TCP over Cognitive Radio Channels
|
|
- Gerard Ralf Merritt
- 5 years ago
- Views:
Transcription
1 1/43 TCP over Cognitive Radio Channels Sudheer Poojary Department of ECE, Indian Institute of Science, Bangalore IEEE-IISc I-YES seminar 19 May 2016
2 2/43 Acknowledgments The work presented here was done with guidance from Prof. Vinod Sharma. It was jointly done with Akash Agrawal, Bhoomika Gupta and Archana Bura.
3 3/43 1 Introduction TCP Congestion Control Cognitive Radio Markov chain Preliminaries 2 System Model 3 Exponential ON and OFF Durations Simulation Results 4 Phase-type ON and OFF Durations Simulation Results 5 Multiple Secondary TCP Flows Simulation Results 6 Conclusion and Future Work
4 4/43 1 Introduction TCP Congestion Control Cognitive Radio Markov chain Preliminaries 2 System Model 3 Exponential ON and OFF Durations Simulation Results 4 Phase-type ON and OFF Durations Simulation Results 5 Multiple Secondary TCP Flows Simulation Results 6 Conclusion and Future Work
5 5/43 Introduction TCP is a dominant transport protocol which provides reliable, in-order, end-to-end data transfer, congestion and flow control, fair allocation of resources. TCP has poor performance in wireless environment as it treats all losses as congestion losses. misinterpreting random channel losses leads to inefficient utilization. TCP performance is also poor in (CR) cognitive radio networks. In such environments, the channel may not always be available. This leads to frequent timeouts and hence poor performance. We develop analytical models for computing TCP throughput over channels with random losses and ON/OFF behaviour.
6 6/43 TCP Congestion Control: Overview The TCP sender sends a window of packets to the receiver. The receiver acknowledges receipt of packets by sending ACKs. TCP receiver sends cumulative ACKs, ACK #n implies that all packets up to n have been received successfully. If ACKs are lost/delayed, the sender infers congestion and reduces its window size else the sender increases the window size. TCP congestion control has two phases Slow start phase: Initialization phase to ramp up quickly to equilibrium. At connection setup state of the network is not known. Congestion Avoidance: steady state phase; probe for additional capacity in network.
7 7/43 Slow start and Congestion Avoidance phases 100 Illustrating Slow start and Congestion Avoidance phase Slow Start 70 Congestion Avoidance Window Size First ssthres value Slow Start Congestion Avoidance time The time is in multiples of RTT (round trip time). The round trip time is the time difference between transmission of a packet from sender and the receipt of its ACK.
8 8/43 Slow start and Congestion Avoidance phases TCP Reno W n : Window size at the end of the n th RTT. ssthres acts as a threshold between the two phases. When W n < ssthres, we have slow start: { 2W n, if no packets of the n th window are lost, W n+1 = max{1, Wn 2 }, if there is a loss. else we have congestion avoidance (AIMD) { W n +1, if no loss in the cycle, W n+1 = max{1, Wn 2 }, if there is a loss. On packet loss, ssthres is set to Wn 2.
9 9/43 TCP: recovery from losses A TCP sender uses two mechanisms to infer packet loss 1 Timeouts 2 Duplicate ACKs: multiple ACKs requesting the same packet. If a packet loss is identified, TCP sender retransmits that packet. TCP typically uses three duplicate ACKs to infer a packet loss. TCP treats timeout as an indication of severe congestion. On timeout, window size is dropped to 1 and slow start mode is used.
10 /43 Cognitive Radio Freq. Bands Primary Transmission ON Time Spectrum Hole Figure: Spectrum under-utilization due to static spectrum allocation. Huge portions of the spectrum are reserved and lay underutilized. Cognitive radio intends to use the spectrum efficiently. In cognitive radio network, secondary users can use the channel when the primary is not using it.
11 11/43 Motivation for ON/OFF Channel For our work, primary use case is CR channel. We model the secondary user s channel as an ON/OFF channel. Packets transmitted in the OFF period are lost. Other use cases where intermittent loss of connectivity happens cellular networks due to hand-offs, mobile ad-hoc networks due to link failures, satellite networks and in networks due to collisions. Over an ON/OFF channel, the channel going OFF causes timeouts adversely affecting TCP performance. Also during the ON periods, random losses can occur due to poor channel conditions.
12 12/43 Markov Chain: Definitions A sequence of random variables {X n : n = 0,1, } is said to be a discrete-time Markov chain if P(X n+1 = i n+1 X n = i n,,x 0 = i 0 ) = P(X n+1 = i n+1 X n = i n ). If the transition probabilities are independent of n, then the Markov chain is said to be homogeneous. The transition probabilities and the initial distribution are sufficient to describe the distribution at any time n. Let P: transition probability matrix (t.p.m.), π n : distribution at time n. Then π n = π 0 P n
13 13/43 Markov Chain: Recurrence and Periodicity State i is said to be transient if there is a non-zero probability that the Markov chain never returns to i. Otherwise, the state is said to be recurrent. If the average time to return to a state i is finite, then i is said to be positive recurrent. The period of a state i is defined to be d(i) = gcd{n : P(X n = i X 0 = i) > 0}. State i is called aperiodic if d(i) = 1.
14 14/43 Markov chain: Communicating classes States i and j are said to communicate if there exists n 1,n 2 such that P n 1 (i,j) > 0,P n 2 (j,i) > 0. The state space of a Markov chain can be partitioned into communicating classes. The properties of recurrence, positive recurrence and transience are class properties, i.e., if state i in communicating class C i is positive recurrent, all states in C i are positive recurrent.
15 15/43 Markov Chain: Steady state distribution A probability distribution π is said to be an invariant distribution for a Markov chain with t.p.m. P if π = πp. Every finite state space Markov chain has an invariant distribution. If a finite state space Markov chain has exactly one recurrent communicating class, then the invariant distribution is unique. Additionally, if the recurrent class is aperiodic then irrespective of the initial distribution lim n π n = π. The distribution π is the steady state distribution of the Markov chain.
16 16/43 1 Introduction TCP Congestion Control Cognitive Radio Markov chain Preliminaries 2 System Model 3 Exponential ON and OFF Durations Simulation Results 4 Phase-type ON and OFF Durations Simulation Results 5 Multiple Secondary TCP Flows Simulation Results 6 Conclusion and Future Work
17 17/43 System Model: Illustration TCP Source ACKs TCP Packets C TCP Receiver TCP packet Lost TCP packet ON OFF channel ACK packet W(t) 10 8 Timeout Random error Timeout Channel State R M 2M 4M 4M 8M ON OFF ON OFF ON Figure: Cognitive radio channel with one secondary TCP source
18 18/43 System Model: Notation S k {0,1} : channel state at the k th TCP window transmission W k : window size at the k th attempt T k : slow start threshold at the k th attempt D k D : duration between k th and (k +1) st attempt On encountering a timeout, TCP uses a binary exponential back-off strategy. First retransmission timeout is set to M = max{r,t min }, where R is RTT of flow. There is also a maximum retransmission timeout duration, T max. D k {R,M,2M,...,T max }
19 19/43 System Model: Evolution The following equations govern the TCP behaviour: When there is no packet loss and no timeout, W k+1 = W k +1, if W k T k = 2W k, if W k < T k. D k+1 = R. When there is a packet loss but no timeout, When there is a timeout, W k+1 = W k 2, T k+1 = W k 2, D k+1 = R. W k+1 = 1, T k+1 = W k 2, D k+1 = 2D k. W k and T k are restricted to W max <.
20 20/43 1 Introduction TCP Congestion Control Cognitive Radio Markov chain Preliminaries 2 System Model 3 Exponential ON and OFF Durations Simulation Results 4 Phase-type ON and OFF Durations Simulation Results 5 Multiple Secondary TCP Flows Simulation Results 6 Conclusion and Future Work
21 Exponential ON and OFF Durations ON and OFF periods are i.i.d. exponential with parameters λ 0 and λ 1 respectively. The tuple {S k,d k,w k,t k } denotes the state of the system. The process {S k,d k,w k,t k } forms a Markov chain 1. Let S(t) : state of the channel at time t. Let P t (i,j) : P(S(t) = j S(0) = i). We need P t (i,j) to find the transition probabilities. 1 When channel is ON, we set D k = RTT = max{, W k}, where : µ Propagation delay and µ : link speed in packets/sec 21/43
22 22/43 Markov Chain Transitions P R(1,1)p w 1,R, W 2, W 2 P mm(0,0) 0,2mM,1,1 P R(1,0) 1,R,W,T 0,M,1, W 2 0,mM,1,T P R(1,1)(1 p w) 1,R,W +1,T OR 1,R,2W,T P mm(0,1) 1,R,1,T P t(i,j): Probability of i to j transition in time t. p w = 1 (1 p) W : Probability of random packet loss. (1,R,W,T): typical ON state; (0,mM,1,T): typical OFF state. Figure: Single-step transitions for the {S k,d k,w k,t k } Markov chain Proposition We have for i j, P t (i,i) = λ j +λ i e (λ 0+λ 1 )t λ 0 +λ 1.
23 23/43 Performance Measures The Markov chain {S k,d k,w k,t k } is a finite state Markov chain. It has exactly one positive recurrent class which is aperiodic. Therefore, it has a unique steady state distribution, π. Using the steady state distribution, we can compute the following TCP performance measures: The probability of retransmission timeout, P o, i.e., the fraction of packets that are timed out: P o = E π[1 {S=0} ] E π [W] (1) The throughput, λ (in packets/sec): λ = (1 p)e π[w1 {S=1} ] E π [D] (2)
24 24/43 Effect of RTT Parameters: pkt size: 1050 bytes, W max : 100, CR linkspeed: 5 Mbps, per (packet error rate): 0.01, α : fraction of time, channel is OFF Effect of RTT and average OFF duration on P o with α = 1/3 Probability of packet RTO, P o RTT = 0.2 sec (Model) RTT = 0.2 sec (ns2) RTT = 0.1 sec (Model) RTT = 0.1 sec (ns2) RTT = 0.05 sec (Model) RTT = 0.05 sec (ns2) Average OFF duration, EY off Throughput in pkts/sec Effect of RTT and average OFF duration on Throughput with α = 1/3 RTT = 0.2 sec (Model) RTT = 0.2 sec (ns2) RTT = 0.1 sec (Model) RTT = 0.1 sec (ns2) RTT = 0.05 sec (Model) RTT = 0.05 sec (ns2) Average OFF duration, EY off Figure: Effect of RTT and E[Y off ] on probability of RTO and TCP throughput
25 25/43 Effect of Packet Error Rate Parameters: pkt size: 1050 bytes, W max : 100, CR linkspeed: 5Mbps, RTT: 0.1 sec Probability of packet RTO, P o Effect of per, p and average OFF duration on P o with α = 1/3 p = 0.01 (Markov Model) p = 0.01 (ns2 simulation) p = (Markov model) p = (ns2 simulation) p = (Markov model) p = (ns2 simulation) p = (Markov model) p = (ns2 simulation) Average OFF duration, EYoff Effect of per, p and average OFF duration on Throughput with α = 1/3 Throughput in pkts/sec p = 0.01 (model) p = 0.01 (ns2) p = (model) p = (ns2) p = (model) p = (ns2) p = (model) p = (ns2) Average OFF duration, EY off Figure: Effect of packet error rate and E[Y off ] on TCP performance
26 Average OFF duration, EY off Average OFF duration, EY off 26/43 Effect of Link Speeds Parameters: pkt size: 1050 bytes, W max : 100, RTT: 0.1 sec Effect of link speed on Probability of retransmission timeout Probability of packet RTO, P o Link speed = 5Mbps (Theory) Link speed = 5Mbps (Simulation) Link speed = 1Mbps (Theory) Link speed = 1Mbps (Simulation) Effect of link speed on Throughput 60 Throughput in packets/sec Link speed = 5Mbps (Theory) Link speed = 5Mbps (Simulation) Link speed = 1Mbps (Theory) Link speed = 1Mbps (Simulation) Figure: Effect of link speed and E[Y off ] on TCP performance
27 27/43 1 Introduction TCP Congestion Control Cognitive Radio Markov chain Preliminaries 2 System Model 3 Exponential ON and OFF Durations Simulation Results 4 Phase-type ON and OFF Durations Simulation Results 5 Multiple Secondary TCP Flows Simulation Results 6 Conclusion and Future Work
28 28/43 Phase-type distribution Phase-type distributions generalize exponential distributions. These include sum of exponentials, mixture of exponentials. These can be represented as a random variable describing time until absorption of a Markov process into an absorbing state. We can characterize them by an initial distribution, ˆπ 0 and a transition rate matrix ˆQ. Each state of the Markov process represents a phase.
29 29/43 Phase-type distribution: examples Exponential ˆπ 0 = [0,1] Erlang ˆπ 0 = [0,1,0] Hyper-exponential ˆπ 0 = [0,p,1 p] ˆQ = ( 0 0 λ λ ˆQ = ˆQ = ) λ λ λ 0 λ λ 1 λ 1 0 λ 2 0 λ 2
30 30/43 Extending Model to Phase-type ON and OFF Cycles The channel state, S(t), now includes the phase information and can be modelled as a CTMC. Q : transition rate matrix for the CTMC S(t) X 0 : OFF states, X 1 : ON states P(t) : transition probability matrix for CTMC S(t) {S k,d k,w k,t k } is a Markov chain where S k X 0 X 1 and transition probabilities can be computed using: P(t) = e Qt.
31 31/43 Performance measures The probability of retransmission timeout, P o, i.e., the fraction of packets that are timed out: P o = E π[1 {S X0 }] E π [W] (3) The throughput, λ (in packets/sec): λ = (1 p)e π[w1 {S X1 }] E π [D] (4)
32 32/43 Computational Complexity We compute steady state distribution iteratively using π k+1 = π k P. The size of the state space of the Markov chain is O( X 0 +X 1 D W 2 max). The number of transitions from a state are of the order O(2 X 0 +X 1 ). Thus each iteration of π k+1 = π k P requires O(2 X 0 +X 1 2 D W 2 max ) computations.
33 33/43 Phase-type Illustration: Erlang3 ON and Erlang3 OFF Periods Parameters: pkt size: 1050 bytes, W max : 100, CR linkspeed: 5 Mbps, RTT: 0.1 sec, per = Probability of retx timeout for different ON and OFF distributions with α = 1/3 Probability of packet RTO, P o Exp Exp (Theory) Exp Exp (Simulation) Erlang3 Erlang3 (Theory) Erlang3 Erlang3 (Simulation) Average OFF duration, EY off Throughput for Exponential ON and Exponential OFF distributions with α = 1/3 60 Throughput in packets/sec Exp Exp (Theory) Exp Exp (Simulation) Throughput for Erlang 3 ON and Erlang 3 OFF distributions with α = 1/3 Erlang3 Erlang3 (Theory) Erlang3 Erlang3 (Simulation) Average OFF duration, EY off Figure: Probability of RTO, throughput with different ON-OFF distributions
34 34/43 1 Introduction TCP Congestion Control Cognitive Radio Markov chain Preliminaries 2 System Model 3 Exponential ON and OFF Durations Simulation Results 4 Phase-type ON and OFF Durations Simulation Results 5 Multiple Secondary TCP Flows Simulation Results 6 Conclusion and Future Work
35 35/43 Multiple Secondary TCP Flows I S1 ACKs 1 D 1 TCP Data S D 2 WAN 2 C :. :. S N ACKs N D N S : Source i i D: Destination i i C: Link capacity of shared CR link : Propagation delay of connection i i Figure: Multiple Secondary flows sharing a single CR link We now extend our results to multiple secondary connections. The N secondary connections share a single CR link. The flows may be subject to different packet error rates.
36 36/43 Multiple Secondary TCP Flows II When queuing is negligible, flows behave independently of each other. When queuing is non-negligible, we have to take into account their interactions. We assume all flows have same propagation delays. {S k,d k,(w j k,tj k ) j=1,2, N} forms a Markov chain. The RTT at the end of k th j=1,2, N transmission = max{, Wj µ }, where : propagation delay of the flows, µ : link speed in packets/sec.
37 37/43 Multiple TCP Flows with Negligible Queuing Parameters: Erlang-2 ON and Erlang-2 OFF, E[Y on ] = 20 sec, E[Y off ] = 10 sec, link speed = 10 Mbps, W max = 100 Table: Multiple TCP Flows with Negligible Queuing PER i i Throughput Throughput P o P o (sec) (ns2) (Theoretical) (ns2) (Theoretical)
38 38/43 Multiple TCP Flows with Non-negligible Queuing Parameters: Erlang-2 ON and Erlang-2 OFF, E[Y on ] = 20 sec, E[Y off ] = 10 sec, link speed = 2 Mbps, W max = 20 Table: Multiple TCP flows with non-negligible queuing PER i i Throughput Throughput P o P o (sec) (ns2) (Theoretical) (ns2) (Theoretical)
39 39/43 1 Introduction TCP Congestion Control Cognitive Radio Markov chain Preliminaries 2 System Model 3 Exponential ON and OFF Durations Simulation Results 4 Phase-type ON and OFF Durations Simulation Results 5 Multiple Secondary TCP Flows Simulation Results 6 Conclusion and Future Work
40 40/43 Conclusion We have studied TCP performance over an ON-OFF channel with random losses. We have developed Markov models for performance analysis of TCP over exponential ON and exponential OFF periods, We extended our model to phase-type ON and phase-type OFF periods. We also extended our model to multiple TCP connections. We validated all our models by comparing our model results with ns2 simulations.
41 41/43 Future Work We compute throughput only numerically, a closed-form approximation for TCP throughput as a function of the ON/OFF channel parameters will be very useful in practice. In the ON/OFF channel, the packets were simply lost in the OFF period. An interesting extension of this work are channels with time-varying capacities. In our work, we have looked at single CR channel. The work can be extended to multi-hop CR networks.
42 42/43 References K. R. Fall, and W. R. Stevens TCP/IP Illustrated: The Protocols, Addison-Wesley Professional, vol. 1, A. Kumar Discrete Event Stochastic Processes: Lecture Notes for an Engineering Curriculum, E. Biglieri, A. Goldsmith, L. Greenstein, N. Mandayam, and H. Poor Principles of Cognitive Radio, in Cambridge University Press, S. Poojary, A. Agrawal, B. Gupta, A. Bura, V. Sharma Throughput of TCP over Cognitive Radio Channels, in IEEE Global Communications Conference (Globecom), Dec, 2015
43 43/43 Thank You! Thank You!
cs/ee/ids 143 Communication Networks
cs/ee/ids 143 Communication Networks Chapter 4 Transport Text: Walrand & Parakh, 2010 Steven Low CMS, EE, Caltech Agenda Internetworking n Routing across LANs, layer2-layer3 n DHCP n NAT Transport layer
More informationWireless Internet Exercises
Wireless Internet Exercises Prof. Alessandro Redondi 2018-05-28 1 WLAN 1.1 Exercise 1 A Wi-Fi network has the following features: Physical layer transmission rate: 54 Mbps MAC layer header: 28 bytes MAC
More informationAnalysis of Scalable TCP in the presence of Markovian Losses
Analysis of Scalable TCP in the presence of Markovian Losses E Altman K E Avrachenkov A A Kherani BJ Prabhu INRIA Sophia Antipolis 06902 Sophia Antipolis, France Email:altman,kavratchenkov,alam,bprabhu}@sophiainriafr
More informationModeling Impact of Delay Spikes on TCP Performance on a Low Bandwidth Link
Modeling Impact of Delay Spikes on TCP Performance on a Low Bandwidth Link Pasi Lassila and Pirkko Kuusela Networking Laboratory Helsinki University of Technology (HUT) Espoo, Finland Email: {Pasi.Lassila,Pirkko.Kuusela
More informationReliable Data Transport: Sliding Windows
Reliable Data Transport: Sliding Windows 6.02 Fall 2013 Lecture 23 Exclusive! A Brief History of the Internet guest lecture by Prof. Hari Balakrishnan Wenesday December 4, 2013, usual 6.02 lecture time
More informationTuning the TCP Timeout Mechanism in Wireless Networks to Maximize Throughput via Stochastic Stopping Time Methods
Tuning the TCP Timeout Mechanism in Wireless Networks to Maximize Throughput via Stochastic Stopping Time Methods George Papageorgiou and John S. Baras Abstract We present an optimization problem that
More informationA Simple Model for the Window Size Evolution of TCP Coupled with MAC and PHY Layers
A Simple Model for the Window Size Evolution of TCP Coupled with and PHY Layers George Papageorgiou, John S. Baras Institute for Systems Research, University of Maryland, College Par, MD 20742 Email: gpapag,
More informationCSE 123: Computer Networks
CSE 123: Computer Networks Total points: 40 Homework 1 - Solutions Out: 10/4, Due: 10/11 Solutions 1. Two-dimensional parity Given below is a series of 7 7-bit items of data, with an additional bit each
More informationModelling TCP with a Discrete Time Markov Chain
Modelling TCP with a Discrete Time Markov Chain José L Gil Motorola josegil@motorola.com ABSTRACT TCP is the most widely used transport protocol in the Internet. The end-to-end performance of most Internet
More informationChapter 5. Elementary Performance Analysis
Chapter 5 Elementary Performance Analysis 1 5.0 2 5.1 Ref: Mischa Schwartz Telecommunication Networks Addison-Wesley publishing company 1988 3 4 p t T m T P(k)= 5 6 5.2 : arrived rate : service rate 7
More informationWindow Size. Window Size. Window Size. Time. Time. Time
A Spectrum of TCP-friendly Window-based Congestion Control Algorithms Λ Shudong Jin Liang Guo Ibrahim Matta Azer Bestavros Computer Science Department Boston University Boston, MA 5 fjins, guol, matta,
More informationAnalysis of TCP Westwood+ in high speed networks
Analysis of TCP Westwood+ in high speed networks 1 E. Altman, C. Barakat, S. Mascolo, N. Möller and J. Sun Abstract TCP Westwood+ is modelled and analyzed using stochastic recursive equations. It is shown
More informationMarkovian Model of Internetworking Flow Control
Информационные процессы, Том 2, 2, 2002, стр. 149 154. c 2002 Bogoiavlenskaia. KALASHNIKOV MEMORIAL SEMINAR Markovian Model of Internetworking Flow Control O. Bogoiavlenskaia Petrozavodsk State University
More informationProcessor Sharing Flows in the Internet
STANFORD HPNG TECHNICAL REPORT TR4-HPNG4 Processor Sharing Flows in the Internet Nandita Dukkipati, Nick McKeown Computer Systems Laboratory Stanford University Stanford, CA 9434-93, USA nanditad, nickm
More informationMARKOV PROCESSES. Valerio Di Valerio
MARKOV PROCESSES Valerio Di Valerio Stochastic Process Definition: a stochastic process is a collection of random variables {X(t)} indexed by time t T Each X(t) X is a random variable that satisfy some
More informationA Mathematical Model of the Skype VoIP Congestion Control Algorithm
A Mathematical Model of the Skype VoIP Congestion Control Algorithm Luca De Cicco, S. Mascolo, V. Palmisano Dipartimento di Elettrotecnica ed Elettronica, Politecnico di Bari 47th IEEE Conference on Decision
More informationA POMDP Framework for Cognitive MAC Based on Primary Feedback Exploitation
A POMDP Framework for Cognitive MAC Based on Primary Feedback Exploitation Karim G. Seddik and Amr A. El-Sherif 2 Electronics and Communications Engineering Department, American University in Cairo, New
More informationMathematical Analysis of IEEE Energy Efficiency
Information Engineering Department University of Padova Mathematical Analysis of IEEE 802.11 Energy Efficiency A. Zanella and F. De Pellegrini IEEE WPMC 2004 Padova, Sept. 12 15, 2004 A. Zanella and F.
More information2 Department of ECE, Jayaram College of Engineering and Technology, Pagalavadi, Trichy,
End-to-End Congestion Control using Polynomial Algorithms in Wired TCP Networs M.Chandrasearan, M.Kalpana, 2 and Dr.R.S.D.Wahida Banu 3 Assistant Professor, Department of ECE, Government College of Engineering,
More informationStochastic Hybrid Systems: Applications to Communication Networks
research supported by NSF Stochastic Hybrid Systems: Applications to Communication Networks João P. Hespanha Center for Control Engineering and Computation University of California at Santa Barbara Talk
More informationcommunication networks
Positive matrices associated with synchronised communication networks Abraham Berman Department of Mathematics Robert Shorten Hamilton Institute Douglas Leith Hamilton Instiute The Technion NUI Maynooth
More informationResource Allocation and Pricing. R. Srikant University of Illinois
Resource Allocation and Pricing R. Srikant University of Illinois References The Mathematics of Internet Congestion Control, Birkhauser, 2004. Pricing: Kelly Distributed Resource Allocation: Kelly, Mauloo
More informationA Stochastic Model for TCP with Stationary Random Losses
A Stochastic Model for TCP with Stationary Random Losses Eitan Altman, Kostya Avrachenkov Chadi Barakat INRIA Sophia Antipolis - France ACM SIGCOMM August 31, 2000 Stockholm, Sweden Introduction Outline
More informationAnalytic Performance Evaluation of the RED Algorithm
Prof. Dr. P. Tran-Gia Analytic Performance Evaluation of the RED Algorithm Stefan Köhler, Michael Menth, Norbert Vicari TCP Model RED Model TCP over RED Results TCP > Reliable transmission > Closed loop
More informationPart I Stochastic variables and Markov chains
Part I Stochastic variables and Markov chains Random variables describe the behaviour of a phenomenon independent of any specific sample space Distribution function (cdf, cumulative distribution function)
More informationP e = 0.1. P e = 0.01
23 10 0 10-2 P e = 0.1 Deadline Failure Probability 10-4 10-6 10-8 P e = 0.01 10-10 P e = 0.001 10-12 10 11 12 13 14 15 16 Number of Slots in a Frame Fig. 10. The deadline failure probability as a function
More information384Y Project June 5, Stability of Congestion Control Algorithms Using Control Theory with an application to XCP
384Y Project June 5, 00 Stability of Congestion Control Algorithms Using Control Theory with an application to XCP . Introduction During recent years, a lot of work has been done towards the theoretical
More informationStochastic Hybrid Systems: Applications to Communication Networks
research supported by NSF Stochastic Hybrid Systems: Applications to Communication Networks João P. Hespanha Center for Control Engineering and Computation University of California at Santa Barbara Deterministic
More informationMarkov Chain Model for ALOHA protocol
Markov Chain Model for ALOHA protocol Laila Daniel and Krishnan Narayanan April 22, 2012 Outline of the talk A Markov chain (MC) model for Slotted ALOHA Basic properties of Discrete-time Markov Chain Stability
More informationrequests/sec. The total channel load is requests/sec. Using slot as the time unit, the total channel load is 50 ( ) = 1
Prof. X. Shen E&CE 70 : Examples #2 Problem Consider the following Aloha systems. (a) A group of N users share a 56 kbps pure Aloha channel. Each user generates at a Passion rate of one 000-bit packet
More informationModeling and Simulation NETW 707
Modeling and Simulation NETW 707 Lecture 6 ARQ Modeling: Modeling Error/Flow Control Course Instructor: Dr.-Ing. Maggie Mashaly maggie.ezzat@guc.edu.eg C3.220 1 Data Link Layer Data Link Layer provides
More informationABSTRACT FLOW CONTROL IN WIRELESS AD-HOC NETWORKS. Georgios Papageorgiou, Doctor of Philosophy, 2009
ABSTRACT Title of dissertation: FLOW CONTROL IN WIRELESS AD-HOC NETWORKS Georgios Papageorgiou, Doctor of Philosophy, 2009 Dissertation directed by: Professor John S. Baras, Department of Electrical and
More informationDiscrete Random Variables
CPSC 53 Systems Modeling and Simulation Discrete Random Variables Dr. Anirban Mahanti Department of Computer Science University of Calgary mahanti@cpsc.ucalgary.ca Random Variables A random variable is
More informationStability Analysis of TCP/RED Communication Algorithms
Stability Analysis of TCP/RED Communication Algorithms Ljiljana Trajković Simon Fraser University, Vancouver, Canada ljilja@cs.sfu.ca http://www.ensc.sfu.ca/~ljilja Collaborators Mingjian Liu and Hui Zhang
More informationStability Analysis of TCP/RED Communication Algorithms
Stability Analysis of TCP/RED Communication Algorithms Ljiljana Trajković Simon Fraser University, Vancouver, Canada ljilja@cs.sfu.ca http://www.ensc.sfu.ca/~ljilja Collaborators Mingjian Liu and Hui Zhang
More informationCapturing Network Traffic Dynamics Small Scales. Rolf Riedi
Capturing Network Traffic Dynamics Small Scales Rolf Riedi Dept of Statistics Stochastic Systems and Modelling in Networking and Finance Part II Dependable Adaptive Systems and Mathematical Modeling Kaiserslautern,
More informationIrreducibility. Irreducible. every state can be reached from every other state For any i,j, exist an m 0, such that. Absorbing state: p jj =1
Irreducibility Irreducible every state can be reached from every other state For any i,j, exist an m 0, such that i,j are communicate, if the above condition is valid Irreducible: all states are communicate
More informationInternet Congestion Control: Equilibrium and Dynamics
Internet Congestion Control: Equilibrium and Dynamics A. Kevin Tang Cornell University ISS Seminar, Princeton University, February 21, 2008 Networks and Corresponding Theories Power networks (Maxwell Theory)
More informationMultiaccess Communication
Information Networks p. 1 Multiaccess Communication Satellite systems, radio networks (WLAN), Ethernet segment The received signal is the sum of attenuated transmitted signals from a set of other nodes,
More informationCongestion Control. Topics
Congestion Control Topics Congestion control what & why? Current congestion control algorithms TCP and UDP Ideal congestion control Resource allocation Distributed algorithms Relation current algorithms
More informationA Stochastic Model of TCP/IP with Stationary Random Losses
1 A Stochastic Model of TCP/IP with Stationary Random Losses Eitan Altman, Konstantin Avrachenkov, Chadi Barakat INRIA, 24 route des Lucioles, 692 Sophia Antipolis, France Email:{altman,kavratch,cbarakat}@sophiainriafr
More informationComputer Networks ( Classroom Practice Booklet Solutions)
Computer Networks ( Classroom Practice Booklet Solutions). Concept Of Layering 0. Ans: (b) Sol: Data Link Layer is responsible for decoding bit stream into frames. 0. Ans: (c) Sol: Network Layer has the
More informationLecture Notes 7 Random Processes. Markov Processes Markov Chains. Random Processes
Lecture Notes 7 Random Processes Definition IID Processes Bernoulli Process Binomial Counting Process Interarrival Time Process Markov Processes Markov Chains Classification of States Steady State Probabilities
More informationMarkov Chains. X(t) is a Markov Process if, for arbitrary times t 1 < t 2 <... < t k < t k+1. If X(t) is discrete-valued. If X(t) is continuous-valued
Markov Chains X(t) is a Markov Process if, for arbitrary times t 1 < t 2
More informationCS276 Homework 1: ns-2
CS276 Homework 1: ns-2 Erik Peterson October 28, 2006 1 Part 1 - Fairness between TCP variants 1.1 Method After learning ns-2, I wrote a script (Listing 3) that runs a simulation of one or two tcp flows
More informationMarkov Chains (Part 3)
Markov Chains (Part 3) State Classification Markov Chains - State Classification Accessibility State j is accessible from state i if p ij (n) > for some n>=, meaning that starting at state i, there is
More informationRecap. Probability, stochastic processes, Markov chains. ELEC-C7210 Modeling and analysis of communication networks
Recap Probability, stochastic processes, Markov chains ELEC-C7210 Modeling and analysis of communication networks 1 Recap: Probability theory important distributions Discrete distributions Geometric distribution
More informationGiuseppe Bianchi, Ilenia Tinnirello
Capacity of WLAN Networs Summary Per-node throughput in case of: Full connected networs each node sees all the others Generic networ topology not all nodes are visible Performance Analysis of single-hop
More informationStochastic process. X, a series of random variables indexed by t
Stochastic process X, a series of random variables indexed by t X={X(t), t 0} is a continuous time stochastic process X={X(t), t=0,1, } is a discrete time stochastic process X(t) is the state at time t,
More informationWiFi MAC Models David Malone
WiFi MAC Models David Malone November 26, MACSI Hamilton Institute, NUIM, Ireland Talk outline Introducing the 82.11 CSMA/CA MAC. Finite load 82.11 model and its predictions. Issues with standard 82.11,
More informationECE 3511: Communications Networks Theory and Analysis. Fall Quarter Instructor: Prof. A. Bruce McDonald. Lecture Topic
ECE 3511: Communications Networks Theory and Analysis Fall Quarter 2002 Instructor: Prof. A. Bruce McDonald Lecture Topic Introductory Analysis of M/G/1 Queueing Systems Module Number One Steady-State
More informationOSCILLATION AND PERIOD DOUBLING IN TCP/RED SYSTEM: ANALYSIS AND VERIFICATION
International Journal of Bifurcation and Chaos, Vol. 18, No. 5 (28) 1459 1475 c World Scientific Publishing Company OSCILLATION AND PERIOD DOUBLING IN TCP/RED SYSTEM: ANALYSIS AND VERIFICATION XI CHEN,
More informationRandom Access Protocols ALOHA
Random Access Protocols ALOHA 1 ALOHA Invented by N. Abramson in 1970-Pure ALOHA Uncontrolled users (no coordination among users) Same packet (frame) size Instant feedback Large (~ infinite) population
More informationLECTURE 3. Last time:
LECTURE 3 Last time: Mutual Information. Convexity and concavity Jensen s inequality Information Inequality Data processing theorem Fano s Inequality Lecture outline Stochastic processes, Entropy rate
More informationMin Congestion Control for High- Speed Heterogeneous Networks. JetMax: Scalable Max-Min
JetMax: Scalable Max-Min Min Congestion Control for High- Speed Heterogeneous Networks Yueping Zhang Joint work with Derek Leonard and Dmitri Loguinov Internet Research Lab Department of Computer Science
More informationABSTRACT FLOW CONTROL IN WIRELESS AD-HOC NETWORKS. Georgios Papageorgiou, Doctor of Philosophy, 2009
ABSTRACT Title of dissertation: FLOW CONTROL IN WIRELESS AD-HOC NETWORKS Georgios Papageorgiou, Doctor of Philosophy, 2009 Dissertation directed by: Professor John S. Baras, Department of Electrical and
More informationMethodology for Computer Science Research Lecture 4: Mathematical Modeling
Methodology for Computer Science Research Andrey Lukyanenko Department of Computer Science and Engineering Aalto University, School of Science and Technology andrey.lukyanenko@tkk.fi Definitions and Goals
More informationCapacity and Delay Tradeoffs for Ad-Hoc Mobile Networks
IEEE TRASACTIOS O IFORMATIO THEORY 1 Capacity and Delay Tradeoffs for Ad-Hoc Mobile etworks Michael J. eely University of Southern California mjneely@usc.edu http://www-rcf.usc.edu/ mjneely Eytan Modiano
More informationGiuseppe Bianchi, Ilenia Tinnirello
Capacity of WLAN Networs Summary Ł Ł Ł Ł Arbitrary networ capacity [Gupta & Kumar The Capacity of Wireless Networs ] Ł! Ł "! Receiver Model Ł Ł # Ł $%&% Ł $% '( * &%* r (1+ r Ł + 1 / n 1 / n log n Area
More informationStochastic Processes
Stochastic Processes 8.445 MIT, fall 20 Mid Term Exam Solutions October 27, 20 Your Name: Alberto De Sole Exercise Max Grade Grade 5 5 2 5 5 3 5 5 4 5 5 5 5 5 6 5 5 Total 30 30 Problem :. True / False
More informationOn Distribution and Limits of Information Dissemination Latency and Speed In Mobile Cognitive Radio Networks
This paper was presented as part of the Mini-Conference at IEEE INFOCOM 11 On Distribution and Limits of Information Dissemination Latency and Speed In Mobile Cognitive Radio Networks Lei Sun Wenye Wang
More informationConcise Paper: Deconstructing MPTCP Performance
04 IEEE nd International Conference on Network Protocols Concise Paper: Deconstructing MPTCP Performance Behnaz Arzani, Alexander Gurney, Sitian Cheng, Roch Guerin and Boon Thau Loo University Of Pennsylvania
More informationReadings: Finish Section 5.2
LECTURE 19 Readings: Finish Section 5.2 Lecture outline Markov Processes I Checkout counter example. Markov process: definition. -step transition probabilities. Classification of states. Example: Checkout
More informationImpact of Cross Traffic Burstiness on the Packet-scale Paradigm An Extended Analysis
Impact of ross Traffic Burstiness on the Packet-scale Paradigm An Extended Analysis Rebecca Lovewell and Jasleen Kaur Technical Report # TR11-007 Department of omputer Science University of North arolina
More informationLecture 7: Simulation of Markov Processes. Pasi Lassila Department of Communications and Networking
Lecture 7: Simulation of Markov Processes Pasi Lassila Department of Communications and Networking Contents Markov processes theory recap Elementary queuing models for data networks Simulation of Markov
More informationService differentiation without prioritization in IEEE WLANs
Service differentiation without prioritization in IEEE 8. WLANs Suong H. Nguyen, Student Member, IEEE, Hai L. Vu, Senior Member, IEEE, and Lachlan L. H. Andrew, Senior Member, IEEE Abstract Wireless LANs
More informationDetecting Stations Cheating on Backoff Rules in Networks Using Sequential Analysis
Detecting Stations Cheating on Backoff Rules in 82.11 Networks Using Sequential Analysis Yanxia Rong Department of Computer Science George Washington University Washington DC Email: yxrong@gwu.edu Sang-Kyu
More informationEE 550: Notes on Markov chains, Travel Times, and Opportunistic Routing
EE 550: Notes on Markov chains, Travel Times, and Opportunistic Routing Michael J. Neely University of Southern California http://www-bcf.usc.edu/ mjneely 1 Abstract This collection of notes provides a
More informationLecture 11: Introduction to Markov Chains. Copyright G. Caire (Sample Lectures) 321
Lecture 11: Introduction to Markov Chains Copyright G. Caire (Sample Lectures) 321 Discrete-time random processes A sequence of RVs indexed by a variable n 2 {0, 1, 2,...} forms a discretetime random process
More informationUnderstanding TCP Vegas: A Duality Model
Understanding TCP Vegas: A Duality Model Steven Low Departments of CS and EE, Caltech, USA slow@caltech.edu Larry Peterson Limin Wang Department of CS, Princeton University, USA {llp,lmwang}@cs.princeton.edu
More informationTCP modeling in the presence of nonlinear window growth
TCP modeling in the presence of nonlinear window growth Eitan Altman, Kostia Avrachenkov, Chadi Barakat Rudesindo Núñez-Queija Abstract We develop a model for TCP that accounts for both sublinearity and
More informationLeopold Franzens University Innsbruck. Responding to Spurious Loss Events in TCP/IP. Master Thesis. Institute of Computer Science
Leopold Franzens University Innsbruck Institute of Computer Science Distributed and Parallel Systems Group Responding to Spurious Loss Events in TCP/IP Master Thesis Supervisor: Dr. Michael Welzl Author:
More informationOn the Throughput-Optimality of CSMA Policies in Multihop Wireless Networks
Technical Report Computer Networks Research Lab Department of Computer Science University of Toronto CNRL-08-002 August 29th, 2008 On the Throughput-Optimality of CSMA Policies in Multihop Wireless Networks
More informationModelling data networks stochastic processes and Markov chains
Modelling data networks stochastic processes and Markov chains a 1, 3 1, 2 2, 2 b 0, 3 2, 3 u 1, 3 α 1, 6 c 0, 3 v 2, 2 β 1, 1 Richard G. Clegg (richard@richardclegg.org) November 2016 Available online
More informationStochastic Hybrid Systems: Modeling, analysis, and applications to networks and biology
research supported by NSF Stochastic Hybrid Systems: Modeling, analysis, and applications to networks and biology João P. Hespanha Center for Control Engineering and Computation University of California
More informationPIQI-RCP: Design and Analysis of Rate-Based Explicit Congestion Control
PIQI-RCP: Design and Analysis of Rate-Based Explicit Congestion Control Saurabh Jain Joint work with Dr. Dmitri Loguinov June 21, 2007 1 Agenda Introduction Analysis of RCP QI-RCP PIQI-RCP Comparison Wrap
More informationInformation in Aloha Networks
Achieving Proportional Fairness using Local Information in Aloha Networks Koushik Kar, Saswati Sarkar, Leandros Tassiulas Abstract We address the problem of attaining proportionally fair rates using Aloha
More informationE8 TCP. Politecnico di Milano Scuola di Ingegneria Industriale e dell Informazione
E8 TP Politecnico di Milano Scuola di Ingegneria Industriale e dell Informazione Exercises o onsider the connection in the figure A =80 kbit/s τ =0 ms R =? τ =? B o o o Host A wants to know the capacity
More informationA New Technique for Link Utilization Estimation
A New Technique for Link Utilization Estimation in Packet Data Networks using SNMP Variables S. Amarnath and Anurag Kumar* Dept. of Electrical Communication Engineering Indian Institute of Science, Bangalore
More informationModeling the Effect of Transmission Errors on TCP Controlled Transfers over Infrastructure Wireless LANs
Modeling the Effect of Transmission Errors on TCP Controlled Transfers over Infrastructure 8 Wireless LANs ABSTRACT Subhashini Krishnasamy Dept of Electrical Communication Engg Indian Institute of Science,
More informationMarkovian Decision Process (MDP): theory and applications to wireless networks
Markovian Decision Process (MDP): theory and applications to wireless networks Philippe Ciblat Joint work with I. Fawaz, N. Ksairi, C. Le Martret, M. Sarkiss Outline Examples MDP Applications A few examples
More informationAn Evolutionary Game Perspective to ALOHA with power control
An Evolutionary Game Perspective to ALOHA with power control E. Altman a, N. Bonneau a, M. Debbah b and G. Caire b a MAESTRO, INRIA Sophia-Antipolis, 004 Route des Lucioles, B.P.93, 0690 Sophia-Antipolis,
More informationControlo Switched Systems: Mixing Logic with Differential Equations. João P. Hespanha. University of California at Santa Barbara.
Controlo 00 5 th Portuguese Conference on Automatic Control University of Aveiro,, September 5-7, 5 00 Switched Systems: Mixing Logic with Differential Equations João P. Hespanha University of California
More informationPower Laws in ALOHA Systems
Power Laws in ALOHA Systems E6083: lecture 8 Prof. Predrag R. Jelenković Dept. of Electrical Engineering Columbia University, NY 10027, USA predrag@ee.columbia.edu March 6, 2007 Jelenković (Columbia University)
More informationLecture 4 Noisy Channel Coding
Lecture 4 Noisy Channel Coding I-Hsiang Wang Department of Electrical Engineering National Taiwan University ihwang@ntu.edu.tw October 9, 2015 1 / 56 I-Hsiang Wang IT Lecture 4 The Channel Coding Problem
More informationPerformance analysis of IEEE WLANs with saturated and unsaturated sources
Performance analysis of IEEE 82.11 WLANs with saturated and unsaturated sources Suong H. Nguyen, Hai L. Vu, Lachlan L. H. Andrew Centre for Advanced Internet Architectures, Technical Report 11811A Swinburne
More informationPrediction Based Cognitive Spectrum Access 1
Prediction Based Cognitive Spectrum Access 1 Boris Oklander Department of Electrical Engineering Technion Israel Institute of Technology Haifa, Israel oklander@tx.technion.ac.il Moshe Sidi Department of
More informationA New TCP/AQM System Analysis
A ew TCP/AQM System Analysis Qin Xu, Fan Li, Jinsheng Sun, and Moshe Zukerman, Fellow, IEEE arxiv:37.24v [cs.i] 4 Jul 23 Abstract The fluid model has been used extensively to guide designs of AQM schemes
More informationIN THIS PAPER, we describe a design oriented modelling
616 IEEE/ACM TRANSACTIONS ON NETWORKING, VOL 14, NO 3, JUNE 2006 A Positive Systems Model of TCP-Like Congestion Control: Asymptotic Results Robert Shorten, Fabian Wirth, and Douglas Leith Abstract We
More informationThroughput-Delay Analysis of Random Linear Network Coding for Wireless Broadcasting
Throughput-Delay Analysis of Random Linear Network Coding for Wireless Broadcasting Swapna B.T., Atilla Eryilmaz, and Ness B. Shroff Departments of ECE and CSE The Ohio State University Columbus, OH 43210
More informationFair Scheduling in Input-Queued Switches under Inadmissible Traffic
Fair Scheduling in Input-Queued Switches under Inadmissible Traffic Neha Kumar, Rong Pan, Devavrat Shah Departments of EE & CS Stanford University {nehak, rong, devavrat@stanford.edu Abstract In recent
More informationRetrospective Spectrum Access Protocol: A Completely Uncoupled Learning Algorithm for Cognitive Networks
Retrospective Spectrum Access Protocol: A Completely Uncoupled Learning Algorithm for Cognitive Networks Marceau Coupechoux, Stefano Iellamo, Lin Chen + TELECOM ParisTech (INFRES/RMS) and CNRS LTCI + University
More informationIntegrity-Oriented Content Transmission in Highway Vehicular Ad Hoc Networks
VANET Analysis Integrity-Oriented Content Transmission in Highway Vehicular Ad Hoc Networks Tom Hao Luan, Xuemin (Sherman) Shen, and Fan Bai BBCR, ECE, University of Waterloo, Waterloo, Ontario, N2L 3G1,
More informationANALYSIS OF THE RTS/CTS MULTIPLE ACCESS SCHEME WITH CAPTURE EFFECT
ANALYSIS OF THE RTS/CTS MULTIPLE ACCESS SCHEME WITH CAPTURE EFFECT Chin Keong Ho Eindhoven University of Technology Eindhoven, The Netherlands Jean-Paul M. G. Linnartz Philips Research Laboratories Eindhoven,
More informationUnderstanding TCP Vegas: A Duality Model
Understanding TCP Vegas: A Duality Model STEVEN H. LOW Caltech, Pasadena, California AND LARRY L. PETERSON AND LIMIN WANG Princeton University, Princeton, New Jersey Abstract. We view congestion control
More informationPerformance Evaluation of Deadline Monotonic Policy over protocol
Performance Evaluation of Deadline Monotonic Policy over 80. protocol Ines El Korbi and Leila Azouz Saidane National School of Computer Science University of Manouba, 00 Tunisia Emails: ines.korbi@gmail.com
More informationCompound TCP with Random Losses
Compound TCP with Random Losses Alberto Blanc 1, Konstantin Avrachenkov 2, Denis Collange 1, and Giovanni Neglia 2 1 Orange Labs, 905 rue Albert Einstein, 06921 Sophia Antipolis, France {alberto.blanc,denis.collange}@orange-ftgroup.com
More informationExact Distribution of Access Delay in IEEE DCF MAC
Exact Distribution of Access Delay in IEEE 8.11 DCF MAC Teerawat Issariyakul, Dusit Niyato, Ekram Hossain, and Attahiru Sule Alfa University of Manitoba and TRLabs Winnipeg, MB, Canada. Email: teerawat,
More informationSTOCHASTIC PROCESSES Basic notions
J. Virtamo 38.3143 Queueing Theory / Stochastic processes 1 STOCHASTIC PROCESSES Basic notions Often the systems we consider evolve in time and we are interested in their dynamic behaviour, usually involving
More informationIntroduction to Wireless & Mobile Systems. Chapter 4. Channel Coding and Error Control Cengage Learning Engineering. All Rights Reserved.
Introduction to Wireless & Mobile Systems Chapter 4 Channel Coding and Error Control 1 Outline Introduction Block Codes Cyclic Codes CRC (Cyclic Redundancy Check) Convolutional Codes Interleaving Information
More information