In this chapter, we consider an example with two traffic services whic iffer in the bandwidth requirement and mean call holding time. Within
h d
each type of service, there are new call and handoff call which have diffe costs incurred by rejection respectively. We assume that the channel has capacity of 48
rent
=
C FCU’s. For the first service, usually a arrowband one, the relevant parameters are set as follows:
2 . 1 ,
6 2
2 =
n
, 1 , 15
1,
,
1 1 2 12 1 1
12 2
1 =a =a = µ =µ =µ = λ = ω = =
a λ ω (4.1)
Since the second service is a wideband one (a34 >a12), we may assume that its mean call holding time is no less than the mean call holding time of the first service µ34 <µ12. In the example, we use the following
arameters:
,
3 3 4 34 3
34 4 3
p
8 , 1 , 7 ,
3 3 4 4 =
0.5, = = =
=
=
=
=
=
=a a µ µ µ λ ω λ ω
a
In order to find the dedicated bandwidth for each class of service with (4.2)
the policy π0, we obt
6
17 4
1
ain from section 3.1.5 as
3
2 7, 18,
, = = =
= C
C (4.3) From section 3.2.3, it is obtained that the ded
C C
icated bandwidth with the olicy π0′ as
27
, 21 34
12 = C =
C (4.4) A channel offered load
p
ρ, defined as
C a
k k
∑
k= = 4
1
ρ
ρ (4.5)
0.9375 what considered as a heavy traffic regime. Here,
is ρk =λk µk.
n1 n2
Figure. 4.1 Channel cost ∆1(⋅,⋅,n3 =0,n4 =0)
n 3
n1
Figure. 4.2 Channel cost ∆1(⋅,n2 =0,⋅,n4 =0)
Figure. 4.3 Channel cost ∆2(⋅,⋅,n3 =0,n4 =0)
1 2
n2 n 3
n n
Figure. 4.4 Channel cost ∆2(n1 =0,⋅,⋅,n4 =0)
n 3
n1
Figure. 4.5 Channel cost ∆3(⋅,n2 =0,⋅,n4 =0)
0 2 4 6 8 10 12 14 16
0 5
10 15
1 2 3 4 5 6 7
n 3 n4
Figure. 4.6 Channel cost ∆3(n1 =0,n2 =0,⋅,⋅)
Figure. 4.7 Channel cost ∆4(⋅,n2 =0,n3 =0,⋅)
0 2 4 6 8 10 12 14
16
0 5
10 15
2 3 4 5 6 7 8
Figure. 4.8 Channel cost ∆4(n1 =0,n2 =0,⋅,⋅) n n
3 n n
1 4
4
We underline the next policy, π1, is derived from the relative cost values of all channel states. Recall from Chapter 2, borrowing capa under 0
city π can happen only if at the initial state some service uses more bandwidth than its allocated portion. After some finite transient period, all services will be using only bandwidth allocated to them. On the contrary the next policy allows calls of one service to take a portion of bandwid allocated to another service if the cost for that is less than a given call cost
Figure. 4.1 through Figure. 4.8, we show some cost functions. For an example, Figure. 4.1 represents the channel cost 1(⋅,⋅, 3 =0, 4 =
, th .
)
∆ n n 0
where the number of type-3 call or type-4 call is a constant, zero. It is obvious that the cost of accepting a type-1 call is above the cost parameter
ω1 in some states. In other words, blocking a type-1 call in these st gets less cost in the future. We can make the same explanation in other figures.
ates
By the way, we get a conclusion after observing these figures that the rejection never happened in type-3 and type-4 call. It is reasonable because the cost parameter ω3 and ω4 are higher than ω1 and ω2. The cost function is increasing, so that higher cost must have less blocking rate.
4
3 n
n +
2
1 n
n +
Figure. 4.9 Channel cost ∆′1(n1 +n2,n3 +n4)
Figure. 4.10 Channel cost ∆′2(n1+n2,n3 +n4)
4
3 n
n +
2
1 n
n +
4
3 n
n +
2
1 n
n +
Figure. 4.11 Channel cost ∆′3(n1+n2,n3 +n4)
4
3 n
n +
2
1 n
n +
Figure. 4.12 Channel cost ∆′4(n1 +n2,n3 +n4)
45
type 1 type 2 type 3 type 4
Required BW (FCUs) 1 3
Arrival rate 15 6 3 1
Departure rate 1 0.5
Cost 1 1 1.2 7 8 g π
πa 6.32731 6.43105 18.8692 19.115 6.9038641
π1 5.80189 5.82261 18.3983 17.5974 6.5609464
Block Rate (%)
π1′ 11.1566 5.0444 14.7979 14.4252 6.2982618
Cost 2 1 6 12 50
πa 6.32731 6.43105 18.8692 19.115 19.6146865
π1 58.8106 1.83558 9.15144 4.64417 15.0990022
Block Rate (%)
π1′ 42.5497 0.203425 20.5107 1.79007 14.7345751
Cost 3 1 10 6 50
πa 6.32731 6.43105 18.8692 19.115 17.7616825
π1 18.7593 2.72926 23.2382 8.30603 12.7873421
Block Rate (%)
π1′ 18.0485 0.069113 47.3404 0.781861 11.6609453
Cost 4 1 4 6 50
πa 6.32731 6.43105 18.8692 19.115 15.4465045
π1 22.2966 3.50294 16.1029 11.3956 12.7815176
Block Rate (%)
π1′ 14.1668 0.142196 47.7179 1.13414 11.3154390
Figure. 4.9 through Figure. 4.12, we show each channel cost
function computed by the tial
us define the next policy
evaluation of the relative cost value of π1 is most complex.
g a
g gπ′ < π < π
1
1 (4.6) e computational burden of policy πa is least and the but th
2 and ty ved cy
Especially, we obt pe
ain that the deri
blocking rates of handof m
f call (type
4) fro poli π1′ are lower e
derived from policy 1
than thos π . It can be observed by the Guard Channel policy.
Consequently, the most import res
1
ant ult is that the average cost per unit time of policy π′ is lower than others. So we have Either policy π1 or policy π1′, the blocking rates of all type call
are rearranged by the relative cost values. According to policy π1, the blocking rate is decreasing in higher-cost call.
According to policy πa, the blo
bl ckin
ock
g rates of type-3 and type-4 call.
ing e- 2
equivalen the
rates of typ 1 and ty th are
pe-call are the same because their required bandwid
t. So does
Guard Channel policy as
1
an ini policy. Let , π′, is derived from the relative cost values
f ba
of all channel states. In the same way
service to take a p o nd ted to another service if the cost for that is less than a given call cost.
In addition,
, widt
the next policy allows calls of one h al
orti n o loca
we also define another policy, πa, by accepting a call if ne.
there is enough bandwidth mor uire er g
into Table. 4.1, we summarize as follow:
e than req d o Aft investigatin
Chapter 5 Conclusion
In our thesis, several aspects of the problem are formulated. The ew call admission control scheme LCCM is proposed for
the number of traffic classes.
The corresponding Markov decision process is suboptimal since we perfo
initial policy Usin and n
multiple-service wireless networks. It is based on the notion of the cost function, derived from the context of Markov decision theory. The proposed algorithm does not depend on
rm only a single iteration the policy iteration process. That is, our is most important.
g the Guard Channel policy to be initial policy from chapter 3 of
chapter 4, we have some profits as follow:
s.
The average cost of the next policy is better than other
The decrease in dimension of Markov chain helps to computation easily.
ture work, we fo
In fu rm the problem which minimizes the expected cost
guarante t a
all with higher cost k
per unit time under some constrains. For example, network provider es that block rate can be under a threshold. It is shown tha c ω get lower block rate in our thesis. Here we get some idea from Markov decision process that the parameter ωk is useful to solve the optimal problem under constrains.
Reference
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] R. Ramjee, R. Nagarajan and D. Towsley, "On optimal call admission
]
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