Towards Performance Modeling of IEEE 802'11 based Wireless Networks: A Unified Framework and its App

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Towards Performance Modeling of IEEE 802.11 based
Wireless Networks A Unified Framework and its
Applications

• Kamesh Medepalli and Fouad A. Tobagi
• Dept. of EE, Standford
• INFOCOM 2006
• Modified and Presented by Yong Yang

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Motivation Goal

• Newer forms of networks offer exciting
  possibilities
• WLAN, wireless ad-hoc networks, wireless sensor
  networks, and wireless mesh networks
• Most of these networks use IEEE 802.11 based
  devices
• Performance modeling of such networks is of great
  practical importance
• Goal a unified analytical model that is
  applicable to
• Saturated or finite load
• Single-hop or multi-hop
• Dynamic data rates

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Outline

• Overview of Bianchis model
• Analytical model to quantify the throughput and
  delay performance of individual users
• Applications of the model to better understand
  the performance of CSMA/CA based networks
• Impacts of Tx Power, Traffic, RTS/CTS and CW
• A Heuristic Measure of Contention - ECI
• Discussions

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Bianchis Model (1)

• Consider an ideal single-hop system with N users
• Let bi,k be the probability that a node is in
  state (i,k) when time?8

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Bianchis Model (2)
(1)

• Note
• By (1) and (2), we have
• So (3) can be written as
• Since , by (1)(2)(5), we
  can get
• Thus, the probability that a station transmits in
  a randomly chosen slot is

(2)
(3)
(4)
(5)
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Bianchis Model (2)

• Now we have
• And at steady state, the retransmission
  probability is
• p 1 (1-?)n-1
• So p and ? can be solve by numerical techniques

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Outline

• Overview of Bianchis model
• Analytical model to quantify the throughput and
  delay performance of individual users
• Applications of the model to better understand
  the performance of CSMA/CA based networks
• Impacts of Tx Power, Traffic, RTS/CTS and CW
• A Heuristic Measure of Contention - ECI
• Discussions

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Overview of the Unified Model

• Let ai be the transmission probability of node i
• Let ßi be the retransmission probability of node
  i
• Consider that node s intends to communicate with
  node d, in finite load and multi-hop scenarios,
  we have
• as Ps having a packet to transmit
• (1 - Ps sense busy due to tx of ds
  hidden nodes having a pkt to tx)
• Ps transmit having a packet and does
  not sense busy
• Denote Pi transmit i having a packet and does
  not sense busy as ai'', using Bianchis model,
  we have
• where L is the number of back-off stages.
• To complete the model, we need to solve
• ?s Ps having a packet to transmit
• ?s Ps sense busy due to tx of ds hidden
  nodes having a pkt to tx
• ßs the retransmission probability

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?s Accounting for Finite Load

• ?s equals the probability of non-empty buffer,
  which can be approximated to be (Queueing Theory)
• Traffic destined to d arrives at s as Poisson of
  rate ?s
• Time taken to successfully transmit a packet from
  s to d is exponentially distributed with mean
  ETs (solved later)
• Note for a stable queue, ?s lt 1/ ETs

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?s Accounting for Asymmetric

• Notations
• S the total set of nodes
• Hi the set of nodes in CS range of node i
• Hi Hi U i
• Hi- S Hi
• ?s is the probability that node s is in back-off
  state, and can be computed as
• where bs is the average time spent in back-off
  when attempting to successfully transmit one
  packet (solved later)

k Hs Hd- (k transmits)
?s
(1- ?s)
s d
i Hs (i transmits)
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ßs the retransmission probability

• A collision occurs if two or more transmissions
  overlap at the receiver.
• No capture effect is considered
• Vs the vulnerable period during which a hidden
  node of s can cause collision at the receiver d
• where TH(s), TPs and TRTS are the transmission
  times for header, payload and RTS packets
  repectively
• Thus,
• where lsd is the packet error rate between node
  s and d.

ßs 1-
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Putting All Together

• Given ?s, Vs, lsd,
• Next we solve ETi and bi at node i

ßs 1-
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Average Tx Time ETi

• ETi is the sum of four components
• di Avg of the minimum successful transmission
  times for a node-is paket
• ui Avg of the minimum successful transmission
  times of packets sent by other nodes between
  successive packets of node-i
• bi Avg back-off time spent by node-i
• ci Avg time spent due to collisions, if any
  (regardless of whether I is involved or not)
• Only consider the basic access. For RTS/CST,
  those components can be computed similarly

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di and bi

• The following holds by definition
• ? is the slot duration
• m is the number of retries
• Wn denotes the average contention window size at
  the n-th retry

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ui successful tx time of others(1)

• qi Probability of successful transmission by a
  node-i
• qi (1- ßi)(1-?i) ai''
• Qi the random variable that represents the
  number of successful packets transmitted by other
  N-1 nodes between two successful transmissions of
  node-i
• where tk,i is the time taken by the k-th
  successful packet belonging to one of N-1 other
  nodes
• To compute Etk,i, we need the probability gj,i
  that a successful packet belongs to j given it
  does not belong to i
• Then,

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ui successful tx time of others(2)

• To compute EQi, we need the probability ?i that
  the next transmission is a successful
  transmission by node-i
• Since Qi is a geometric random variable,
• Finally,

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ci collision time

• xi Pa successful transmission by node-i at
  least one node in Hi has transmitted
• yi Pan unsuccessful transmission is made at
  least one node in Hi has transmitted
• The number of collisions seen by node-i before it
  can successfully transmit is geometric with
  parameter xi / (xi yi).
• Thus,
• where wi is average transmission time of the
  largest packets plus ACK timeout

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Throughput and Delay

• Finally,
• Saturation throughput
• Delay for a node i with incoming traffic at rate
  ?i, the mean delay (queueing plus service) is

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Outline

• Overview of Bianchis model
• Analytical model to quantify the throughput and
  delay performance of individual users
• Applications of the model to better understand
  the performance of CSMA/CA based networks
• Impacts of Tx Power, Traffic, RTS/CTS and CW
• A Heuristic Measure of Contention - ECI
• Discussions

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Discussions

• Never consider interfering links
• Not justify that ai'' can be computed by
  Bianchis model
• Topologies in experiments are too simple
• Communication pairs are separated far away
• ECI is NOT easily computed by using local
  information