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In wireless/mobile networks, users freely change their service points, while they are communicating with other users. In order to support the mobility of mobile nodes, Mobile IPv6 (MIPv6) is proposed by the Internet Engineering Task Force (IETF), in which a mobile node must inform its home agent the binding of its home address and the current care-of-address (CoA). The home agent forwards packets to CoA when it receives packets for the mobile node. There is a significant problem in MIPv6 due to its inability to support micromobility caused by long delays and high packet losses during a handoff. Hierarchical Mobile IPv6 (HMIPv6) is proposed to separate mobility into micromobility [within one domain or within the same mobility anchor point (MAP)] and macromobility (between domains or between MAPs). HMIPv6 reduces handoff latency by employing a hierarchical network structure and minimizing the location update signaling with external network. The two-layer network structure of HMIPv6 is very suitable for supporting the vertical handoff and the horizontal handoff in wireless overlay networks. Wireless overlay networks can consist of two layers. Functions of access routers can be implemented in low-layer networks and functions of MAPs can be implemented in high-layer networks. Or we can have an access router collocated with a low-layer network and an MAP collocated with a high-layer network. In either way, the micromobility in HMIPv6 is equal to the horizontal handoff in wireless overlay networks and the macromobility in HMIPv6 is equal to the vertical handoff in wireless overlay networks. However, a significant delay still occurs in macromobility management. This paper considers handover operations. We analyze the handoff delay and find that the DAD time represents a large portion of handoff delay. We also note that we can assign a unique on-link care-of address (LCoA) to each mobile node and switch between one-layer IPv6 and two-layer IPv6 addressing. By this way, we propose a Stealth-time HMIP (SHMIP) which can reduce the effect of the DAD time on the handoff delay and, thus, reduce the handoff time significantly. To further reduce packet losses, we also adopt prehandoff notification to request previous MAP to buffer packets for the mobile node. By simulations, - we show that the proposed scheme can realize low handoff delays and low packet losses during macromobility.