A bibliography on applications of random walks in theoretical chemistry and physics

Liyanage, Liwan; Gulati, Chandra; Hill, James M.

doi:10.1016/0378-4487(82)80019-8

Cited by 8 publications

(6 citation statements)

References 254 publications

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“…However, it diverges at z = 1 when m1 = 0. Thus, the singularity of P (0, s | z) at z = 1 comes only from the first term of the sum given by (16). It is convenient therefore to separate out the singular and non-singular parts of P (0, s | z) as follows…”

Section: Appendix a Proof Of Lemmamentioning

confidence: 99%

“…is holomorphic at z = 1. The first term involved in (17) corresponds to the term m1 = 0 in (16), and the second term, ϕN ( s, z), corresponds to the sum 1 ≤ m1 ≤ N − 1.…”

Section: Appendix a Proof Of Lemmamentioning

confidence: 99%

“…In addition, these results often provide lower and upper bounds on system performance and not a closed form analytical evaluation [14,3,19]. Instead, our take in this paper is to obtain a fundamental insight into random walk performance by constructing an analytical model that owes much to the powerful analytic tools developed in the physics community [15,17,16]. In particular, we address here the problem of data gathering in WSNs comprised of a large number of sensor nodes and a smaller number of sink nodes to gather, process and control data.…”

Section: Introductionmentioning

confidence: 99%

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Random Walk Based Routing Protocol for Wireless Sensor Networks

Mabrouki¹,

Lagrange

Froc³

2007

Proceedings of the 2nd International ICST Conference on Performance Evaluation Methodologies and Tools

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In recent years, design of wireless sensor networks using methodologies and mechanisms from other disciplines has gained popularity for addressing many networking aspects and providing more flexible and robust algorithms. We address in this paper the problem of random walk to model routing for data gathering in wireless sensor networks. While at first glance, this approach may seem to be overly simplistic and highly inefficient, many encouraging results that prove its comparability with other approaches have been obtained over the years. In this approach, a packet generated from a given sensor node performs a random motion until reaching a sink node where it is collected. The objective of this paper is to give an analytical model to evaluate the performance of the envisioned routing scheme with special attention to two metrics: the mean system data gathering delay and the induced spatial distribution of energy consumption. The main result shows that this approach achieves acceptable performance for applications without too stringent QoS requirements provided that the ratio of sink nodes over the total number of sensor nodes is carefully tuned.

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Section: Appendix a Proof Of Lemmamentioning

confidence: 99%

“…is holomorphic at z = 1. The first term involved in (17) corresponds to the term m1 = 0 in (16), and the second term, ϕN ( s, z), corresponds to the sum 1 ≤ m1 ≤ N − 1.…”

Section: Appendix a Proof Of Lemmamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Random Walk Based Routing Protocol for Wireless Sensor Networks

Mabrouki¹,

Lagrange

Froc³

2007

Proceedings of the 2nd International ICST Conference on Performance Evaluation Methodologies and Tools

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“…Of course, the point of view does not always concern spectral aspects. We mention the two surveys [60, 128] and the bibliography [80], and we point out a few papers: [66, 67, 69, 70, 96, 97, 98] for infinite lattice-type graphs and [61, 62, 72, 112] for trees and free products.…”

Section: Some Remarks On Applications In Chemistry and Physicsmentioning

confidence: 99%

A Survey on Spectra of infinite Graphs

Mohar

Woess

1989

Bulletin of the London Mathematical Society

252

190

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“…Moreover, most of the works concentrate on the evaluation of the mean value of the data delivery delay [13], which makes difficult to get statistically robust conclusions about the relevance of the random walk efficiency. Instead, our take in this paper is to obtain a complete insight into the data delivery delay induced by a random walk by constructing an analytical model that owes much to the powerful analytic tools developed in the physics community [20], [21], [24]. In particular, this model enables us to study both the central tendency and the dispersion of the data delivery delay through close form derivations.…”

Section: Introductionmentioning

confidence: 99%

On the Data Delivery Delay taken by Random Walks in Wireless Sensor Networks

Mabrouki

Froc

Lagrange

2008

2008 Fifth International Conference on Quantitative Evaluation of Systems

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In recent years, the use of random walk techniques in wireless sensor networks has attracted considerable interest among numerous research efforts. The popularity of this approach is attributed to the natural properties of random walks such as locality, simplicity, low-overhead and inherent robustness. However, throughout the variety of research works that assess the effectiveness of random walk techniques, most results are derived from a qualitative view or by means of simulations. Furthermore, when analytical tools are used, the obtained results often provide bounds on various performance metrics of interest, which may have little consequences for practical applications. Instead, our goal in this paper is to quantify the effectiveness of such techniques based on the derivation of closed-form expressions. In particular, we focus on the data delivery delay taken for the random walk to deliver messages from sensor to sink nodes and study its statistics through closed-form derivations.

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A bibliography on applications of random walks in theoretical chemistry and physics

Cited by 8 publications

References 254 publications

Random Walk Based Routing Protocol for Wireless Sensor Networks

Random Walk Based Routing Protocol for Wireless Sensor Networks

A Survey on Spectra of infinite Graphs

On the Data Delivery Delay taken by Random Walks in Wireless Sensor Networks

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