The design of hand off algorithms depends to a large extent on the user mobility pattern defined by the speed and direction of movement. For a fast moving MT, the speed is the dominant parameter in determining the cell boundary crossing. (a) Explain why, with fast moving mobiles, speed is more dominant in characterizing the use mobility pattern than direction? (b) Consider the situation in which, when the MS initiates and establishes a connection, its current location is 10 km from the cell boundary along the direction it is currently traveling. Also, the mobile is moving at a speed uniformly distributed between 40 km/hr and 60 km/hr. Calculate the mean time for the mobile to reach the cell boundary. (c) In an MAHO scheme, the mobile sends profiles containing the signal strengths received from all neighboring BSs in the same MSC. If a profile is sent every three minutes on average, what is the mean number of profiles sent before the mobile crosses the boundary