Extended Formulation of TCP Vegas Inspiredby a Controller Structure of Cell Cycle Pathway Networks
Jian-Qin Liu*, Kenji Leibnitz**, Masayuki Murata*** National Institute of Information and Communications Technology (NICT),Kobe Advanced ICT Research Center (KARC), Biological ICT Group,588-2, Iwaoka, Iwaoka-cho, Nishi-ku, Kobe, Hyogo, 651-2492 Japan** Osaka University, Graduate School of Information Science and Technology,
Department of Information Networking, Advanced Network Architecture Laboratory,
1-5 Yamadaoka, Suita, Osaka, 565-0871 Japan

細胞周期・パスウェイ・ネットワークの制御器によるTCP Vegas の拡張定式化
劉 健勤*

ライプニッツ 賢治**

村田 正幸**

独立行政法人 情報通信研究機構 神戸研究所
未来 ICT 研究センター バイオ ICT グループ
〒651-2492 兵庫県神戸市西区岩岡町岩岡 588-2***

大阪大学 大学院情報科学研究科 情報ネットワーク学専攻
先進ネットワークアーキテクチャ講座〒565-0871 大阪府吹田市山田丘 1-5

Abstract An extended form of the Transmission Control Protocol (TCP) inspired by signaltransduction networks of cell cycle is formulated where TCP Vegas is selected as a reference
for the TCP dynamics.
概要 本稿では、細胞周期のシグナル伝達ネットワークからのヒントによって、拡張された TCP Vegas を定式化される、ここで TCP Vegas は TCP ダイナミックスのための参照として選択される。
1. Introduction
The molecular signaling mechanism of cellcycles in yeast shows dynamic features on
cyclin signals, where the period of signalingis robust to variations of parameters of thecorresponding pathway networks [1,2]. The
cyclin and related molecules in the cell cycleof yeast are important for sustaining the cell
reproduction process. From modeling andsimulation of the signal transduction
network [3,4,5] of yeast cells, we can get abetter understanding of the biological
function of cells. Further, the aspects of thecellular signaling mechanism from the1viewpoint of informatics can be a hint for us
to study and enhance not only existing
information network protocols, but also eventhose for communication networks in thenear future.
With the recently growing interest in
exploring the dynamics of biologically-inspired networking [6], we notice that
there is a striking resemblance between thecyclin-centered cellular signaling process
and the temporal process of the congestion(control) window size (cwnd) in TCP [7,8].
A generalized formulation of TCP was

Figure 1: The controller structure for the signaltransduction network that consists of Cln2 andClb5 with feedbacks

Let Cln2 be the metaphor for thecongestion (control) window sizeandClb5 represents, wherepresented in [7,8], which was inspired by thedynamics of signal transduction networks ofcell cycle in yeast. In this report, we discuss
an extended TCP mechanism under thecondition that two variables of thecorresponding cellular signaling process areextracted, which is the combination of TCP
Vegas and an additional dynamics on thecongestion window.

refers to the round trip time (RTT) including
the propagation delay.
Let us consider the following Masterequation(1)
which is an extension of the generalizedversion of the TCP window size equationgiven in [9] by Wei et al. in the form of.

2. A Pathway-Inspired TCP Model
Based on our previous discussions in [7,8],
we set the variables of the cell cycle
dynamics model as Cln2 and Clb5, which
are embedded in a feedback controller(2)

It can be seen that Eqns. (1) and (2) aresimilar except for the feedback factor
which corresponds to the extended form of
our proposed TCP dynamics.
We setas constant and replacestructure. By modeling the dynamics of thispathway network that takes a form of acascade with feedbacks, we can formulate acontroller in terms of informatics. The
corresponding controller structure is given
in Fig.1.

byto obtain

Then we also define

2.

TPC Vegas andwith

Extended TCP dynamics= TPC Vegas +.
Let, i.e.,take the form of a sign function,

where

then the discrete formulation (quantization)
becomes
andwhererefers to the discrete form ofthe term

are polynomial functions

on the variables, respectively.
There, the itemis the object forthe mass function in a triangular shapemonotonically increasing from 0 to 1 anddecreasing from 1 to 0.
The term,stability analysis and controller synthesis.
By observation where the denominatorcan be related to

becomes zero, we canin TCP Vegas.

calculate the solution to the stability. The
item of

3. Stability Analysis of TCP Dynamics:
Free of Any Transformation
As Wei et al. inferred [9] the stability of
TCP Vegas is studied by analyzing the TCP
transmission processes by using the Laplacetransformation. The congestion (control)
window size is normally used for the packet
model, but it is not so easy to carry out atheoretical analysis of TCP Vegas directly onthe packet form in existing methods ofoptimization theory. What captures ourattention is whether or not a method ofstability analysis exists without anytransformation (e.g. Laplace transformation)in terms of automatic control theory.
Based on the above-mentioned inference,
it is obvious that the stability of the extended
TCP Vegas proposed above equals to theproblem of the analysis of the summation ofis the reason

for designing the structure of the robust
controller
withselectionof
thecorresponding parameters of the polynomialfunctions. This gives rise to richer
dynamical features on the TCP control
mechanism with a controller structure asillustrated in Fig. 2.

Figure 2: Proposed controller structure ofTCP Vegas

34. Conclusion
By designing a discrete form of a controller[3] Gomperts, B.D. Kramer, IJ.M., Tatham,
P.E.R., Signal Transduction, San Diego:
Academic Press, 2002.

of a two-variable pathway network of yeast,
we obtain an extended TCP dynamics whose[4] Liu, J.Q., Shimohara, K., BiomolecularComputation for Bionanotechnology, Artech
House, 2007.

stability can be analyzed freely of anytransformation.

[5] Liu, J.Q. and Leibnitz, K., Modeling thebiological dynamics of cellular signaling forcommunication networks, in: Bio-inspired
Computing and Communication Networks,
Auerbach Publications, Taylor & FrancisGroup, CRC, 2009 (in press).

Here, the channel is assigned proportionallywith

theloadaccording

to

their

utility/capacity under the fairness of packet
transmission;
strategies

arethecongestion
designedtocontrol
obtain[6] Leibnitz, K., Wakamiya, N., Murata, M.,
Biologically-Inspired Self-Adaptive Multi-Path Routing in Overlay Networks, Communications of the ACM, 49(3), March 2006,
pp. 62-67.

equilibriums of TCP dynamics – the steadystates – that affords the stable transition
process leading to the robustness under thecondition that delay, loss and throughput are[7] Liu, J.Q., Leibnitz, K., Murata, M.,
Comparison of the Information Processing
Mechanism in Cellular Signal Transduction
and TCP Congestion Control from theViewpoint of Information Networking, IPSJTechnical Report MBL-46-11, Sept. 25,
2008, (in Japanese).

treated as random variables. Such an
approach provides us a direct observational
way to understand the dynamic features ofthe congestion window control in TCP inorder to design a more fair and robust[8] Liu, J.Q., Leibnitz, K., Murata, M.,
Nature-based Information Networking: On
Exploring Robustness in TCP Inspired by
Cellular Signaling, to be presented at 2ndWorkshop
onComputingandCommunications from Biological Systems:
Theory and Applications (CCBS), Nov.
2008, Awaji, Japan.

control mechanism, which is expected tohelp us to improve the performance of signaltransmission by TCP.
References[1] Chen, K.C., Calzone, L., Csikasz-Nagy,A., Cross F.R., Novak, B., Tyson, J.J.,
Integrative Analysis of Cell Cycle Control in
Budding Yeast, Molecular Biology of theCell, 15(8), Aug. 2004, pp. 3841-3862.

[9] Wei, D.X., Jin, C., Low, S.H., Hedge, S.,
FAST TCP: motivation, architecture,algorithms,performance,IEEE/ACM
Transactions on Networking, 14(6), Dec
2006, pp. 1246-1259.

[2] Zhang, Y., Qian, M., Ouyang, Q., Deng,
M., Li, F., Tang, C., Stochastic model ofyeast cell-cycle network, Physica D, 219(2006), pp. 35-39.

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