Introduction System Model Numerical Results Future Work & Conclusions References Performance Analysis Of Bufferless 802.11 MAC Queues Ashwin Rao 2006SIY7513 Supervisors Dr. Anirban Mahanti Dr. Arzad Kherani
Introduction System Model Numerical Results Future Work & Conclusions References Outline Introduction System Model Numerical Results Future Work & Conclusions References
Introduction System Model Numerical Results Future Work & Conclusions References Introduction • Safety applications [8] • Main motivation for vehicular networks • Use broadcast services of Medium Access Control(MAC) layer • MAC of vehicular communication stack (1609.4 [1]) similar to IEEE 802.11 [2] • IEEE 802.11 MAC based on CSMA/CA
Introduction System Model Numerical Results Future Work & Conclusions References IEEE 802.11 MAC: An Overview Unicast Transmission • Sample backoff value in the range (0 , w ) • Decrement counter on channel idle • Transmit packet when counter reaches 0 • Positive acknowledgement from destination = ⇒ no collision • On collision repeat cycle for w = 2 m CW min where, m ← backoff stage(no. of previous attempts) CW min ← minimum contention window Broadcast Transmission • No acknowledgements • No retransmission
Introduction System Model Numerical Results Future Work & Conclusions References Motivation Figure: Queuing Model Considering Security Probability of collisions determine arrivals from lower layers Need to analyse P(Coll)
Introduction System Model Numerical Results Future Work & Conclusions References Related Work • Bianchi [3] - Markov chain for saturated MAC queues • Malone et. al [7] - Extenstion for unsaturated queues (Unicast Traffic) • Kumar et. al [6] - generalisation of [3] • Chen et. al [4] - extension of [3] for saturated MAC queues and broadcast traffic • Moreno et. al [9, 10] - simulations using probability of reception as a performance metric • Choi et. al [5] - 2 State markov chain for wireless channel to study hidden node problem.
Introduction System Model Numerical Results Future Work & Conclusions References Outline Introduction System Model Numerical Results Future Work & Conclusions References
Introduction System Model Numerical Results Future Work & Conclusions References Assumptions Figure: Broadcast of fixed size packets in a single cell. • n homogeneous nodes placed in a single cell • The data exchanged is of a fixed size = ⇒ busy periods of a fixed number of slots ( L ). • The nodes having a packet attempt to transmit with a probability β in each slot. • The arrival rate λ is very small resulting in at most one packet at the MAC queue of each node. • Cycle of busy and idle periods
Introduction System Model Numerical Results Future Work & Conclusions References Markov Chain At Each Node (a) Busy and Idle States of channel (b) Markov Chain at each node Consider a node at the end of a busy period • State 0 = ⇒ no packet • State 1 = ⇒ packet to transmit, undergoing backoff process • π = ⇒ Steady state probability of having a packet • At each node if a packet • arrives in a cycle = ⇒ 0 to 1 transition • is transmitted in a cycle = ⇒ 1 to 0 transition
Introduction System Model Numerical Results Future Work & Conclusions References Steady State Transition Probabilities P 10 • Transition from State 1 at beginning of cycle to State 0 at end of cycle • P 10 ( k ) = ⇒ Transition from 1 to 0 when k other nodes have a packet to transmit • k nodes having packet = ⇒ j (0 ≤ j ≤ n − k − 1) other nodes can have arrival in next slot • No transmission attempt (1 − β ) by given node = ⇒ P 10 ( k + j ) in next slot n − k − 1 ! n − k − 1 λ j (1 − λ ) n − k − 1 − j (1 − β ) k +1 P 10 ( k + j ) + β X P 10 ( k ) = j j =0 n − 1 ! n − 1 π k (1 − π ) n − 1 − k P 10 ( k ) X P 10 = k k =0
Introduction System Model Numerical Results Future Work & Conclusions References Steady State Transition Probabilities ... contd. P 01 • Transition from State 0 at beginning of cycle to State 1 at end of cycle “ 1 − (1 − β ) k ” “ 1 − (1 − λ ) L +1 ” P 01 ( k ) = n − k − 1 ! n − k − 1 λ j (1 − λ ) ( n − k − 1 − j ) (1 − β ) k X + j j =0 ((1 − λ ) P 01 ( k + j ) + λ P 11 ( k + j )) where P 11 ( k ) = 1 − P 10 ( k ) n − 1 ! n − 1 π k (1 − π ) n − 1 − k P 01 ( k ) X P 01 = k k =0
Introduction System Model Numerical Results Future Work & Conclusions References Steady State Transition Probabilities ... contd. Figure: Markov Chain at each node π P 10 = (1 − π ) P 01 P 01 ∴ π = P 01 + P 10
Introduction System Model Numerical Results Future Work & Conclusions References Outline Introduction System Model Numerical Results Future Work & Conclusions References
Introduction System Model Numerical Results Future Work & Conclusions References Simulation Parameters Parameter Value Number of nodes ( n ) 3 to 250 Probability of transmit 1 / 16 and 1 / 8 in a given slot β (CW = 32, 16) Probability of packet arrival 1 / 1000, 1 / 2500 and 1 / 5000 100 ∗ 10 − 3 in a given slot λ 20 ∗ 10 − 6 = 5000 Number of slots required for 25, 50 and 100 250 ∗ 8 a transmission L (busy slots) 6 ∗ 10 6 ∗ 20 ∗ 10 − 6 ≈ 17 Table: Simulation Parameters Simple discrete event simulator written that abstract the busy and idle cycles.
Introduction System Model Numerical Results Future Work & Conclusions References π and fraction of packets undergoing collision when L = 25 π when L = 25 Fraction of packets undergoing collisions when L = 25 0.4 1 λ =1/1000, β =1/ 8 λ =1/1000, β =1/16 λ =1/1000, β =1/8 λ =1/2500, β =1/ 8 0.9 λ =1/1000, β =1/16 λ =1/2500, β =1/16 λ =1/2500, β =1/8 Fraction of packets undergoing collision λ =1/5000, β =1/ 8 λ =1/2500, β =1/16 0.8 λ =1/5000, β =1/16 λ =1/5000, β =1/8 λ =1/5000, β =1/16 0.3 0.7 0.6 0.2 0.5 π 0.4 0.3 0.1 0.2 0.1 0 0 0 25 50 75 100 125 150 175 200 0 25 50 75 100 125 150 175 200 Number of Nodes Number of Nodes (a) (b) Collisions and π increase as • Arrival rate lambda increases • Probability of transmission attempt β decreases Adapting λ has a greater impact on P ( coll ) than adapting n and β .
Introduction System Model Numerical Results Future Work & Conclusions References π and fraction of packets undergoing collision when λ = 1 / 5000 π when λ =1/5000 Fraction of packets undergoing collisions when λ = 1/5000 0.4 1 L = 100, β = 1/ 8 L = 100, β = 1/16 L = 100, β =1/8 L = 50, β = 1/ 8 0.9 L = 100, β =1/16 L = 50, β = 1/16 L = 50, β =1/8 Fraction of packets undergoing collision L = 25, β = 1/ 8 L = 50, β =1/16 L = 25, β = 1/16 0.8 L = 25, β =1/8 L = 25, β =1/16 0.3 0.7 0.6 0.2 0.5 π 0.4 0.3 0.1 0.2 0.1 0 0 0 25 50 75 100 125 150 175 200 0 25 50 75 100 125 150 175 200 Number of Nodes Number of Nodes (c) (d) Collisions and π increase as • L increases Increasing L is detrimental to system performance
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Introduction System Model Numerical Results Future Work & Conclusions References Future Work • Equation of π and P ( coll ) in terms of λ , β , n , L • Sensitivity Analysis of π and P(coll) • Using equation of P ( coll ) in network of queues
Introduction System Model Numerical Results Future Work & Conclusions References Conclusions • Adapting λ has a greater impact on P ( coll ) than adapting n and β . • Increasing L is detrimental to system performance
Introduction System Model Numerical Results Future Work & Conclusions References Outline Introduction System Model Numerical Results Future Work & Conclusions References
Introduction System Model Numerical Results Future Work & Conclusions References References I IEEE Trial-Use Standard for Wireless Access in Vehicular Environments (WAVE) - Multi-channel Operation, IEEE Std 1609.4-2006 . 2006. IEEE Standard for Information technology-Telecommunications and information exchange between systems-Local and metropolitan area networks-Specific requirements - Part 11: Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications . June 12 2007, pp. C1–1184. Bianchi, G. Performance analysis of the IEEE 802.11 distributed coordination function. Selected Areas in Communications, IEEE Journal on 18 , 3 (2000), 535–547.
Introduction System Model Numerical Results Future Work & Conclusions References References II Chen, X., Refai, H. H., and Ma, X. Saturation performance of IEEE 802.11 broadcast scheme in ad hoc wireless lans. In Vehicular Technology Conference, 2007. VTC-2007 Fall. 2007 IEEE 66th (Sept. 30 2007-Oct. 3 2007), pp. 1897–1901. Choi, J.-M., So, J., and Ko, Y.-B. Numerical analysis of IEEE 802.11 broadcast scheme in multihop wireless ad hoc networks. Information Networking (2005), 1–10. Kumar, A., Altman, E., Miorandi, D., and Goyal, M. New insights from a fixed-point analysis of single cell ieee 802.11 wlans. IEEE/ACM Trans. Netw. 15 , 3 (2007), 588–601.
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