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Computer simulation project. Consider again the mobility in cellular networks for case 4 described in this chapter, but this time, we want to simulate the handoff for three states: stop, variable speed, and constant speed. For the variable-speed case, assume that the mobile user moves with a constant acceleration of K1m/h. Assume 25 m/h ≤ k ≤ 45 m/h within city and 45 m/h ≤ k ≤ 75 m/h for highway. Let dB be the distance a vehicle takes to reach a cell boundary, ranging from −10 miles to 10 miles.

(a) Plot the probability of reaching a cell boundary for which a handoff is required. Discuss why the probability of reaching a boundary decreases in an exponential manner.

(b) Show that the probability of reaching a cell boundary for a vehicle that has a call-in progress is dependent on db.

(c) Show the probabilities of reaching a cell boundary as a function of a vehicle’s speed.

(d) Discuss why the probability of reaching a cell boundary is proportional to the vehicle’s speed and that the probability of requiring a handoff decreases.