Computational Intelligence - February 2017 - 33

❏ " R k 1, R k 2, ..., R k Sk , : the indexes of roads of

The calculation of location update cost between
type k ( k = 1, 2, ..., K ), where K is the
total number of road types and S k is the
different TAs is therefore transformed into counting
total number of roads of type k.
the average traffic flow on each grade of road crossing
❏ " k s 1, k s 2, ..., k s N , : the indexes of cells
the TA boundaries.
passed by road s of type k (k = 1,
2, ..., K, s = 1, 2, ..., S k), w h e r e N ks
(N ks # N ) is the total number of cells
passed by this road.
Since it is very common that a lot of roads need to be conIn addition to the two objectives, there are also many constructed in cities with a high population density, we also assume
straints that the model should satisfy, as described here. For the
that each cell has at least one road passing through. As we have
sake of readability of the section, the following notations
explained, boundary crossings can be used as a measure of locaare used:
tion update cost, and the total location update cost in a network
1 cell i is assigned to MME q
can be measured by the total number of mobile user TA boundx iq = '
0 otherwise
ary crossings. In this paper, we develop this idea and use the aver1 cell i and cell j are adjacent
age road traffic flow as the measure of location update cost. The
y ij = '
average road traffic flow can be used to estimate TA boundary
0 otherwise
crossings according to the hypothesis. The calculation of location
1 cell i is assigned to TA h
l ih = '
update cost between different TAs is therefore transformed into
0 otherwise.
counting the average traffic flow on each grade of road crossing
the TA boundaries. The first objective of the proposed model is
More explicitly, our multi-objective TA planning model is:
to minimize location update cost, which can be expressed as:
ks

flc =

K

S k N ks -1

// /

d ks ks
n

n +1

m k sn k sn +1,

(1)

k =1 s =1 n =1

where k sn and k sn +1 represent the indexes of two cells. If cell i
and cell j are assigned to the same TA, dij = 0, otherwise dij = 1.
m ks ks
represents the traffic flow between cell k sn and cell k sn +1
on type k roads. The average traffic flow on each road can be
estimated by statistical methods in real situations. User traffic
flow on each road for rush hour would normally be used to
obtain results compatible with good quality of service. In our
simulations, we assume that average user traffic flow on each
type of road over rush hour is subject to uniform distributions
over certain intervals. Other distributions can also be easily
applied to simulate the traffic flow on each type of road without disturbing the applicability of the proposed model and
optimization procedures.
The second objective of the model is to minimize the paging
cost. When the network search for a UE, it pages the TA where
the UE is registered. The paging cost of cell i can be measured
by its paging load p )i , which is determined not only by the cost
of paging the mobile users in cell i, but also the cost of paging
the other users belonging to the TA where cell i is contained. p )i
can be calculated by p )i = p i + / j pj (1 - d ij), where pi and pj
represent the paging load generated by the UEs in cell i and cell j,
respectively. dij has the same meaning with above description.
Generally speaking, it is independent of whether a UE is called,
and the paging cost generated by each cell is also independent.
Thus, the total paging cost of the whole network should be the
summation of the total paging costs of the N cells:
n

n +1

N

N

i =1

i =1

f pc = / p )i = / (p i + / p j (1 - d ij)) .

(2)

minimize *

flc = / Kk = 1 / Ss =k 1 / n = 1 d ks ks
N k s -1

n

f pc = /

N
i =1

n +1

m k sn k sn +1

` p i + / j p j (1 - d ij) j

,

(3)

subject to the following constraints:
1) Each cell must be assigned to exactly one MME.

/ x iq = 1, 6i.

(4)

q

2) Each cell must be assigned to exactly one TA.

/ l ih = 1, 6i.

(5)

h

3) Each MME must be assigned to the TA to which its corresponding cell is assigned.
If

/ l ih l jh = 1,
h

then / x iq x jq = 1, 6h 6q.

(6)

q

4) The paging capacity of each BS must not be exceeded.
p )i 1 P BS, 6i,

(7)

where p ) is the total paging load in TA i.
5) The paging traffic capacity of each MME must not be
exceeded.

/ x iq p i 1 T MME, 6q,

(8)

i

where pi represents the traffic load in cell i.

j

FEbruary 2017 | IEEE ComputatIonal IntEllIgEnCE magazInE

33



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