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 T d : Packet delivery delay. C d : Number of packet copies just before delivery. G d : 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 Absorbing Markov Chain (AMC) Number of copies in the network Absorption when destination receives the packet

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 C d : Expected number of transmissions G d :

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

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.