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Analytical Studies of Energy–Time Efficiency of Blocking Expanding Ring Search

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Abstract

This paper investigates the energy–time efficiency of the Blocking Expanding Ring Search algorithms (BERS) using an extended graph model. BERS is an energy efficient alternative that was developed recently based on the Expanding Ring Search (ERS). ERS is widely applied in reactive routing protocols for mobile ad hoc networks. Most studies in this area focus on minimising either energy consumption or search latency, but few look into the strong correlation between the energy saving and the increased latency incurred. We analyse, in this study, the concurrency mechanism of BERS and have developed BERS*, an enhanced scheme based on BERS. Our results show that, among the three schemes (BERS*, BERS and ERS), BERS* incurs the least latency when the hop number of the route nodes is greater than 3, and has achieved the best performance in terms of energy–time efficiency when the hop number of the route nodes is greater than 7. We have also discovered the conditions that allow collective optimisation of BERS* and ERS.

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Abbreviations

BERS:

Blocking expanding ring search

BERS*:

Enhanced blocking expanding ring search

END:

Flood termination instruction

ERS:

Expanding ring search

TTL:

Time to live

MANET:

Mobile ad hoc network

RREQ:

Route request

RREP:

Route reply

d, D:

Destination

E x :

Energy consumption for x

H :

Hop number

H r :

Hop number of a route node

MAX H :

Maximum number of rings

N i , N j :

Neighbour nodes

s, S:

Source

T x :

Latency for x

n i :

Number of nodes at ring i

n r :

Number of route nodes

(u, v):

Direct communication channel between u and v

uv:

One-hop transmission from u to v

u→→ v:

Multi-hop propagation from u to v

uu:

u Waiting for 1 unit of time

u→→ u:

u Waiting for ≥ 2 units of time

x || y:

Events x and y take place in parallel

ud || vd:

Parallel events with a collision at d

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Correspondence to Ida M. Pu.

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Pu, I.M., Shen, Y. Analytical Studies of Energy–Time Efficiency of Blocking Expanding Ring Search. Math.Comput.Sci. 3, 443–456 (2010). https://doi.org/10.1007/s11786-010-0038-1

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