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( b B )
1+ sgn
1−
min1
U1( b1)
= ( b1
≥ 0)
(3)
2
b) Stream Class Service. It is also a real-time service,
its characteristics are that the demand of data transmitting
rate is higher and bit error rate is lower, but it can bear
larger delay and jitter, the speed commonly between a
interval range. When the real bandwidth is b 2 , the utility
function U 2 (b 2 ) can be
represented as :
1
U b = ≤b ≤B
e
( )
1+ ( 1/ ε −1)
2ln( 1/ ε 1 )/
B
( 0 )
2 2 −rb
2 max2
2 2
r = −
2 max2
The ε represents the lower utility value user get when
b 2 is lower than B min2 , and it also determine the sensitive
extent of the stream class service towards delay.
c) Interactive Class Service. Its characteristics are that
the demand of bit error rate is lower, and the data
transmitting rate can also be small or large according to
specific service. It has certain demand of delay and jitter,
but lower than conversational class service. When the real
bandwidth is b 3 , the utility function U 3 (b 3 ) can be
represented as:
1+ sgn( b3 −Bmin3) ln ( b3 / Bmin3)
U3( b3)
=
2 ln ( Bmax 3
/ Bmin 3)
( 0 ≤b
≤ B )
3 max3
d) Background Class Service. Its characteristic are that
it has less constrains of delay and has more elasticity
towards data transmitting rate, when the bandwidth is low,
service can be provided but the performance is not good
enough. When the bandwidth is b 4 , utility function U 4 (b 4 )
can be represented as:
( )
( b4
+ )
( B + )
ln 1
U b = ≤b ≤ B
( 0 )
4 4 4 max4
ln
max 4
1
2) Maximizing System Utility.
In mobile environment, the call that requested to
access wireless cell can be sorted into two types: new call
and handoff call. Too much interrupts will cause users’
complaints because the interrupts switching is hard to
accept by user, and will also cause negative impact to the
entire system benefit.
Therefore, the utility function need to be defined
extended as follows.
If it is a new call request and the required bandwidth
the service can not be satisfied, the utility value of the
service will fall down to 0, as it is defined before.
⎧ 0 bi
≤Bmin
i
⎪
U ( b) = ⎨u ( b)
B ≤b ≤B
⎪
⎩ 1 Bmax
i
≤ bi
ni i i i mini i maxi
(4)
(5)
(6)
(7)
If it is a handoff call request and the required
bandwidth of the service can not be satisfied, the utility
value of the service will get to be a negative number
which indicates the negative impact to the entire benefit.
⎧ − 1 bj
≤ Bmin
j
⎪
U ( b ) = ⎨u ( b ) B ≤b ≤B
⎪
⎩ 1 Bmax
j
≤ bj
hj j j j min j j max j
The proportion of each class service should be taken
into consideration when calculating the entire utility of the
wireless cell for that each class in the system may cause
different extent influence to the cell’s entire utility. The
proportion is set by the system administrator. Suppose the
proportion of the influence to system’s entire utility that
conversational class, stream class, interactive class,
4
background class has is Spec i , and ∑ Speci
= 1 ,the
i = 1
whole capacity of link circuit of a wireless cell L is C, so
the maximum prospective entire benefit NUF(L) of this
cell can be represented as :
4
( ) ec ( )
Max NUF L = Max n ⋅Sp ⋅ u b +
and meet
4
∑
i=
1
∑
i=
1
i i ni i
( )
Max n ⋅Sp ec ⋅u b
4 4
i i hi i
∑ n ⋅ b + ∑ n ⋅b ≤ C ,
i i j j
i= 1 j=
1
0 ≤ b ≤ B ,0≤b ≤ B
i max i j max j
However, non-linear formula (9) is hard to solve and
to calculate the bandwidth that each user should be
allocated due to the limitation of the inequality .
In the framework of PRMRAM, there is no need to
solve it positively, because the real bandwidth allocated to
the user is realized by action policy, and the amount of the
resource that the dynamic action policy gives is brought
from the predicating information.
User can be accessed directly if the system’s
remaining capacity is enough. When the system’s
remaining capacity is not enough and if there are more
than one user calling for access, it will be calculated using
utility policy, to judge which user getting the remaining
capacity will cause the maximum benefit to the entire
system utility and user utility.
3) Users’ QoE Maximization.
Another system expecting state in the superior level
management requirement is to maximize the utility of
individuals, which is the QoE maximization. It can be
represented as:
( ) = ⎛ 1 T i
i ⎜ ⎞
i()
T
∫0
⎝
⎟
i ⎠
k
1
i() = ∑ i j( i j)
k j = 1
Max QoE Max u t dt
u t u b
(8)
(9)
(10)
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