Fig. 1. Evolution of {S_t}_t and relay node buffer occupancy.

Fig. 2. Random walk on circle.

Fig. 3. Contact distance between two mobile nodes.

Fig. 4. Time-evolution of relay node buffer for random walk model over a circle for different values of ratio, .

Fig. 5. Mean relay buffer size as a function of the ratio for random direction mobility and for different value of R.

Fig. 6. Values of π_s obtained for the random direction model over a segment of length L. Various distributions for the speed were taken.

Fig. 7. Simulation results showing π_s for random waypoint model over a square of side-lengths L for different values of transmission range, R. Also shown are corresponding values from Section 5.2.

Fig. 8. Time-evolution of relay buffer for three relay nodes moving according to random waypoint model inside a square of side-length 4000 m, with fixed and symmetric source and destination node w.r.t. to square center. Here r_s = 0.9r_d (the stable case).

Fig. 9. Time-evolution of relay buffer for relay nodes moving according to random waypoint model inside a square of side-length 4000 m, with fixed and symmetric source and destination nodes w.r.t.to square center. Here r_s = 1.1r_d (the unstable case).

Fig. 10. Network throughput as function of number of relay nodes in square region of side-length 4000 m with fixed source and fixed destination nodes.

Fig. 11. Long-term arrival rate at queue m of relay node n from source node k as function of number of relay nodes N, where K = 4, M = 5, , and r_Sk=1.

Fig. 12. Probability of two-hop route as function of number of nodes. All nodes move according to random waypoint model inside square of side length 4000 m.

Fig. 13. Percentage of relative error between model in (41) and simulation as a function of r_s/r_d for different values of R and w and for r_d = 1, μ = 100 m, and v = 10 m/s.

Fig. 14. Normalized contact time distribution for different values of R/V and travel time T comparing with Eq. (45). Nodes move according to random direction model inside a square of side-length with L = 4000 m.

Fig. 15. Normalized contact time distribution. Nodes move according to the random waypoint model inside a square of side-length L = 4000 m.

The numerical values of the u(i) and v_f(i) for the random waypoint model

Validation of Eq. (46) for r_s/r_d = 0.99 and r_d = 10

Relative difference between mean buffer size at t and mean buffer size at cycle time for random waypoint

Relative difference between mean buffer size at t and mean buffer size at cycle time for random direction