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A mobility-based load control scheme in Hierarchical Mobile IPv6 networks

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Abstract

By introducing a mobility anchor point (MAP), Hierarchical Mobile IPv6 (HMIPv6) reduces the signaling overhead and handoff latency associated with Mobile IPv6. In this paper, we propose a mobility-based load control (MLC) scheme, which mitigates the burden of the MAP in fully distributed and adaptive manners. The MLC scheme combines two algorithms: a threshold-based admission control algorithm and a session-to-mobility ratio (SMR)-based replacement algorithm. The threshold-based admission control algorithm gives higher priority to ongoing mobile nodes (MNs) than new MNs, by blocking new MNs when the number of MNs being serviced by the MAP is greater than a predetermined threshold. On the other hand, the SMR-based replacement algorithm achieves efficient MAP load distribution by considering MNs’ traffic and mobility patterns. We analyze the MLC scheme using the continuous time Markov chain in terms of the new MN blocking probability, ongoing MN dropping probability, and binding update cost. Also, the MAP processing latency is evaluated based on the M/G/1 queueing model. Analytical and simulation results demonstrate that the MLC scheme outperforms other schemes and thus it is a viable solution for scalable HMIPv6 networks.

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Notes

  1. That is, load balancing among HAs and security issues are beyond scope of this paper.

  2. Although the residence times are typically non-exponential in wireless/mobile networks, the analysis based on the simplified exponential assumption has been widely used [12–14], and provides useful mean value information.

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Acknowledgments

This work was supported by the Korea Research Foundation Grant funded by the Korean Government (KRF-2008-314-D00354).

Author information

Authors and Affiliations

  1. School of Electrical Engineering, Korea University, Seoul, South Korea

    Sangheon Pack

  2. School of Computer Science and Engineering, Seoul National University, Seoul, South Korea

    Taekyoung Kwon & Yanghee Choi

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  1. Sangheon Pack
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  2. Taekyoung Kwon
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  3. Yanghee Choi
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Corresponding author

Correspondence to Sangheon Pack.

Additional information

The preliminary version of this paper was presented at IEEE Global Telecommunications Conference (GLOBECOM) 2004, Dallas, USA, November 2004.

Appendix 1

Appendix 1

1.1 Derivation of π(i, j) in the TLC/MLC schemes

As shown in Fig. 7, the Markov chain for the TLC scheme (and the MLC scheme) has a state space, \(S=\{(i,\,j)| 0 \leq i \leq K, 0 \leq i+j \leq C\}\), and the following balance equations are established:

  1. (1)

    i = 0 and j = 0:

    $$ (\lambda_O+\lambda_N)\cdot \pi(0,0)=\mu_N \cdot \pi(1,0)+\mu_O \cdot \pi(0,1); $$
  2. (2)

    i = 0 and 0 < j < K:

    $$ (\lambda_O+\lambda_N+j \mu_O)\cdot \pi(0,j)=\lambda_O \cdot \pi(0,j-1) +\mu_N \cdot \pi(1,j)+(j+1)\mu_O \cdot \pi(0,j+1); $$
  3. (3)

    i = 0 and K≤j < C:

    $$ (\lambda_O+j \mu_O) \cdot \pi(0,j)=\lambda_O \cdot \pi (0,j-1)+\mu_N \cdot \pi(1,j)+(j+1)\mu_O \cdot \pi(0,j+1); $$
  4. (4)

    i = 0 and j = C:

    $$ C \mu_O \cdot \pi(0,C)=\lambda_O \cdot \pi(0,C-1); $$
  5. (5)

    0 < i < K and j = 0:

    $$ (\lambda_O+\lambda_N+i\mu_N)\cdot \pi(i,0)=\lambda_N \cdot \pi(i-1,0) +(i+1)\mu_N \cdot \pi(i+1,0)+\mu_O \cdot \pi(i,1); $$
  6. (6)

    0 < i < K and 0 < j < K−i:

    $$ \begin{aligned} (\lambda_O+\lambda_N+i \mu_N+j \mu_O) \cdot \pi(i,j)&=\lambda_N \cdot \pi(i-1,j)+\lambda_O \cdot \pi(i,j-1)\\ &+(i+1)\mu_N \cdot \pi(i+1,j)+(j+1)\mu_O \cdot \pi(i,j+1); \end{aligned} $$
  7. (7)

    0 < i < K and j = K−i:

    $$ \begin{aligned} (\lambda_O+i\mu_N+j \mu_O) \cdot \pi(i,j)&=\lambda_N \cdot \pi(i-1,j) +\lambda_O \cdot \pi(i,j-1)\\ &+(i+1)\mu_N\cdot \pi(i+1,j)+(j+1)\mu_O \cdot \pi(i,j+1); \end{aligned} $$
  8. (8)

    0 < i < K and K−i < j < C−i:

    $$ \begin{aligned} (\lambda_O+i \mu_N+j \mu_O)\cdot \pi(i,j)&=\lambda_O \cdot \pi(i,j-1)+(i+1)\mu_N \cdot \pi(i+1,j)\\ &+(j+1) \mu_O\cdot \pi(i,j+1); \end{aligned} $$
  9. (9)

    0 < i < K and j = C−i:

    $$ (i\mu_N+j\mu_O)\cdot \pi(i,j)=\lambda_O \cdot \pi(i,j-1); $$
  10. (10)

    i = K and j = 0:

    $$ (\lambda_O+K \mu_N)\cdot \pi(K,0)=\lambda_N \cdot\pi(K-1,0) +\mu_O \cdot \pi(K,1); $$
  11. (11)

    i = K and 0 < j < C−K:

    $$ (\lambda_O+K\mu_N+j \mu_O)\cdot \pi(K,j)=\lambda_O \cdot \pi(K,j-1)+ (j+1)\mu_O \cdot \pi(K,j+1); $$
  12. (12)

    i = K and j = C−K:

    $$ (K \mu_N+(C-K)\mu_O)\cdot \pi(K,C-K)=\lambda_O \cdot \pi(K,C-K-1). $$

Each balance equation can be represented as a form of \(\pi(i,\,j)=A\pi(i-1,\,j)+B\pi(i+1,\,j)+C\pi(i,\,j-1)+D\pi(i,\,j+1)\), where A, B, C, and D are constants. Then, the steady state probability can be computed using an iterative algorithm and the normalization condition, \(\sum\nolimits_{i=0}^{K} \sum\nolimits_{j=0}^{C-i} {\pi(i,j)}=1\). In the iterative algorithm, ɛ is a sufficiently small value and |S| represents the cardinality of S.

Iterative algorithm

  • Step 1: t is set to 0.

  • Step 2: For all (i, j) ∈S, πt(i, j) is initialized as 1/|S|.

  • Step 3: For all (i, j) ∈ S, \(\pi^{t+1}(i,j) \leftarrow \pi^{t}(i,j)\).

  • Step 4: For all \((i,j) \in S\), compute πt+1(i,j) by balance equations, \(\pi^{t+1}(i,\,j)=A \pi^{t}(i-1,\,j)+B \pi^{t}(i+1,\,j)+C\pi^{t}(i,\,j-1)+D\pi^{t}(i,\,j+1)\).

  • Step 5: For all (i, j) ∈ S, if |πt+1(i, j)−πt(i, j)| < ɛ, the iteration is terminated. Otherwise, \(t \leftarrow t+1\) and go to Step 3.

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Pack, S., Kwon, T. & Choi, Y. A mobility-based load control scheme in Hierarchical Mobile IPv6 networks. Wireless Netw 16, 545–558 (2010). https://doi.org/10.1007/s11276-008-0152-z

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