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The handoff algorithm employed in a cellular network has a significant impact on overall network performance, but evaluation of handoff performance has for the most part been done using only crude approximations or brute-force computer simulation. We introduce a new discrete-time approach to analyze the performance of handoff algorithms based on pilot signal strength measurements. We derive exact analytical expressions and develop a recursive numerical procedure to evaluate handoff performance metrics for a mobile station moving along a straight-line trajectory in a cellular network employing hard handoff. The numerical procedure provides a computational solution to a level-crossing problem in discrete time. Our discrete-time approach provides valuable analytical insight into the performance impact of handoff algorithms. Moreover, our numerical procedure for discrete-time handoff analysis provides an accurate and efficient tool for the design and dimensioning of high-performance handoff algorithms. The accuracy of the numerical procedure is validated by simulation.