Handover mechanisms in next generation heterogeneous wireless ...

DYNAMIC NEIGHBOUR TRUST INFORMATION RETRIEVAL FOR GLOBAL ROAMING
Ring 6
Ring 5
Ring 4
Ring 3
Ring 2
Ring 1
Ring 2 Ring 3 Ring 4 Ring 5 Ring 6
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absorbing state
Figure 4.7 The hexagonal random walk model
Using the method proposed in [79], the expectation of the transition probabilities for the
mobile user moving within Ring n can be derived. The state transition follows a Markov
chain as shown in Figure 4.8.
2
�n � 3�
�
6�n�3�
2
1
�n � 2�
�
6�n�2�
Figure 4.8 Transition probabilities for the random walk model
1
1/6
1/6
2
1/6
1/6
�n � 2�
�
6�n�2�
Its transition probability matrix is denoted as P. Let S i,
n represent the number of cell
crossings the movement takes for its first entrance into boundary ring given that X 0 � i .
Random variable S i,
n is known as the first passage time from i to n [80].
represent the probability mass function for S i,
n . Thus, we get:
�S � m��
P�X�nX�n,
, X � n | X � i�
( m)
i,
n
1
1/6
1/6
q is used to
( m)
qi, n � P i,
n
m , m�1
� 1
0
n=1, 2, …