A Stable Traffic Engineering Technique for Performance Enhancement of the Non-TCP Elastic Flows *

Transcription

1 JOURNAL OF INFORMATION SCIENCE AND ENGINEERING 30, (2014) A Stable Taffic Engineeing Technique fo Pefomance Enhancement of the Non-TCP Elastic Flows * Ian Telecom Reseach Cente (ITRC) Tehan, Ian pgoudazi@itc.ac.i Due to the polifeation of the divesity in use behavios and taffic demands, taffic engineeing mechanisms have become an inevitable task in data netwoks. Nowadays, most commonly used algoithm in end hosts is the popula TCP and its vaiants (such as MulTCP). These ae loss based schemes theefoe exhibit oscillatoy behavio which educes netwok pefomance. Moeove, since the pice fo all sessions is nomally based on the aggegate thoughput, losses that ae caused by TCP may affect othe sessions as well and aggessively educe thei thoughput and also have a dastic effect on the oveall thoughput/goodput of the netwok. In this pape a novel taffic engineeing mechanism in the fom of the selective picing is poposed in which diffeent pices ae imposed on the netwok esouces fo diffeent uses. The poposed mechanism not only educes the packet loss atio, but also inceases the goodput pefomance of the non-tcp elastic sessions such as Popotional o Minimum Potential Delay schemes. Stability popety of the algoithms ae investigated and some numeical analysis is pesented to validate the esults. Keywods: ate allocation, WRR, MulTCP, diffeentiated picing, active queue management 1. INTRODUCTION Rate contol is one of the impotant tasks of end hosts in avoiding congestion in data netwoks. The most pevalent algoithm implemented in opeating systems nowadays is vaiations of TCP. Impovement to this algoithm has long been of majo consideation by eseach goups and as a esult new impoved substitutions ae poposed, as we will discuss in the pape. But the compatibility of new algoithms with the conventional ones should be studied. It is shown that in the conventional envionments of usual Active Queue Management (AQM) used in intemediate nodes, the competition between the TCP and othe ate allocation methods would decease the oveall pefomance. Othe vaiants of TCP algoithm ae XCP [1], Fast TCP [2] and MulTCP [3]. Two diffeent methods exist fo accomplishing congestion contol in the data netwoks. One is window-based method in which the numbe of outstanding packets in the netwok is egulated by adjusting the size of a congestion window to a efeence value [4, 5]. In the ate-based method, we look at the netwok taffics as fluid flows and algoithms such as the Kelly s method ae used in ode to achieve some fainess citeia in ate allocation [6]. Thee ae diffeent fainess citeia such as max-min, popotional and minimum Received Apil 22, 2012; evised July 20 & August 18, 2012; accepted August 29, Communicated by Xiaohong Jiang. * This wok was suppoted by ITRC. 1115

2 1116 potential delay fainess [7]. Selecting a fainess citeion depends on the netwok s designe stategy. Fo example in the max-min citeion, the focus is on the uses with lowest ates wheeas in popotional citeion the objective is to maximize the sum of the logaithms of the use ates and penalize moe the uses who use long outes in the netwok. In minimum potential delay citeion, L. Massoulié et al. define a delay measue in tems of the use ates and ty to minimize that [7]. In this pape we assume that the netwok taffic can adapt itself to the netwok conditions. In othe wods, we use the tem elastic fo the taffic as it was intoduced by S. Shenke in [8] and used in the Kelly s pape [6]. Examples of such taffic type ae TCP taffic in the cuent Intenet and ABR taffic in the ATM netwoks. As it is known, lage netwoks such as the Intenet have been designed to be decentalized and depend on the well-defined behavio fom end-hosts. The inceasing complexity and size of these netwoks make centalized ate allocation impactical. Without a centalized contol, the netwok uses have a geat deal of feedom in shaing the available bandwih in the netwok. To achieve the flow contol, congestion avoidance and bandwih allocation, the eseaches have poposed diffeent ate allocation algoithms to be implemented at the end-hosts in a decentalized manne [9-12]. The most widely used flow contol/congestion avoidance mechanism in the cuent Intenet is TCP, which is a window-based mechanism. TCP, howeve, does not necessaily lead to a fai o efficient ate allocation of the available bandwih [4]. Kelly et al. have poposed an algoithm that esults in popotional fainess citeion and they used a Lyapunov function appoach fo stability analysis of thei ate allocation method [6]. Mo and Waland [4] have poposed and studied anothe fai window-based end-toend congestion contol mechanism, which is simila to TCP Vegas [13] but has a moe sophisticated window-updating ule. They have shown that the popotional fainess can be achieved by thei (, 1)-popotionally fai algoithm and max-min fainess can be achieved as a limit of (, )-popotionally fai 1 algoithm as goes to infinity. In [14], Shakkottai et al. examined how tansit and custome pices ae set in a netwok consisting of multiple Intenet Sevice Povides (ISPs). They show that some ISPs may be geogaphically co-located so that they compete fo the same set of end uses. The authos examined the existence of equilibium pice stategies in this situation and showed how positive pofit can be achieved using theat stategies. In [15], Hande et al. intoduce a famewok to quantify the pecise tade-off in the distibution of benefits among ISPs, content-povides, and end-uses. Thei poposed famewok genealizes the well-known utility maximization based ate allocation model, which has been extensively studied as an inteplay between the ISP and the end-uses, to incopoate picing of content-povides. They deived the esulting equilibium pices and data ates in diffeent ISP maket conditions. In [16] Hande et al. popose a distibuted ate allocation stategy which can be used fo inelastic (eal-time) flows. They conside non-concave utility functions, which tun utility maximization into difficult, nonconvex optimization poblems. Finally they pesent conditions unde which the standad pice-based distibuted algoithm can still convege to the globally optimal ate allocation despite nonconcavity of utility functions. 1 Heeafte, we assume that all (, )-popotionally fai flows ae descibed as non-tcp ones.

3 A STABLE TRAFFIC ENGINEERING TECHNIQUE IN NETWORKS 1117 Bui et al. [17] extend ecent esults on fai and stable esouce allocation in wieless netwoks to include multicast sessions, in paticula multi-ate multicast. Thei solution fo multi-ate multicast is based on scheduling vitual (shadow) taffic that moves in evese diection fom destinations to souces. The mentioned shadow scheduling algoithm can also be used to contol delays in wieless netwoks. Xue et al. [18] popose a new pice-based esouce allocation famewok in wieless ad hoc netwoks to achieve optimal esouce utilization and fainess among competing end-to-end flows. It is clea that fainess is a desiable featue of a ate allocation algoithm. Uses pefeences can be captued by appopiate utility functions. Due to the vaious equiements of diffeent applications, it is likely that the uses will have diffeent utility functions [8]. Fo example, suppose that a use is tansfeing a file. The pe-tansfe delay is invesely popotional to the ate it eceives. Hence, the delay might be modeled as the utility function of the use which is a function of its ate. This eveals this fact that although fainess is a desiable popety, fainess by itself may not be sufficient. A good ate allocation mechanism should not only be fai, but also should allocate the available bandwih in such a way that the oveall utility of the end-uses is maximized [19]. In the cuent wok, using a new diffeentiated picing scheme as an AQM algoithm fo intemediate nodes the oveall pefomance of non-tcp uses would be impoved. This impovement is in tems of the educed packet loss atio and incease goodput fo elastic sessions 2. By definition, goodput of a session is the effective pat of the thoughput o goss tansmitted packet ate of the session. Fo example, in the case of packet loss in TCP, some pats of the peviously tansmitted packets ae etansmitted and ae eceived by the eceive moe than once and so, ae edundant. The pesented wok is simila to [14, 15] in the fact that, it is shown that the mentioned picing stategy is stable and the netwok will each eventually to equilibium pices. The main contibution of the cuent wok and its diffeence with simila appoaches such as [14, 15] etc. is the fact that in the cuent wok, the picing is done pe-session (in contast to the aggegate picing in [14, 15] and simila woks) and the netwok opeato (ISP) can povide enhanced sevice levels fo an specific use based on an inceased pice level which is imposed on that use. The est of the pape is oganized as follows. In the Section 2, a mathematical fomulation the discete time vesions of MulTCP and (, )-fai models has been pesented. Then in section 3, the diffeentiated picing famewok would be intoduced and its stability popety would be investigated. Section 4 is devoted to the pefomance analysis of the poposed taffic engineeing technique and the pefomance of the poposed method has been investigated fo two diffeent taffic models. Finally, in the last Section, some concluding emaks have pesented and some eseach highlights fo the futue woks have descibed. 2. BACKGROUND In the following pats, two popula (, )-fai (non-tcp) and MulTCP models have been intoduced. 2 The cuent wok is an extended vesion of ou ealie pape A diffeentiated picing famewok fo impoving the pefomance of the elastic taffics in data ntwoks published in Intenational Jounal of Compute Engineeing and Technology, Vol. 1, Jan

4 (, )-Fai Model Conside a netwok with a set J of esouces o links and a set of uses and let C j denotes the finite capacity of link jj. Each use has a fixed oute R, which is a nonempty subset of J. When the allocated ate to the use is x, use eceives utility U (x ). The utility U (x ) is an inceasing, stictly concave and continuously diffeentiable function of x ove the ange x 0. Futhemoe, assume that the utilities ae additive so that the aggegate utility of ate allocation X = (x, ) is: U (x ). This is a easonable assumption since these utilities ae those of independent netwok uses. Finally, let the utility and capacity vectos to be U = (U (.), ) and C = (C j, jj) espectively. The Kelly s discete time algoithm fo eaching to the optimal solution of popotional-fai is as follows [6], x [ n 1] x k ω x μ j. (1) jr Whee {x} + max(0, x) and j [n] = p j ( x s). (2) s :jr s Paamete k contols the speed of convegence in Eq. (1). p j (y) is the amount that link j penalizes its aggegate taffic y, pice pe unit ate j [20], and is a non-negative, continuous inceasing function (see Fig. 1). Fig. 1. A sample penalty function. One of the intepetations is that using Eq. (1), the system ties to equalize with x [n]. μ j by adjusting x [n] [21]. jr In [6] it is shown that the unique, optimal and popotionally-fai equilibium point of Eqs. (1)-(2) is: ω x p ( x ),. (3) j s jr s:jrs It is necessay to mention that as Kelly et al. have discussed in [6], we may use the following fom of the link penalty function

5 A STABLE TRAFFIC ENGINEERING TECHNIQUE IN NETWORKS 1119 p j (y) = (y c j + ) + / 2, 0, jj. (4) Whee, c j is the capacity of jth link and > 0 is a small positive constant. Finally, we conside the moe geneal (, )-fai ate allocation algoithm (the Kelly s algoithm o popotional fainess is the special case with = 1 and the minimum potential delay fai algoithms is anothe special case with = 2). The discete time vesion of this algoithm would be [8] Whee x [ n1] { x[] n k ( ω ( x[]) n λ [])}. n (5) λ p j xs[ n] (6) jr sj is the aggegate pice. 2.2 MulTCP Model Anothe algoithm which we use in ou simulation is the geneal MulTCP model (which usual TCP is the special case with m = 1). The fluid flow model fo MulTCP is [7] d 2 m m x x ( t) ( t) 2 2 T T 2m. (7) Whee the is the aggegate pice, T is the ound tip time (RTT) of the flow and m is a natual numbe. The discete time vesion of Eq. (7) which will be used in pactical implementations would be 2 m m x x [ n 1] x 2 2 T T 2m. (8) In othe wods, as poposed by Cowcoft et al. in [3], MulTCP aims at popotional multiple flowshaes along a congested link by assigning a weight m to the aggegate. AIMD 3 (m; 1/(2m)) is used in MulTCP, instead of AIMD(1; 1/2) in the standad TCP, fo emulating the behavio of m concuent TCP connections using the same congestion window loop. The ationales behind AIMD(m; 1/(2m)) ae [22] Incease paamete a = m. The congestion window size of a single TCP flow is inceased by one packet pe RTT in the standad TCP. Accodingly, the congestion window size of m vitual TCP flows is inceased by m packets pe RTT in MulTCP. Decease paamete b = 1/(2m). If one packet is lost, only one of the m TCP flows halves its congestion window size W. Accodingly, the congestion window size becomes (m 1)W + W/2 = (1 1/(2m))mW in MulTCP. 3 Additive Incease Multiplicative Decease [4].

6 DIFFERENTIATED PRICING FRAMEWORK In the following subsections, we have intoduced the diffeentiated picing mechanism and in the sequel, stability analysis has been accomplished to pove the stability popeties of the distibuted algoithms. 3.1 Diffeentiated Picing In flat picing scheme, a fom of penalty function such as that used in Eq. (4) can be used but in diffeentiated picing, a fom of tangential biased picing function such as the following equation will be used [23] p j (y) = j. tan (p.y/(2c j )), jj and. (9) The incued pice is completely link and flow dependent and the amount of link pice can be contolled by paamete j > 0. The geate paamete j will esult in moe penalized use taffic and moe stavation in the dedicated netwok esouces. It must be mentioned that the choice of the tangential biased picing mechanism in Eq. (9) is completely optional. As discussed in Section 2 and Fig. 1, the penalty function P(y) must have some fundamental popeties (nonnegative fom, continuity and monotonically inceasing popety with espect to its agument y ) and these popeties can be independent fom its mathematical fomulation [6]. Any mathematical fom may be selected fo epesenting the penalty function if and only if the selected fom satisfies the mentioned popeties. We have selected the biased tangential fom in Eq. (9) because of its ease of mathematical tactability. The impotant diffeence between the poposed picing method and taditional aggegate-ate picing pesented in Eq. (4) is the fact that, the picing mechanism in Eq. (9) is selective fo each use (woks in a pe-session basis) and can be intelligently contolled by the netwok povide based on a pe-established sevice level ageement (SLA) between the netwok opeato (ISP) and the individual uses. 3.2 Stability Analysis In eality, fo pactical implementation puposes, the window-based vesions of the ate allocation algoithms in Eqs. (10) and (11) must be used. If we assume that eceives congestion window sizes ae set to unity and sende congestion window size in (, )-fai and MulTCP models ae updated accoding to elations (9) and (12) espectively [24-27]. cwnd cwnd [ n 1] { cwnd k T ( ω d [ n])} T[ n] (10) Whee CWND 2 m m CWND [ n 1] CWND [ ] d n T T 2 mt (11)

7 A STABLE TRAFFIC ENGINEERING TECHNIQUE IN NETWORKS 1121 d T d (12) is an appoximation fo the aggegate pice [n] andd is the flow s popagation delay and its ound tip time is T. Also, cwnd and CWND ae the so-called congestion-window [26] of the sendes in the (, )-fai and MulTCP models espectively. In [24] and efeences theein, it is shown that by exploiting the following Lyapunov function, the stability popety of Eq. (11) can be deived. V ( x) 2m T actan x T 2m 0 jj x s: js s p ( y) dy The stability popeties of the window-based (, )-fai model in Eq. (10) can be poved afte defining some peliminay tems. Assume that fo simplicity we epesent the congestion window of flow in Eq. (10) by w. Also assume that we have the following two definitions X w 1 : ; s : X ( w X d ). T 1 2 Theoem: The function V( w): s is a Lyapunov function fo the Eq. (10). The 2 unique value w * minimizing V(.) is the stable point of the system to which all of the tajectoies convege. j Poof: The window-based Eq. (10) can be tansfomed to its continuous time equivalent as follows: dw w kt ( ω ( T d )) T. (13) Based on the pevious definitions, the Eq. (13) can be simplified as dw kt s. (14) By diffeentiating V(.) we have dv ( w) 2 ds 1 s. (15) Based on the definition of s and some mathematical computations, it can be easily shown that we have ds X dx dw 2 ( 1) w X d X. (16) Also, fom definitions of X and s we can wite

8 1122 dx k s. (17) Finally, based on the Eqs. (14)-(17) it can be shown that dv ( w) 2 ks X ( T d ). (18) T 2 As, k, X, T, and T d all ae non-negative tems, we have dv ( w) 0. (19) Consequently, V(w) is a Lyapunov function and vecto w * = (w * ), = 1,, M (M is the numbe (, )-fai flows) is a stable point of the system to which all of the tajectoies convege. Note: It must be mentioned that in the equilibium point of the system (10) we have * * w * * * * 1 * * 1 w * * d X T d X X d X T d * T T ( ) ( ) ( ) ( ) ( ). (20) Hence we can wite fom Eq. (20): * * w X d. (20) * 1 X Whee is the so-called total backlog [4]. * 1 ( X ) 4. PERFORMANCE ANALYSIS The numeical analysis section is composed of two pats. In pat one, a macoscopic fluid-flow model [6] has been adopted fo modeling the netwok taffic and in pat two, we have used moe pactical micoscopic window-based taffic model as those in [4, 9]. 4.1 Fluid-Flow Taffic Model Assume that a simple netwok topology with one bottleneck common link exists (Fig. 2) and its esouces ae shaed by N diffeent elastic (MulTCP and non-tcp) flows. Assume that N = 5 and the bottleneck link (with capacity of 20 Kbps) is shaed by a TCP (m = 1), two MulTCP with paametes m = 2 and m = 3, a popotionally fai scheme ( = 1) and a minimum potential delay fai ( = 2) flows. In the sequel, we descibe two diffeent picing scenaios which ae the taditional flat picing and the poposed diffeentiated picing ones and compae thei pefomances. In fist picing method, we just simulate these algoithms in a simple usual envi-

9 A STABLE TRAFFIC ENGINEERING TECHNIQUE IN NETWORKS 1123 Fig. 2. Netwok topology 1. onment without disciminating between these flows i.e. we have used the flat picing as in Eq. (4) with = The allocated ates to these sessions and the oveall thoughput ae deived based on discete-time Eqs. (5) and (8) and ae depicted in the Fig. 3 (a). In this figue, the aconyms (P) and (MPD) stand fo (Popotional) and (Minimum Potential Delay) fainess citeia, espectively. Also the unit fo bit-ate is selected to be Kbps. As it can be veified in this figue, thee exist 8 loss events (we calculate a loss events if the oveall thoughput exceeds the capacity). The oscillatoy behavio is inevitable since it is intinsic to TCP. But the oveall thoughput can be impoved as we will see in the next picing method. We have summaized the statistics elated to this scenaio in the Table 1. In the second picing method, using the poposed diffeentiated picing scheme, which uses a new tangential biased picing scheme (Eq. (9)) fo all sessions, the loss ate educed to zeo and we can obseve some impovement in the mean oveall utilization of the netwok (Fig. 3 (b) and Table 2). Table 1. Simulation esults in the flat picing. Mean Oveall thoughput Mean MulTCP(m=2) thoughput Loss numbes 8 Mean MulTCP(m=3) thoughput Mean TCP thoughput Mean MPD thoughput Mean MPD thoughput As it can be veified in the Fig. 3 (b), the mean allocated ates to P and MPD flows have been inceased but the allocated ates to non-tcp flows do not change significantly with espect to the pevious flat picing case (Fig. 3 (a)) and this fact leads to the impoved oveall netwok pefomance. In this case, we have paid moe attention to P and MPD flows in pice of moe penalizing othe MulTCP and TCP flows. In othe wods, we assign highe j values which ae equal to fo MulTCP and TCP flows and lowe j values which ae selected to be fo P and MPD flows. The simulation statistics about this case ae listed in the Table 2. The simulation esults in this table show that the mean thoughput of P and MPD methods ae impoved by a facto of 3 in this case.

10 1124 Table 2. Simulation esults in the diffeentiated picing. Mean Oveall thoughput Mean MulTCP(m=2) thoughput Loss numbes 0 Mean MulTCP(m=3) thoughput Mean TCP thoughput Mean MPD thoughput Mean MPD thoughput (a) (b) Fig. 3. Rates achieved by sessions in flat (a) and diffeentiated (b) picing. 4.2 Window-Based Taffic Model In this pat, a simila appoach such as that of Waland [4] and Başa [25] has been adopted fo simulating the ates allocated to the uses with specific popagation delays. We have used the OPNET discete-event simulato [28]. Window-based Eqs. (10) and (11) have been used fo esouce assignment to the (, )-fai and MulTCP flows espectively. We have used the moe geneal netwok topology in Fig. 4 with multiple bottleneck links (bottleneck links ae shown in ed in this figue). The links popagation delays ae set to 5 ms. We have assumed that souces have data fo sending at all times (geedy souces). The links buffe sizes ae set to 30 packets and so packet loss may occu in the netwok. We have used k = fo all in Eq. (10). We assume taffic consists of point to point tansfes of individual documents of finite size aiving accoding to a Poisson pocess [29]. We have used go back n method fo e-sending the packets that ae double acknowledged. Fo implementing the taffic engineeing o diffeentiated picing in this scenaio, links scheduling disciplines ae selected to be of Weighted Round Robin (WRR) type with geate weights fo flows with moe pioity (non-tcp flows in this wok). In anothe wok, the flows ae penalized moe by assigning less shae of bandwih o less weight in the implemented WRR sevice discipline. As in TCP, slow-stat method is used fo initializing the ate allocation fo implementing the Eq. (10) [26]. As Eqs. (10) and (11) use only the RTT and popagation delay of the connection, they can be implemented in an end-to-end manne even in the cuent Intenet. The topology of Fig. 4 is composed of 41 elastic uses and 116 links. It is as-

11 A STABLE TRAFFIC ENGINEERING TECHNIQUE IN NETWORKS 1125 sumed that each use s taffic composed of two non-tcp (P and MPD) flows and one TCP flow. The utility function paametes associated with the non-tcp flows ae listed in the Table 3. Bottleneck link capacities ae selected to be 150Kbps and othe link capacities ae selected to be 10Mbps. The WRR algoithm which is implemented in each node uses the weights listed in Table 4 fo each packet type. Table 3. Non-TCP flows utility function paametes. use use use use use use Table 4. Associated weights in each node fo each packet type. MulTCP Non-TCP Type M = 1 M = 2 M = 3 P MPD Weight Fig. 4. Netwok topology 2. In Figs. 5 (a) and (b), the aggegate ates of the P and MPD (non-tcp) flows tavesing the bottleneck links 86 and 93 ae compaed with the aggegate ate of TCP flows. As it can be veified, the allocated ates to non-tcp flows behave in moe stable manne with espect to the TCP one. Also, the allocated ates to non-tcp flows have TCPfiendly chaacteistics. In Figs. 6 (a) and (b), the aggegate ate of the bottleneck links 48 and 107 ae compaed between TCP method, window-based vesion of MulTCP with paametes m = 3, m = 4 and m = 5 in Eq. (11), a popotionally (P) fai scheme ( = 1) and a minimum potential delay (MPD) fai ( = 2) flows. As can be veified in this figue, MulTCPs

12 1126 (a) (b) Fig. 5. Flow pefomances in bottleneck links 86 (a) and 93 (b). (a) (b) Fig. 6. Flow pefomances in bottleneck links 48 (a) and 107 (b). have a compaable aveage ate in compaison with the TCP. It can be veified fom the Figs. 6 (a) and (b) that inceasing the m value inceases the oscillatoy behavio in the aggegate allocated ate. As descibed in Section 2.2, this may be due to the fact that by inceasing m, the pecent of ate eduction in confontation with a loss effect educes by the facto of m. In Fig. 7 (a), the packet loss ates of the P and MPD (non-tcp) flows and TCP flows (simple TCP and MulTCP with m = 10) ae depicted vesus the numbe of elastic uses. It can be veified in this figue that non-tcp flows benefit fom lowe mean packet loss levels with espect to TCP ones. Also it can be concluded that MulTCP has a lowe aveage loss ate in compaison with the TCP. The ationale behind this lowe loss ate is the design philosophy of the MulTCP which is diected to educe the loss phenomenon [22]. In Fig. 7 (b), the goodput (efficient thoughput) of the P and MPD (non-tcp) flows and TCP flows (simple TCP and MulTCP with m = 3) ae depicted vesus the numbe of elastic uses. It can be veified in this figue that non-tcp flows have appoximately

13 A STABLE TRAFFIC ENGINEERING TECHNIQUE IN NETWORKS 1127 (a) (b) Fig. 7. Packet loss (a) and Goodput (b) pefomance compaisons. highe mean ates than thei TCP countepats but behave in a TCP-fiendly manne. Again, it can be concluded that the mean goodput pefomance of the MulTCP is supeio to that of TCP and is compaable to nontcp P and MPD flows. 5. CONCLUSIONS Using a new taffic engineeing mechanism in the fom of diffeentiated picing scheme, we showed that the oveall thoughput of the netwok could be inceased without significant decease in TCP sessions thoughput. Also it is shown that by incopoating intelligent picing mechanisms, the packet loss pefomance of the netwok can also be impoved. The eason can be the fact that we achieved this goal by deceasing the unnecessay packet dops caused by TCP using the poposed diffeentiated picing scheme, theefoe avoiding unnecessay eductions and oscillations of othe sessions. The stability popeties of the algoithms ae investigated and thei pefomances ae compaed via simulation in two diffeent scenaios consideing two diffeent taffic models. Consideing this type of picing fo non-elastic o eal-time taffic fo impoving the pefomance of such taffic types and thei associated stability analysis can be consideed fo futue eseach. REFERENCES 1. D. Katabi, M. Handley, and C. Rohs, Intenet congestion contol fo high bandwih-delay poduct netwoks, in Poceedings of ACM SIGCOMM, 2002, pp C. Jin, D. X. Wei, and S. H. Low, FAST TCP: Motivation, algoithms, pefomance, in Poceedings of INFOCOM, 2004, pp J. Cowcoft and P. Oechslin, Diffeentiated end-to-end Intenet sevices using a weighted popotional fai shaing TCP, in Poceedings of ACM SIGCOMM Compute Communication Review Achive, Vol. 28, 1998, pp

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15 A STABLE TRAFFIC ENGINEERING TECHNIQUE IN NETWORKS D. Betsekas and J. Tsitsiklis, Paallel and Distibuted Computation, Englewood Cliffs, Pentice-Hall, NJ, F. P. Kelly, Mathematical modeling of the intenet, in Poceedings of the 4th Intenational Congess on Industial and Applied Mathematics, 1999, pp T. Alpcan and T. Başa, Utility-based congestion contol schemes fo intenet-style netwoks with delays, in Poceedings of IEEE INFOCOM, 2003, pp A. S. Tanenbaum, Compute Netwoks, 3d ed., Pentice Hall, NJ, S. Keshav, Engineeing Appoach to Compute Netwoking, 1st ed., Addison Wesley Pofessional, MA, OPNET discete-event simulato, L. Massouli and J. W. Robets, Bandwih shaing and admission contol fo elastic taffic, Telecommunication Systems, Vol. 15, 2000, pp Pejman Goudazi was bon in Shiaz-Ian in He eceived the B.S. degee in Electonics fom Shaif Univesity of Technology Tehan-Ian in He also eceived his M.Sc. and Ph.D. degees in Electical Engineeing both fom Isfahan Univesity of Technology, Isfahan-Ian in 1998 and 2004 espectively. D. Goudazi is an Assistant Pofesso and faculty membe in Reseach Institute fo ICT (ITRC) since His main eseach inteests ae wieless video communication, distibuted esouce allocation algoithms, soft computing, stability analysis and sevice quality assuance in data netwoks.