TCP over Cognitive Radio Channels

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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!

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