c, we can see that the nature of is as follows. Since utilizes queuing elay as a congestion signal, it can ajust its winow size without inucing any packet loss when a new TCP connection joins the network. However, cannot achieve fairness among existing connections an a new connection. Fig. 9. Fig. 1. Convergence 1 1 1 H Propose 1 1 5 1 5 1 Bottleneck Link Banwith [Mbps] Convergence time with respect to bottleneck link banwiths Convergence 1 1 1 1 H Propose.1 1 5 1 5 Share Link Delay [msec] Convergence time with respect to bottleneck link elays Although nees RTT information to control the winow size, the new connection cannot successfully measure the minimum RTT ue to the queuing elay cause by the existing connection. When a connection stops a transmission an exits from the network, the remaining connections enjoy equal throughput because the buffer becomes temporarily empty, an the existing connections can measure the precise values for minimum RTT. On the other han, Figure 11 shows that the propose mechanism converges the winow sizes very quickly, so that no packet loss occurs when a new connection joins the network. Furthermore, when the TCP connection leaves the network, the propose mechanism connections quickly fill the unuse banwith. Borrowing the terminology of biophysics, we say that TCP connections are competitive, but still symbiotic even against the environmental changes. Aaptability to changes in the available banwith is also an important characteristic of the transport layer protocol. To confirm that performance of the propose mechanism, we set N tcp = 1, BW = 1 [Mbps], τ = 5 [msec],

Winow Size [packets] 16 14 1 1 8 6 4 1st flow n flow 3r flow 4th flow 5th flow Winow Size [packets] 16 14 1 1 8 6 4 1st flow n flow 3r flow 4th flow 5th flow Winow Size [packets] 16 14 1 1 8 6 4 1st flow n flow 3r flow 4th flow 5th flow Winow Size [packets] 16 14 1 1 8 6 4 1st flow n flow 3r flow 4th flow 5th flow 4 6 8 1 a H 4 6 8 1 4 6 8 1 b c Fig. 11. Effect of changes in number of connections 4 6 8 1 Propose Mechanism Fig. 1. Throughput [Mbps] 1 1 8 6 4 H Propose 5 1 15 Aaptability to change in available banwith throughput bw 1 = 1 [Mbps], τ 1 = 5 [msec], an change r up so that the available banwith of the bottleneck link is 8 [Mbps] at 5 [sec], 65 [Mbps] at 5 1 [sec], 5 [Mbps] at 1 15 [sec], an 8 [Mbps] at 15 [sec]. Figures 1 an 13 present the changes in the throughput of a TCP connection an the queue size of the bottleneck link buffer for, H,, an the propose mechanism. The results obviously show the effectiveness of the propose mechanism, which gives goo aaptability to the changes in the available banwith. Furthermore, no packet loss occurs even when the available banwith suenly ecreases. On the other han, connections experience packet losses uring simulation time, an link utilization is much lower than 1%. Although H an can retain their link utilization because of a sufficient buffer, they have largely fluctuating RTTs cause by queuing elays. an the propose mechanism experience no packet loss an retain their link utilization with small RTTs, but the propose mechanism has a smaller queue size than. This is one of the avantages of the propose mechanism, which uses an inline measurement technique, which means that the propose mechanism is quite robust against environmental changes of the network. E. Effect of Heterogeneity in Physical Banwith In the above subsections we emonstrate the effectiveness of the propose mechanism with respect to various aspects. However, in a sense, these results are expecte as a result of the newly evelope congestion control mechanism base on the banwith measurement technique. A more striking feature of the propose mechanism is etaile in the following results. Here, we investigate the effects of the heterogeneity of access networks such as the ifferences in access link banwith. We set N tcp =,τ = 4 [msec], bw 1 = 1 [Mbps], bw = [Mbps], τ 1 = τ = 5 [msec], an we change BW from 5 [Mbps] to 3 [Mbps]. UDP traffic is not injecte into the network. Figure 14 shows the changes in the throughput of the two TCP connections in an the propose mechanism with respect to BW. The figure shows that TCP Reno shares the bottleneck link banwith fairly, regarless of the value of BW. On the other han, the propose mechanism shows an interesting characteristic. When BW < bw 1, the two TCP connections share bottleneck link banwith fairly. However, when bw 1 < BW < bw, the bottleneck link banwith is istribute proportionally to the ratio of bw 1 an bw. This property can be explaine using the equation of the propose mechanism. Using Equation 8, the converge transmission rate for connection i, enote by ˆN i, which has a ifferent physical link banwith i, can be calculate as follows: ˆN i = i n i=1 BW 7 i This equality is satisfie when γ<1. This equation means that the bottleneck link banwith is share proportionally to the physical banwith of each TCP connection. Since the physical banwith of the network path is efine as the banwith of the tightest link between TCP hosts a sener an a receiver, the simulation results shown in Figure 14 agree with Equation 7. We argue that this characteristic is ieal for an Internet congestion control strategy. Throughout the history of the Internet, the ratio of the banwith of access networks to backbone networks has been changing over time [9]. Compare with access networks, the resources of backbone networks are sometimes scarce an sometimes plentiful. We believe that when backbone resources are few, they shoul be share fairly between users, regarless of their access link banwith. On the other han, when backbone resources are sufficient, they shoul be share accoring to the access link banwith. The characteristics of the propose mechanism, shown in Figure 14 an Equation 7, realize such a resource sharing strategy. V. Conclusion In this paper, we propose a new congestion control mechanism for TCP base on inline network measurement. The propose mechanism obtains information about the physical an available banwiths from inline network measurement via ImTCP. Using banwith information, the propose mechanism ajusts its winow size with an algorithm base on mathematical moels borrowe from biophysics. Consequently, the propose mechanism can converge its winow size to an ieal value an avoi the perioic packet loss experience by. Through mathematical analysis, we confirm that the propose mechanism has goo scalability to not only link ban-

Queue Size [packets] 1 8 6 4 H Propose Convergence 3 5 15 1 5 1 Mbps access link Mbps access link Convergence 3 5 15 1 5 1 Mbps access link Mbps access link 5 1 15 Fig. 13. Aaptability to change in available banwith queue size 5 1 15 5 3 5 1 15 5 3 Share Link Delay [msec] Share Link Delay [msec] a b Propose Mechanism Fig. 14. Effect of ifferent access link banwiths with but also propagation elay between the sener an receiver hosts. Other transport layer protocols such as, HighSpee TCP, Scalable TCP, an cannot provie such scalability. Furthermore, base on the results of mathematical analysis regaring competition between an the propose mechanism, although the realization of fairness between them was observe to be ifficult, we believe that the propose mechanism is a possible solution for transport layer protocols for future high-spee networks. Furthermore, through extensive simulations, we have confirme that the propose mechanism oes exhibit the analytically etermine characteristics. Therefore, the propose mechanism is effective regarless of network banwith or elay an can solve many of the problems associate with an its variants. For future work, we will confirm aitional characteristics of the propose mechanism, which inclue fairness among connections with ifferent RTTs an the effect of measurement errors on the physical an available banwiths. We are now implementing the propose mechanism on the FreeBSD system. Experiments on the actual network are also important research tasks. References [1] S. Shenker, L. Zhang, an D. D. Clark, Some observations on the ynamics of a congestion control algorithm, ACM Computer Communication Review, vol., no. 5, pp. 3 39, Oct. 199. [] L. Guo an I. Matta, The war between mice an elephants, Technical Report BU-CS-1-5, May 1. [3] Z. Fu, P. Zerfos, H. Luo, S. Lu, L. Zhang, an M. Gerla, The impact of multihop wireless channel on TCP throughput an loss, in Proceeings of IEEE INFOCOM 3, Apr. 3. [4] S. 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