shizhen zhao, luoyi fu , xinbing wang department of electronic engineering
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Fundamental Relationship between Node Density and Delay in Wireless Ad Hoc Networks with Unreliable Links. Shizhen Zhao, Luoyi Fu , Xinbing Wang Department of Electronic Engineering Shanghai Jiao Tong University, China Qian Zhang Department of Computer Scien Engineering Hong Kong, China. - PowerPoint PPT PresentationTRANSCRIPT
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Fundamental Relationship between Node Density and Delay in Wireless Ad Hoc Networks with Unreliable LinksShizhen Zhao, Luoyi Fu, Xinbing WangDepartment of Electronic EngineeringShanghai Jiao Tong University, China Qian ZhangDepartment of Computer Scien EngineeringHong Kong, China
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Fundamental Relationship between Node Density and Delay in Wireless Ad Hoc Networks with Unreliable Links*Outline BackgroundLarge-scale NetworksRandom Connection ModelFirst Passage Percolation Model Network Model & Objective Main Results and Intuitions Simulation Results Concluding Remarks
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*Large-scale Networks Network size is growing.Number of users is growingNeed more base stations
Unreliable links.Communication between adjacent nodes is not always available
Cause of the unreliability.Increased interferenceSevere environmentSleep-wake scheduling
Fundamental Relationship between Node Density and Delay in Wireless Ad Hoc Networks with Unreliable Links
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*Random Connection Model (RCM) Ramdom Connection ModelStationary point process (e.x. Poisson point process)Connection function A non-increasing function h() defined on positive reals An edge exists between nodes x1 and x2 with probability h(|x1-x2|)
Phase transition.Condition:
There exists a critical node density , such that If , an infinite large cluster exists. if , all clusters are finite almost surely.
Fundamental Relationship between Node Density and Delay in Wireless Ad Hoc Networks with Unreliable Links
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*Random Connection Model (RCM) Poisson Boolean ModelSpecial case of RCM with
Two nodes are connected if and only if their distance is smaller or equal to
Fundamental Relationship between Node Density and Delay in Wireless Ad Hoc Networks with Unreliable Links
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*First Passage Percolation ModelFirst Passage Percolation Model.Assign a random variable to each link .Define the passage time for a path :
Define the first passage time between nodes and :
Remark.Use first passage time to model delayUse the random variable to model the unreliability of links
Fundamental Relationship between Node Density and Delay in Wireless Ad Hoc Networks with Unreliable Links
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*OutlineBackgroundNetwork Model & ObjectiveNetwork ModelObjectiveMain Results and IntuitionsSimulation Results Concluding RemarksFundamental Relationship between Node Density and Delay in Wireless Ad Hoc Networks with Unreliable Links
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*Network Model-ConnectivityDelay is a basic concern in designing and implementing large scale wireless networks. However, the premise of communication is connectivity.
In large scale wireless network with unreliable links, it is too costly to maintain full connectivity. Therefore, we consider a slightly weaker connectivity-connectivity in percolation sense.Random Connection Model (RCM)Instantaneous and Long-term ConnectivityInstantaneous Critical Density ( ) and Long-term Critical Density ( )Fundamental Relationship between Node Density and Delay in Wireless Ad Hoc Networks with Unreliable Links
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*Network Model-ConnectivityFundamental Relationship between Node Density and Delay in Wireless Ad Hoc Networks with Unreliable Links
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{
Cause of Delay
Waiting Delay
Scheduling and Routing
Network Resources
Propagation Speed
Lack of Instantaneous Connectivity
}
Propagation Delay(Denoted by )
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*Network Model-DelayUsually, the time needed for links to change state is much larger than the time scale used in scheduling, routing, etc. Therefore, we assume that it won't take much time for transmission between connected node pairs. In this paper, we mainly focus on the delay caused by the lack of instantaneous connectivity which is closely related to the node density in such a netwok.
Fundamental Relationship between Node Density and Delay in Wireless Ad Hoc Networks with Unreliable Links
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*Network Model-DelayWe assign the delay to each link in the following way,
where is the connection function, and is the length of link .Applying first passage percolation model here, we could define the first passage time for node and :
Fundamental Relationship between Node Density and Delay in Wireless Ad Hoc Networks with Unreliable Links
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*Objective Previous result:
We study:Detailed relationship between and node density . Two steps: Ignore the propagation delay ( ).Consider the propagation delay ( ).Fundamental Relationship between Node Density and Delay in Wireless Ad Hoc Networks with Unreliable Links
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*OutlineBackgroundNetwork Model & ObjectiveMain Results and IntuitionsMain resultsIntuitionsImpact of Propagation DelaySimulation Results Concluding RemarksFundamental Relationship between Node Density and Delay in Wireless Ad Hoc Networks with Unreliable Links
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*Main ResultsProperties of , There exists , such that For any , is a monotone decreasing function
Fundamental Relationship between Node Density and Delay in Wireless Ad Hoc Networks with Unreliable Links
0
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*Main ResultsUpper bound and lower bound of
is a constantg() is the connection function is the size of a cluster E() is the expectation
Fundamental Relationship between Node Density and Delay in Wireless Ad Hoc Networks with Unreliable Links
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*Intuitions-Upper Bound For two nodes and , the first passage time is bounded by the the passage time along any path connecting and .
least number of hopsaverage delay of one hopdistantce of one hopBasic idea: and are connected by a sequence of hops with distance smaller or equal to Fundamental Relationship between Node Density and Delay in Wireless Ad Hoc Networks with Unreliable Links
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*Intuitions-Upper Bound Existance of such pathsThe long-term critical density can be viewed as the critical density of the Poisson Boolean Model with transmission range
(Proposition 2 in [14]) Let be the critical density for the Poisson Boolean Model when the transmission range is , then
The critical density for is , and . Therefore, such a path exists.
Fundamental Relationship between Node Density and Delay in Wireless Ad Hoc Networks with Unreliable Links
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*Intuitions-Upper Bound Least Number of hops of such pathsScale the network up by , then each hop of such paths becomes , and
We can show that
Then, we can see that
Fundamental Relationship between Node Density and Delay in Wireless Ad Hoc Networks with Unreliable Links
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Intuitions-Lower Bound Waiting occurs at the boundry of a cluster
*MMMMMMMMMCluster to Cluster transmissionFundamental Relationship between Node Density and Delay in Wireless Ad Hoc Networks with Unreliable Links
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*Intuitions-Lower Bound Delay between and
Motivation: The minimum number of clusters between and gives a lower bound of delay
Let the size of a cluster be , then the minimum number of clusters is lower bounded by
number of clusters-1Fundamental Relationship between Node Density and Delay in Wireless Ad Hoc Networks with Unreliable Links
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*Impact of Propagation Delay Upper Bound The average delay of one hop changes
Lower Bound
The minimum number of clusters is lower boundedby
average delay of one hop changesFundamental Relationship between Node Density and Delay in Wireless Ad Hoc Networks with Unreliable Links
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*OutlineBackgroundNetwork Models & ObjectiveMain Results and IntuitionsSimulation Results without Propagation Delaywith propagation delayConcluding RemarksFundamental Relationship between Node Density and Delay in Wireless Ad Hoc Networks with Unreliable Links
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*Without Propagation DelayFundamental Relationship between Node Density and Delay in Wireless Ad Hoc Networks with Unreliable Links
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*With Propagation DelayFundamental Relationship between Node Density and Delay in Wireless Ad Hoc Networks with Unreliable Links
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*OutlineIntroductionK-hop Clustered Network ModelsMain Results and IntuitionsThe Impact of Mobility Concluding RemarksFundamental Relationship between Node Density and Delay in Wireless Ad Hoc Networks with Unreliable Links
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*Concluding Remarks We have studied the first passage delay of large scale network with unreliable links.
In two senarios (with propagation delay and without propagation delay), we sketch by excavating its properties;provide upper bound and lower bound to .
Fundamental Relationship between Node Density and Delay in Wireless Ad Hoc Networks with Unreliable Links
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Thank you !