Modeling the Performance of Wireless Sensor Networks

1
Modeling the Performance of Wireless Sensor
Networks

• (CS710) Special Issues on Computer Architecture
• C.-F. Chiasserini and M. Garetto
• IEEE INFOCOM 2004
• 4 November 2004
• Presented by Dongwook Kim

2
Contents

• Introduction
• System description and assumptions
• System model
• Results
• Conclusions and future work

3
Introduction (1/2)

• Efficient use of energy in wireless sensor
  networks
• The limited availability of energy within network
  nodes
• A node with no energy can cease sensing and
  routing data and degrade the coverage and
  connectivity level of the entire network
• Development of Markov model of a sensor network
  whose nodes may enter a sleep mode
• Low-power consumption and reduced operational
  capabilities in sleep
• Investigation of the system performance in
  presence of on-off sleep cycles
• Energy consumption, network capacity, data
  delivery delay

4
Introduction (2/2)

• Markov chain
• A discrete-time stochastic process with the
  Markov property
• A sequence X1, X2, X3, of random variables
• The domain of these variables is state space
• In field of computing, a model of sequences of
  events where the probability of an event
  occurring depends upon the fact that a preceding
  event occurred
• Markov property
• The probabilities of discrete states in a series
  depend only on the properties of the immediately
  preceding state or the next preceding state
• With the value of Xn being the state at time n,
  if the conditional distribution of Xn1 on past
  states is a function of Xn alone

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System description and assumptions (1/4)

• Network Topology
• A network composed of N stationary, identical
  sensor nodes
• Sensors are uniformly distributed over a disk of
  unit radius (1)
• The sink node is located at the center of the
  disk
• All nodes have a common maximum radio range r
• For any sensor, there exists at least one path
  connecting the sensor to the sink
• All sensors have a buffer of infinite capacity
• The time is divided into time slots of unit
  duration
• Transmission/reception of each data unit takes
  one time slot
• The wireless channel is error-free

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System description and assumptions (2/4)Sensor
behavior

• Two operational states active and sleep
• Active state is divided into three operational
  states transmit, receive, idle
• Sensor state in terms of cycles active (A) and
  sleep (S) phase
• Active phase follows geometric dist. with p
• Initial phase R can transmit, receive or idle
• Possible phase N can only transmit its buffer
  data
• Sleep phase follows geometric dist. with q

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System description and assumptions (3/4)Data
routing (Network)

• Sensors have knowledge of their neighboring
  nodes, as well as of the possible routes to the
  sink
• Each sensor constructs its own routing table
  where it maintains up to M routes
• Energy consumption in use of generic route

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System description and assumptions (4/4)Channel
access (MAC)

• The transmission is successful if
• Channel contention
• Collision free in data
• CSMA/CA mechanism with handshaking (MACA and
  MACAW)

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System model (1/12)Sensor model 1/4

• Modeling of the behavior of a single sensor by
  developing a discrete-time Markov chain (DTMC)
  model

j
i
(1) W all next-hops are unable to receive
because they are in phases S or N (2) F at least
one next-hop is in phase R (3) w, f
probabilities of the each state
(1) Phase (S, R, N) (2) The number of data units
stored in the sensor buffer 0 infinity (3)
Different phases are indexed with data
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System model (2/12)Sensor model 2/4

• P is transition matrix whose element P(s0, sd)
• Input parameters
• p (active ? sleep), q (sleep ? active), g (data
  generation prob.)
• , - the prob. that a data unit is
  received, transmitted in a time slot
• Data unit transmission is in phase R and N only

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System model (3/12)Sensor model 3/4

• Stationary distribution of the complete DTMC by
• The average number of data units generated in a
  time slot
• The sensor throughput T, the average number of
  data units forwarded by the sensor in a time slot
• The average buffer occupancy

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System model (4/12)Sensor model 4/4

• Validation of our sensor model by computing the
  unknown parameters
• r 0.25, N 400, p q 0.1, g 0.005 (a
  heavy load condition)

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System model (5/12)Network model 1/2

• Average generation rate (external arrival rate)
  of the generic sensor i, total arrival rate
  at the sink that is the network capacity C
• Derivation of internal arrival rate (average
  transmission rate) at each sensor , we use
  flow balance equations
• R is the matrix of transition probabilities
  between sensors of network
• R(i, j) represents the fraction of outgoing
  traffic of sensor i that is sent to its next-hop j

Ni,j The set of next-hops that have higher
priority than j in the routing table of i K A
normalization factor
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System model (6/12)Network model 2/2

• Validation
• Network load 0.6
• Each point in the plot stands for an element of
  vector

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System model (7/12)Interference model 1/3

• Computation of the parameter for each node
• If there is no contention, would be equal to
  1
• Example for estimating the parameter of node
  A
• Two next-hops, B and C
• (X,Y) denotes the transmission form the node X to
  Y
• (D,E), (E,A), (H,C), (F,G) is total interferers
• (H,I) is partial interferers
• It does not prevent A from sending data to B

average transmission rate between n and its
generic receiver m
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System model (8/12)Interference model 2/3
(D,E), (E,A)

• Estimate of the generic sensor i
• Computation of the probability that a
  transmission in which n is involved as either
  transmitter or receiver, totally inhibits i s
  transmission
• The term is equal to 1 if there
  exists at least one next-hop of i within the
  transmission range of n
• The term is equal to 1 if n s
  transmission is a total interferer, otherwise it
  account for partial interferer

Violating (4)
(H,C), (F,G)
Violating (5)
(H,I)
If the next-hops of i outside the transmission
rage of n are also unable to receive because they
are in phases S or N, it is total interferer
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System model (9/12)Interference model 3/3

• Then,
• This value is a transmission probability
  conditioned
• The sensor buffer is not empty
• At least one-next hop is available
• The correct values of to be used should
  also be conditioned

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System model (10/12)Fixed Point Approximation
(FPA)

• Use of FPA for obtaining a global system solution
  which does not require to get any parameter
  values from simulation
• We need to estimate parameters wi and fi
• The stationary probability of state W for sensor
  i
• The transition probability fi
• wi

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System model (12/12) Performance metrics

• Average transfer delay
• Average number of time slots required to deliver
  a data unit from a source node to the sink
• The network energy consumption per time slot
• The sum of the energy consumption at each node
  due to the operational state of the sensor
• The energy required to transmit and receive data
  units
• The energy spent during transitions from sleep to
  active state

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Results (1/2)

• System parameters
• r 0.25, N 400, p q 0.1, M 6
• p q corresponds to the case where a sensor
  spends an equal amount of time in sleep and in
  active mode
• Theoretical network load, G gNq/(pq), 0ltGlt1
• e.g., where g 0.005, N 400, G 1 (maximum
  network load)

Farthest source node from the sink
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Results (2/2)
p 0.1, M 3

• q/p 1 means that on average an equal number of
  nodes are in sleep and active mode
• The fraction of active sensors grows with
  increasing values of q/p

• as p increases, the transition frequency grows

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Conclusions and future work

• An analytical model which enables us to
  investigate the trade-offs existing between
  energy saving and system performance
• Consideration of variation with sensors dynamics
  in sleep/active mode
• Validation of our model with comparing simulation
  results
• Good accuracy
• First analytical model that specifically
  represents the sensor dynamics, while taking into
  account channel contention and routing issues