Spatial node distribution of the random waypoint mobility model with applications

Hyytiä, Esa; Lassila, Pasi; Virtamo, Jorma

doi:10.1109/tmc.2006.86

Cited by 298 publications

(200 citation statements)

References 17 publications

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“…Among many mobility models in the literature, the random waypoint model is commonly used in ad hoc networks and is analyzed in depth by Bettstetter et al [37] and Hyytiä et al [38]. Future work will investigate the behaviors due to different mobility models.…”

Section: Resultsmentioning

confidence: 99%

The Critical Grid Size and Transmission Radius for Local-Minimum-Free Grid Routing in Wireless Ad Hoc and Sensor Networks

Yi¹,

Wan²,

Su³

et al. 2010

The Computer Journal

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In grid routing, the plane is tessellated into equal-sized square cells. Two cells are called neighbor cells if they share a common edge, and two nodes are called routing neighbors if they are in neighbor cells and within each other's transmission range. If communication parties are in the same cell, packets can be transmitted directly; otherwise, packets are forwarded to routing neighbors that are in cells closer to destination cells. As a greedy strategy, grid routing suffers the existence of local minima at which no neighbor nodes exist for relaying packets. To guarantee deliverability, in this paper, we investigate two vital parameters of grid routing, called the grid size and the transmission radius. Assume that nodes are represented by a Poisson point process with rate n over a unit-area square, and let l denote the grid size and r the transmission radius. First, we show that if l = β ln n/n for some constant β and r = √ 5l, then β = 1 is the threshold for deliverability. In other words, there almost surely do not exist local minima if β > 1 and there almost surely exist local minima if β < 1. Next, for any given β > 1, we give sufficient and necessary conditions to determine the critical transmission radius (CTR) for deliverability. Then, we show that as β ∼ = 1.092, the CTR r ∼ = 2.09 √ ln n/n is the minimum over all β > 1. Simulation results are given to validate this theoretical work.

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Section: Resultsmentioning

confidence: 99%

The Critical Grid Size and Transmission Radius for Local-Minimum-Free Grid Routing in Wireless Ad Hoc and Sensor Networks

Yi¹,

Wan²,

Su³

et al. 2010

The Computer Journal

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show abstract

“…1) Shortest paths and lower bound: Scalar flux for the shortest paths (SP) is straighforward to compute also in this case (cf., [24]), yielding the maximum at the origin,…”

Section: B Unit Squarementioning

confidence: 99%

Near-Optimal Load Balancing in Dense Wireless Multi-Hop Networks

Hyytiä

Virtamo²

2008

2008 Next Generation Internet Networks

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Abstract-We consider the load balancing problem in wireless multi-hop networks. In the limit of a dense network, there is a strong separation between the macroscopic and microscopic scales, and the load balancing problem can be formulated as finding continuous curves ("routes") between all source-destination pairs that minimize the maximum of the so-called scalar packet flux ("traffic load"). In this paper we re-formulate the problem by focusing entirely on the so-called d-flows (vector flow field of packets with a common destination x) and by looking at the equation these flows have to satisfy. The general solution to this equation can be written in terms of a single unknown scalar function, ψ(r, x), related to the circulation density of the dflow, for which function the optimization task can be presented as a problem of variational calculus. In this approach, we avoid completely dealing with systems of paths and calculating the load distribution resulting from the use of a given set of paths. Once the optimal solution for ψ(r, x) is found the corresponding paths are obtained as the flow lines of the d-flows. In the example of a unit disk with uniform traffic demands we are able to find a set of paths which is considerably better than any previously published results, yielding a low maximal scalar flux and an extraordinarily flat load distribution. We further illustrate the methodology for a unit square with comparable improvements achieved.

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“…The probability density of finding a user situated at a distance x of the convex cluster center C 1 and in a circular sub-cell of radius r i placed at a distance d i of the service area center is defined by [5]: The arrival rate s a ðC i Þ of a user in a sub-cell C i…”

Section: Probability Densitymentioning

confidence: 99%

Optimal performance of heterogeneous networks based on the bit rate

et al. 2016

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Networks LTE(4G) and Wi-Fi complementarity establish a heterogeneous system of wireless and mobile networks. We study and analyze the optimal performances of this heterogeneous system based on the bit rate, the blocking probability and user connection loss. Random Waypoint is the user mobility model. User's provided mobile terminal equipped with multiple accesses interfaces. We have developed a Markov chain to estimate the performances obtained from the heterogeneous networks system, which allowed us to propose an average bit rate value in a sub-zone of this system then the average blocking probability user connection in this zone. We have also proposed a sensitivity factor of maximal decrease of these selection network parameters. This factor informs about the heterogeneous networks congestion and dis-congestion system.

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Spatial node distribution of the random waypoint mobility model with applications

Cited by 298 publications

References 17 publications

The Critical Grid Size and Transmission Radius for Local-Minimum-Free Grid Routing in Wireless Ad Hoc and Sensor Networks

The Critical Grid Size and Transmission Radius for Local-Minimum-Free Grid Routing in Wireless Ad Hoc and Sensor Networks

Near-Optimal Load Balancing in Dense Wireless Multi-Hop Networks

Optimal performance of heterogeneous networks based on the bit rate

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