Fig. 1. LU area for (a) distance-based scheme (D = 1) and (b) direction-based scheme (D = 2). The LU area is formed by the gray cells.

Fig. 2. Hexagonal architecture for wireless cellular networks.

Fig. 3. Six moving directions of the MT in the hexagonal cellular architecture.

Fig. 4. (a) The orientation of the LU area is d₀ and the MT moves out of the LU area in direction d₅; (b) a new LU area is formed orientated in direction d₅ with the same shape.

Fig. 5. The adaptive LU areas designed by heuristic algorithm for different mobility patterns, (a) IID, (b) directional, (c) turning, (d) ping-pong, (e) h-spin, and (f) t-spin.

Fig. 6. Designed LU areas for directional pattern under different call-to-mobility ratios, (a) ρ = 1, (b) ρ = 0.5, and (c) ρ = 0.2.

Fig. 7. Designed LU areas for h-spin pattern under different call-to-mobility ratios, (a) ρ = 1, (b) ρ = 0.5, and (c) ρ = 0.2.

Fig. 8. Designed LU area for ping-pong pattern with different cost ratio c_u/c_p, (a) c_u/c_p = 3, (b) c_u/c_p = 10, and (c) c_u/c_p = 15.

Fig. 9. Designed LU area for t-spin pattern with different cost ratio c_u/c_p, (a) c_u/c_p = 3, (b) c_u/c_p = 10, and (c) c_u/c_p = 15.

Fig. 10. Effect of the variance value, V of the cell residence time distribution on the location management cost for directional pattern under different call-to-mobility ratios.

Fig. 11. Total location management cost versus call-to-mobility ratio for ALU, DSLU and DRLU under different mobility patterns using blanket paging strategy, (a) IID, (b) directional, (c) turning, (d) ping-pong, (e) h-spin, and (f) t-spin.

Fig. 12. Total location management cost versus call-to-mobility ratio for ALU, DSLU and DRLU under different mobility patterns using optimal sequential paging strategy (D = 2), (a) IID, (b) directional, (c) turning, (d) ping-pong, (e) h-spin, and (f) t-spin.