(1) P
W
[t]: probability that the MT connects with the WLAN at time instant t.
(2) P
G
[t]: probability that the MT connects with the 3G network at time instant t.
(3) P
W|G
[t]: probability that the MT connects with the WLAN at time instant t given that it is associated with the 3G net-
work at time instant t-1.
(4) P
G|W
[t]: probability that the MT connects with the 3G network at time instant t given that it is associated with the
WLAN at time instant t-1.
We assume the MT is in the WLAN initially without loss of generality, therefore P
W
[0] = 1 and P
G
[0]=0.P
W
[t] and P
G
[t] can
be calculated by the following formulations,
P
W
½t þ 1¼P
WjG
½t þ 1P½tþð1 P
GjW
½t þ 1ÞP
W
½tð6Þ
P
G
½t þ 1¼P
GjW
½t þ 1P½tþð1 P
WjG
½t þ 1ÞP
G
½tð7Þ
Conditional probabilities P
W|G
[t + 1] and P
G|W
[t + 1] depend on the decision method. Similar with [22], we also define these
probabilities as:
P
GjW
½t þ 1¼PrðLT½t þ 1Þ < D
HO
jW½t ; RSS½t þ 1 < T
MO
Þð8Þ
where W[t] represents the situation that the MT connects with WLAN, and T
MO
is a predefined threshold of MO. The second
condition in Eq. (8) is important to the MT with low velocity. We can work out the transition probability by,
P
GjW
½t þ 1¼
R
c
1
R
1
c
f
Z½tþ1Z½t
ðZ
1
; Z
2
ÞdZ
1
dZ
2
Q
c
l
Z
½t
d
Z
½t
ð9Þ
where Z½ t¼RSS½tD
HO
R½t, and
l
Z
[t] and
r
Z
[t] are the expectation and standard deviation of Z[t]. Q(x) is the complementary
error function, and P
W|C
[k + 1] can be worked out by,
P
WjG
½t þ 1¼
PrððRSS½t þ 1Þ > T
MI
jRSS½t < T
MI
Þ
Prð
RSS½t < T
MI
Þ
ð10Þ
where T
MI
is a predefined threshold of MI. The transition probabilities based calculation of the handoff probabilities are sim-
ilar to the methods adopted in [25].
The number of handoffs, presented by N
HO
, has much impact on the signaling flow, and it is the total number of MI and
MO. Therefore, N
HO
is determined by the instantaneous probability of MI and MO, and can be worked out by:
P
MO
½t þ 1¼P
GjW
½t þ 1P
W
½t ð11Þ
P
MI
½t þ 1¼P
WjG
½t þ 1P
G
ð12Þ
The expectation of N
HO
is,
EfN
HO
g¼EfN
MO
gþEfN
MI
g¼
X
t
max
t¼1
ðP
MO
½tþP
MI
½tÞ ð13Þ
where t
max
is the time instant when the MT arrives at the edge of the WLAN, and it is determined by the MT’s velocity and the
coverage of the WLAN. N
MO
and N
MI
are the expected numbers of MOs and MIs, respectively. The flow chart of MSA-VHO can
be seen in Fig. 2.
3. MDP-based multi-attribute handoff decision algorithm
Because the transition probability between different system states has no relationship with the past state, and the deci-
sion is dependent on the combination of multiple parameters, our considered network model matches well with the Markov
process. Fig. 3 illustrates the network system where more than one WLAN network exists.
The formulated Markov process based vertical handoff decision model includes five elements: decision epoch, state, ac-
tion, transition probability and reward. During each decision epoch, the MT decides whether to remain in the current net-
work or switch to other networks.
3.1. Markov based handoff decision model
We consider the MT chooses an action a based on its current state information. The state space is denoted by s. For each
state s
e
S, the state information includes the network identification number indicating which network the MT currently con-
nects with, the available bandwidth and the average delay of each candidate network. X
t
denotes the state at decision epoch
Z. Ning et al. / Computers and Electrical Engineering 40 (2014) 456–472
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