Handover mechanisms in next generation heterogeneous wireless ...

DYNAMIC NEIGHBOUR TRUST INFORMATION RETRIEVAL FOR GLOBAL ROAMING
q can be derived recursively as follows:
( m)
i,
n
( 1)
q i,
n � pi
, n
�
�
i,
k
k �0,
k �n
( m�1)
k , n
�
�
( m)
q � p q � p q � p q
n=2, 3, …
i,
n
k �0
i,
k
( m�1)
k , n
- 71 -
i,
n
( m�1)
n,
n
The matrix form of the equation can be represented as:
4.8)
Q n=2, 3, … (Equation
where � � ) (
( m)
m
q
( m)
( m�1)
( m�1)
� PQ � PQd
Q � and Q d denote a diagonal matrix formed by the diagonal elements of
i,
n
( 1)
Q. We can also get Q � P . The cumulative first-passage-time probability is denoted as:
4.9)
� �
( m)
i,
n � qi,
n
m�1
q (Equation
Thus, we can get the mean number of cell crossings of Ring n:
where �S �
� � � �
Si,
n �
m�1
( m)
E m�
q
(Equation 4.10)
i,
n
E i,
n is the expectation of the number of cell crossings the mobile takes for its
first entrance into boundary cells.
The cumulative fist-passage-time probabilities are employed to study the movement of a
mobile user in a region. It is observed that the mobile user will eventually be absorbed
at the boundary ring (with
q 1)
irrespective of its initial position. The mathematical
i,
n �
analysis of the ring sojourn time is in accordance with the intuitive perception that the
mobile users closer to the boundary ring will move out of the region first. For the region
of 6 rings, on average, a mobile user will end up being absorbed at the boundary ring
after 50 cell crossings as shown in Figure 4.9.