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Convergence in the Calculation of the Handoff Arrival Rate: A Log-Time Iterative Algorithm

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Abstract

Modeling to study the performance of wireless networks in recent years has produced sets of nonlinear equations with interrelated parameters. Because these nonlinear equations have no closed-form solution, the numerical values of the parameters are calculated by iterative algorithms. In a Markov chain model of a wireless cellular network, one commonly used expression for calculating the handoff arrival rate can lead to a sequence of oscillating iterative values that fail to converge. We present an algorithm that generates a monotonic sequence, and we prove that the monotonic sequence always converges. Lastly, we give a further algorithm that converges logarithmically, thereby permitting the handoff arrival rate to be calculated very quickly to any desired degree of accuracy.

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Correspondence to Dilip Sarkar.

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Keywords

  • Information System
  • Markov Chain
  • Wireless Network
  • Nonlinear Equation
  • Arrival Rate