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Outline
q Introduction q Queuing Network Model q Main Results q Deviation from Real Networks q Simulation Results
Queuing Delay and Achievable Throughput in Random Access Wireless - - PowerPoint PPT Presentation
Queuing Delay and Achievable Throughput in Random Access Wireless - - PowerPoint PPT Presentation
Queuing Delay and Achievable Throughput in Random Access Wireless Ad Hoc Networks Nabhendra Bisnik and Alhussein Abouzeid Rensselaer Polytechnic Institute Troy, NY bisnin@rpi.edu, abouzeid@ecse.rpi.edu Outline q Introduction q Queuing
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Outline
q Introduction q Queuing Network Model q Main Results q Deviation from Real Networks q Simulation Results
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Important Questions
q Important questions:
q How throughput scales with network size? q How delay scales with network size? q Relation between delay and throughput? q What are the tradeoffs?
q We developed queuing network models to
analyze delay and throughput of multihop wireless ad hoc networks
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Delay in Multihop Wireless Networks
q End-to-end delay is sum of queuing and
transmission delays at intermediate nodes
q Queuing delay depends on
q Packet arrival process – how much traffic is
handled by network?
q Node density – how many interferers are there? q MAC protocol – how the channel is shared? q Traffic pattern – how many times a packet is
transmitted before it reaches destination
q Modeling all the factors is quite challenging
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Throughput in Multihop Wireless Networks
q Maximum achievable per node throughput of
a network is the maximum rate at which the nodes of a network may generate traffic while keeping delay finite
q Maximum achievable throughput is inversely
proportional to
q Average time a node takes to serve a packet q Average number of flows served by a node
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Related Work
q Gupta and Kumar “Capacity of Wireless
Networks”
q Under optimal scheduling, per node throughput
scales as
q E.Gamal et al “Throughput Delay Trade-off in
Wireless Networks”
q D(n) = (n T(n)) q Assuming that:
q Packet size scales with throughput q Infinite backlog at source q Centralized and deterministic scheduling
q Delay is proportional to number of hops traversed
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Outline
q Introduction q Queuing Network Model q Main Results q Deviation from Real Networks q Simulation Results
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Network and Interference Model
q Network consists of n nodes that are distributed
uniformly and independently distributed over a unit torus
q Transmission rate of each node = W bits/sec q Interference Model: node i can successfully
forward a packet to node j only if
q rij r(n) q rjk > r(n) nodes k transmitting simultaneously with i
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q : Neighbors of A – All nodes within distance r(n) of A q + : Interfering neighbors of A – All nodes within distance 2r(n)
- f A
A
Transmission of A is guaranteed to be successful if none of the interfering neighbors of A transmit simultaneously
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MAC Model
q Before transmitting a packet each node counts
down a random timer
q The duration of the time is exponentially
distributed with mean 1/
q Once the timer of a node expires it starts
transmitting and at the same instant the timers of all interfering nodes is frozen
The MAC model captures the collision avoidance mechanism of IEEE 802.11 and is still mathematically tractable
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Traffic Model
q Each node is source, destination and relay of traffic q Size of each packet is fixed and equals L bits q Each node generates packets at rate packets/sec q When a node receives a packet from its neighbor:
q The packet is absorbed by the node with probability p(n)
(absorption probability)
q The packet is forwarded to a randomly chosen neighbor with
probability 1-p(n)
q In other words, the fraction of packets received by a
node that are destined to it equals p(n)
p(n) characterizes the degree of locality of traffic – Low p(n) average hops between a source destination pair is large
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Queuing Network Model
q In order to characterize delay, ad hoc network
modeled as G/G/1 queuing network
q Each node of the network is a station of
queuing network
q Incorporate queuing delays at source and
relay in delay analysis
q Diffusion approximation used to analyze the
resulting queuing network
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The queuing network
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Outline
q Introduction q Queuing Network Model q Main Results q Deviation from Real Networks q Simulation Results
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Main Results
q Mean service time ( )– Average time it takes for
a node to serve a packet
Where,
Service time in absence
- f interference
Term introduced by interfering neighbors
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q Transmitter and receiver, in absence of interference q Service time = Wait for timer to expire + transmission time =
Interpreting the Service Time Result
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q Now suppose there are k interferes, each with packet arrival rate
- q Fraction of time for which the channel is occupied by the
interferers = q The fraction of time the channel is available to the transmitter = q In our model = i and k = 4nA(n), therefore
Interpreting the Service Time Result
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Main Results
q Average end-to-end delay ( ) – Average time in
which packet reaches the destination after being generated at source
Where,
The value of end-to-end delay is governed by and SCVs of service and inter-arrival times.
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Main Results
q Maximum achievable throughput ( )
- r,
Where,
As expected, MAT varies inversely with mean path length, node density and communication radius of nodes
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Comparison with Kumar-Gupta Results
q When parameters of our model are comparable
to that of Kumar-Gupta model i.e. and
- r
The bound is similar to Gupta-Kumar bound but is not achievable. This is expected as channel capacity is wasted due to random access.
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Outline
q Introduction q Queuing Network Model q Main Results q Deviation from Real Networks q Simulation Results
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Deviation from Real Networks
q The MAC model does not take into account the
packet collisions – an essential feature of random access MAC
q We assume all interfering nodes freeze their
transmission timer as soon as a packet transmission begins.
q In reality a node freezes its timer only when it
“hears” a transmission
q Thus, a transmission is successful if all
interfering neighbors hear the transmission before their timers expire
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Probability of Success
q If a node has I interfering neighbors then q The expected probability of success, Ps is given
by
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Improved Performance Bounds
q Taking packet collision into account, for a more
practical MAC the average service time is bounded by
q Maximum achievable throughput is bounded by
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Plots of the Deviation
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Optimal Timer Rate
q The optimal timer rate, , for which is
maximized is solution of this equation
q If ,
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Outline
q Introduction q Queuing Network Model q Main Results q Deviation from Real Networks q Simulation Results
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Simulation Results
Comparison of theoretical and simulation results
Diffusion Approximation yields pretty good results.
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Conclusion and Future Work
q Developed queuing network models for multihop
wireless ad hoc networks
q Used diffusion approximation to evaluate average
delay and maximum achievable per-node throughput
q Investigated the deviation of results from real life
networks
q Future work: extend analysis to many to one
cases, taking deterministic routing into account
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