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Ahmad Al Hanbali INRIA Sophia-Antipolis Maestro team Co-authors: Philippe Nain and Eitan Altman.

Performance of Ad Hoc Networks with Two-Hop Relay Routing and Limited Packet Lifetime. Ahmad Al Hanbali INRIA Sophia-Antipolis Maestro team Co-authors: Philippe Nain and Eitan Altman. Two-hop relay protocol with limited copy lifetime. TTL starts. TTL expires. Performance Metrics.

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Ahmad Al Hanbali INRIA Sophia-Antipolis Maestro team Co-authors: Philippe Nain and Eitan Altman.

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  1. Performance of Ad Hoc Networks with Two-Hop Relay Routing and Limited Packet Lifetime Ahmad Al Hanbali INRIA Sophia-Antipolis Maestro team Co-authors: Philippe Nain and Eitan Altman.

  2. Two-hop relay protocol with limited copy lifetime TTL starts TTL expires

  3. Performance Metrics • Td : Packet delivery delay. • Cd : Number of packet copies just before delivery. • Gd : Total number of packet transmissions before delivery.

  4. Assumptions • Nodes inter-meeting times are i.i.d. exponential r.v.s of mean 1/λ. • TTL of packet copies are i.i.d exponential r.v.s of mean 1/μ. • Number of nodes N+1. • When TTL expires, node drops its copy. • The source has one packet to transmit. • Packet of the source never timeouts.

  5. Number of copies in the network Absorption when destination receives the packet Absorbing Markov Chain (AMC)

  6. Fundamental Matrix of the AMC • P the transition probability matrix of the embedded Markov chain is of form • Def: The fundamental matrix M=(I-Q)-1 . • Theorem: m(i,j) the (i,j)-entry of M gives the expected number of visits to state j before absorption, given that the chain starts at i.

  7. Results • Expected delivery delay: • Distribution of number of copies Cd : • Expected number of transmissions Gd:

  8. Tab: Relative error between the model and the simulation of RWP and RD for R/L=0.5% and μ=0.0001. Model Validation

  9. K-limited Two-hop routing Reference [1] A. Al Hanbali, P. Nain, E. Altman, “Performance Evaluation of Packet Relaying in Ad Hoc Networks”, INRIA RR-5860, March 2006.

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