Proceedings of the 32nd Hawaii International Conference on System Sciences - 1999
Proceedings of the 32nd Hawaii International Conference on System Sciences - 1999
A New Adaptive Channel Assignment Algorithm in Cellular Mobile
Systems
Yongbing ZHANG
Institute of Policy and Planning Sciences, University of Tsukuba, Ibaraki 305-8573, Japan
Abstract
In this paper, a new adaptive channel assignment algorithm in cellular mobile systems is proposed and examined in comparison with a dynamic load balancing strategy, the load balancing with selective borrowing (LBSB)
algorithm. The new algorithm is based on the xed
channel assignment strategy as its underlying scheme;
that is, it assigns a xed number of channels to each cell
permanently. At run-time, it attempts to balance dynamically the imbalance of available channels between
the cells. Two thresholds, the light and heavy thresholds, are introduced to classify the cells in the system
into three classes according to the number of available
channels in the cells: light, moderate, and heavy cells.
Each cell is assumed to know its own exact state (the
number of the available channels) and to which class it
belongs at any given instant. The MSC keeps the state
information of the cells and runs the channel borrowing
algorithm to borrow free channels from the light cells for
the heavy cells whenever it nds any heavy cells. The
moderate cells are not allowed to borrow any channels
from any other cells nor lend any channels to any other
cells. When making a borrowing decision, the states of
the co-channel cells of a potential lender cell are also
taken into account to prevent potential channel borrowing loop. The results indicate that the new algorithm
performs better than the LBSB algorithm with respect
to the call blocking probability.
1 Introduction
The rapid growth in the demand for mobile communications has led the industry into intense research and
development eorts towards a new generation of cellular systems. The limited resources (frequence channels)
in cellular systems can be reused in such systems in
noninterfering cells. Ecient utilization of the scarce
channels for cellular systems, however, is one of the major challenges in cellular system design. Many schemes
have been proposed to assign channels to the cells such
that the available channels are eciently used and thus
the channel reuse is maximized [7]. The performance
index used for measuring the eciency of a channel assignment scheme is the call blocking probability. These
schemes can be classied into xed [8], dynamic [7, 1],
and exible [6] assignment schemes.
The xed assignment strategy is to assign a set of
channels to each cell permanently. The same set of
channels is reused by another cell at some distance
away. The minimum distance at which the channel can
be reused with no interference is called co-channel reuse
distance. The advantage of the xed assignment strategy is its simplicity, however, its disadvantage is that if
the number of calls exceeds the number of channels assigned to a cell the excess calls have to be blocked. Variations of this scheme have been proposed by researchers
to reduce the call blockade using channel borrowing
techniques [4, 3, 5, 2]. Eklundh [3] proposed a directed
retry strategy (DR) wherein a new user in a cell where
there is no free channel tries to nd a free channel from
its neighboring cells. The user, however, should be in
the overlap region between the two cells. Karlsson and
Eklundh [5] proposed an extensive version of DR. Jiang
and Rappaport [4] proposed a channel borrowing without locking strategy (CBWL) wherein a cell where free
channel is exhausted tries to borrow some free channels
from its neighboring cells. To avoid interference with
the other co-channels of the lender, the borrowed channels are used with reduced power. Das et al. [2] proposed a load balancing strategy with selective borrowing
strategy (LBSB) wherein a cell attempts to selectively
borrow channels before the available channel in a cell
is exhausted. The LBSB algorithm borrows channels
for a cell needing free channels from not only its neighboring cells but also other cells in its compact pattern.
It has been shown in [2] that the LBSB algorithm outperforms the other channel borrowing strategies with
respect to the call blocking probability.
In the channel assignment algorithm under LBSB,
the degree of coldness of a cell is dened to be the ratio
of the number of the available channels to the number
of channels assigned by the xed assignment scheme
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Proceedings of the 32nd Hawaii International Conference on System Sciences - 1999
Proceedings of the 32nd Hawaii International Conference on System Sciences - 1999
in a cell. The degree of coldness is used for measuring the degree of available channels in a cell. If it is
greater than some threshold value then the cell is classied as a cold cell. Otherwise, it is classied as a hot
cell. The MSC (Mobile Switch Center) runs periodically to check whether there exist any hot cells and
attempts to borrow free channels from cold cells to hot
cells. For searching a potential channel lender (a cold
cell) for a hot cell, the number of hot co-channel cells
of the potential lender cell and the distance to the potential lender cell are taken into account as well as the
coldness degree of the potential lender cell. This algorithm performs quite well when the call arrival rate
is not high. At high call arrival rate, however, a cell
with a coldness degree near to the value of the threshold may lapse into a ping-pong state being switched
back and forth between cold and hot states, resulting
in useless channel borrowing and lending. Moreover,
since the states of the co-channel cells of a lender are
not taken into account, locking a hot co-channel cell
in order to avoid interference may cause extra channel
borrowing in the hot co-channel cell. Under an extreme
condition, a borrowing loop may occur, degrading the
channel utilization further.
In this paper, a new adaptive channel assignment algorithm is proposed. The new algorithm is examined
in comparison with only the LBSB algorithm, since
the LBSB algorithm is the best among the previously
described algorithms. The new algorithm uses a twothreshold scheme with a heavy and a light thresholds to
classify the cells in the system into three classes according to their states (the number of the available channels): light, moderate, and heavy cells. This scheme is
used for preventing a cell from ping-pong state changes
being switched back and forth between light and heavy
states. A heavy cell is limited to borrow channels from
only the light cells and a light cell is limited to lend
channels to only the heavy cells. Each cell communicates with the MSC autonomously, and therefore the
message exchanges between the MSC and the cells are
processed concurrently. The channel borrowing algorithm is run on-demand by the MSC whenever there
exist heavy cells needing free channels. The values of
the light and heavy thresholds are determined adaptively corresponding to the system state (the average
number of the available channels in the system) and
therefore the algorithm is expected to be ecient even
when the system load (call arrival) uctuates. Furthermore, the new algorithm takes into account not
only the states of the potential light cells but also the
states of their co-channel cells. This scheme prevents
the system from a potential borrowing loop and waste
of resources.
The rest of this paper is organized as follows. Section 2 describes the cellular system model. Section 3
presents the new channel assignment algorithm. The
comparison of the new adaptive algorithm and the
LBSB algorithm proposed by Das et al. [2] is described
in Section 4. Finally, Section 5 concludes the paper and
presents the future research.
2 Cellular System Model
The cellular system model in this paper is as follows. A
given geographical area consists of a number of hexagonal cells, each served by a base station (BS). The
base station and the mobile users communicate through
wireless links using frequency channels. A number of
cells are served by a mobile switching center (MSC) and
each MSC is connected with the xed communications
network. Each cell is allocated a xed set of C frequency channels and the same set of channels is reused
in other cells suciently far away without interference.
The minimum distance is called co-channel reuse distance. A group of cells using distinct channels forms a
compact pattern. The co-channel cells are determined
by two shift parameters, si and sj . For example, in
a system with 7-cell compact patterns, the co-channel
cells are determined by the shift parameters 2 and 1.
The number of cells in a compact pattern is given by
N = s2i + si sj + s2j .
The number of channels available in cell i is denoted
by ci. To classify the cells into dierent classes, a light
threshold, Tl, and a heavy threshold, Th , are used and it
is assumed that C Tl > Th 0. If the number of the
available channels in cell i is equal to or greater than the
light threshold, that is, ci Tl , then cell i is classied
as a light cell. If the number of the available channels
in cell i, on the other hand, is equal to or less than the
heavy threshold, that is, ci Th, cell i is classied as a
heavy cell. Otherwise, cell i is classied as a moderate
cell. A heavy cell is allowed to borrow channels from
light cells, but a light cell is not allowed to borrow any
channels from any other cells. A moderate cell, on the
other hand, is neither allowed to borrow any channels
from any other cells nor lend any channels to any other
cells. It is assumed that each cell knows its own state
(the number of the available channels) at any given
time.
The values of Tl and Th are determined by using
the average number of the available channels at a cell,
cavg , and a parameter 1lh showing the dierence of the
values of Tl and Th. Let Tl = bcavg c and Th = Tl 0
1lh where 1lh > 0 and Th cmin , and cmin denotes
the minimum value that Th can take. The value of Tl
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Proceedings of the 32nd Hawaii International Conference on System Sciences - 1999
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l3
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Figure 1: Departing users in a cell
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therefore is bounded to equal 1lh + cmin. The value of
the light threshold is adjusted adaptively according to
the system state and therefore this scheme is ecient
even when the call arrival rate uctuates. The average
number of the available channels in a cell is computed
at the MSC based on the information collected from
the cells.
The MSC keeps the state information of the cells in
the system. When the state of a cell changes or when
the number of the available channels in a cell changes
larger than a threshold 1 even though the state remains unchanged, the cell sends an update message to
the MSC. It is assumed that each cell sends the message
to the MSC independently and the MSC can process
the requests from the cells concurrently.
The mobile users in a cell are classied as either local
or departing. To classify the users in a cell as local or
departing, a shaded area between two adjunct cells is
considered as that in [2] as shown in Figure 1.
A departing user is designed as follows. A shaded
area between between two adjunct cells, i and j
is considered (areas marked with (2) and (3) in
Figure 1). The shaded area is denoted by a parameter p0 showing the percentage of the shaded
region to the whole cell area. Typical values of p0
are 80%, 90%, etc. When a user enters the shaded
area the BS starts a timer for time units. A
departing user in a cell is one who is within the
shaded area and receiving a steadily diminishing
signal strength from the BS of the cell for the last
time units of . If the signal strength stops diminishing within the time period, the departing user
will be reset to be local.
A user who is not departing is local. Note that a
i
l6
6
Figure 2: Co-channel cells (Shift parameters si = 4 and
sj = 1)
local user can be located in the shaded area or not
(areas marked (1) and (2) in Figure 1).
Each cell has six neighboring cells and those cells
are numbered from 1 to 6. An array, NumDepart[n],
n = 1; 2; :::; 6 is used to store the number of departing
users in a cell heading towards its neighboring cells. A
heavy cell sends the array to the MSC along with the
other state information when its state changes.
For each cell i, six nearest co-channel cells, in which
the same set of channels are used, are determined by
the shift parameters, si and sj . When a channel of a
cell is lent to another cell, some of its co-channels in the
nearest cho-channel cells have to be locked in order to
avoid co-channel interference with the borrowing cell.
All of the six co-channels can be locked in a conservative way, but it is apparently unnecessary. A co-channel
locking scheme described in the next section shows that
locking at most three co-channels is sucient.
3
Channel
Borrowing
Algorithm
The channel borrowing algorithm is run on-demand by
the MSC whenever there exist any heavy cells needing
to borrow free channels. For each heavy cell, the MSC
determines its compact pattern so that it is located as
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Proceedings of the 32nd Hawaii International Conference on System Sciences - 1999
Proceedings of the 32nd Hawaii International Conference on System Sciences - 1999
the central cell. It then searches the appropriate light
cells based on the following selection priorities for the
heavy cell needing to borrow channels, and borrows the
required channels and locks the related co-channels.
1. Search for the neighboring light cells towards
which departing users are heading.
2. Search for the neighboring light cells other than
those described above.
3. Search for the other light cells in the compact pattern.
In contrast to the LBSB algorithm, the new algorithm
does not require that the lender candidates be ordered
according to their load states and the states of the
candidates be recomputed after borrowing each channel. Instead, it can choose an arbitrary lender from the
lender candidates for channel borrowing and borrow a
set of channels each time.
To determine a lender cell for a heavy cell, the new
algorithm takes into account the state of the lender cell
as well as the states of the co-channel cells of the potential lender cell. Since a co-channel cell of a light cell
may be a heavy cell, locking co-channels in such a cochannel cell causes the situation in the cell even worse.
This results in extra channel borrowing in the heavy
co-channel cells and, in the extreme, a channel borrowing loop may occur, degrading the system performance
seriously. In order to prevent this situation happening,
the algorithm proposed in this paper prohibits, after
channel borrowing, any co-channel cell of a lender cell
from becoming heavier than the borrower cell.
For each heavy cell k, the MSC runs the following
channel borrowing algorithm according to the priorities listed below until either the borrowing request from
cell k is satised, or the light cells are exhausted. The
required number of channels that a heavy cell k needs
to borrow from light cells is denoted by bk and determined by bk = (Tl 0 1) 0 ck . The owchart for the new
algorithm is shown in Figure 3.
1. Borrow channels from the light neighboring
cells towards which departing users are heading.
1. Find the light neighboring cells and for which there
are non-zero NumDepart entries.
2. Select those light cells as the lender candidates.
Borrow channels from such a light cell where
NumDepart[n] is non-zero until either the light
cell state alters, or any co-channel cell of the
lender cell becomes heavier than the borrower
cell, or the number of borrowed channels equals
Start process request
Yes
There are light neighbors towards which
departing users are heading?
Borrow channels
No
No
Yes
Finish
Request satisfied?
Yes
There are light neighbors towards which
no departing users are heading?
Borrow channels
No
No
Yes
Request satisfied?
Finish
Yes
There are other light cells in the
compact pattern ?
Borrow channels
No
Finish
Figure 3: The new channel borrowing algorithm
NumDepart[n]. Lock each lent channel in the
lender and its relative co-channel cells in order to
avoid interference.
2.
Borrow channels from the light neighbor-
ing cells towards which no departing users are
heading.
1. Find the light neighboring cells and select them as
the lender candidates.
2. Borrow channels from such a light cell until either
the lender cell state alters, or any co-channel cell of
the lender cell becomes heavier than the borrower
cell, or the borrowing request is satised. Lock
each lent channel in the lender and its relative cochannel cells in order to avoid interference.
3. Borrow channels from the other light cells in
the compact pattern.
The procedure needed here is the same as the previous one except the lender candidates are those excluding the neighboring cells in the compact pattern such
that cell k is located as the center cell.
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Proceedings of the 32nd Hawaii International Conference on System Sciences - 1999
Proceedings of the 32nd Hawaii International Conference on System Sciences - 1999
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As described in Section 2, a light cell is not allowed to
borrow any channels from any other cells. If the number of the available channels in a cell exceeds the light
threshold while the cell has still borrowed any channels
from any other light cells, the cell has to return the
borrowed channels until ck = (Tl 0 1). The channel return is processed inversely to the selection priorities for
channel borrowing. That is, a cell returns the borrowed
channels to the lender cells according to the priorities
listed below.
1. Return the channels that belong to the cells other
than its neighbors in the compact pattern.
2. Return channels that belong to its neighboring
cells but towards which no users are heading.
3. Return channels that belong to its neighboring
cells towards which departing users are heading.
In order to determine which nearest co-channel cells
should lock the co-channels of a lender cell, the following co-channel locking scheme is used. The cells in the
system are divided into six sets as shown in Figure 2
using six dotted lines, l1; l2 ; :::; l6 so that there is only
one nearest co-channel cell in each set. The co-channel
cells of cell i are determined anticlockwise and numbered by 1,2,...6. In this paper, it is only shown for the
case of si and sj being greater than zero. It is easy to
show, although omitted here, for the case of either si
or sj being zero.
Before describing the co-channel locking algorithm,
an example is used to explain the idea where si = 4
and sj = 1 as shown in Figure 2. It can be seen that
when cell i lends a channel x to cell k (a cell between
two dotted lines, l2 and l3 ), there is no need to lock its
co-channels in cells 4, 5, and 6, since channel x will be
used in borrower cell k that is farther than lender cell
i from those co-channel cells. Note also that cell 1 has
no need to lock the co-channel of x in this example. It
is therefore conservative to lock the co-channels of x in
cells 1, 2, and 3. When cell i lend a channel y to cell j
(a cell on a dotted line, l5 ), the situation becomes little
complicated. There is however apparently no need to
lock the co-channels of y in cells 1 and 2 with the same
reason as described before. In cells 3 and 6, at least
one cell has no need to lock the co-channel of y and
the cell is determined by the values of si and sj . When
si > sj as shown in Figure 2, cell 3 has no need to lock
the co-channel of y. Locking the co-channels in cells 4,
5, and 6 is therefore sucient to avoid the co-channel
interference.
The co-channel locking algorithm for the case of
si; sj > 0 can be briefed in the following for lender
cell i and borrower cell k.
Figure 4: Simulated cellular system.
1. Split the cells in the system centered at cell i into
six sets by six lines l1; l2 ; :::; l6 as shown in Figure
2.
2. If cell k is not on a dotted line but located in between lj and lj+1 , then lock the co-channels in
cells j 0 1; j, and j + 1. Here, the line number j is
treated as a ring from 1 to 6 so that when j = 1
then j 0 1 = 6 and when j = 6 then j + 1 = 1;
3. If cell k is on a line, lj , then lock the co-channels
in cells j 0 1 and j. Furthermore, if si sj then
lock the co-channels in cell j + 1; otherwise lock
the co-channels in cell j 0 2.
Channel assignment scheme proposed by Das et al.
[2] is used here. That is, the channel requests are
processed according to the priorities listed below: (1)
Hand-o requests from the neighboring cells; (2) Local
original calls; (3) Local user channel reassignment requests from a borrowed channel to a local channel; and
(4) Departing user channel reassignment requests from
a local channel to a borrowed channel. When a departing user goes towards a light cell, the borrowed channel
borrowed from the destination cell is unlocked as soon
as the user enters that cell and does a soft hand-o.
4
Simulation Results
Simulation was used to evaluate the performance of
the new channel assignment algorithm and compare it
with the LBSB algorithm proposed by Das et al. [2].
The results shown in the gures were obtained with
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Proceedings of the 32nd Hawaii International Conference on System Sciences - 1999
Proceedings of the 32nd Hawaii International Conference on System Sciences - 1999
0.12
Neighbor
2
Neighbor
1
Neighbor
3
0.10
γ
Neighbor
6
Neighbor
5
Call Blocking Prob
0.08
θ
Neighbor
4
LBSB, C=20
LBSB, C=30
LBSB, C=40
NEW, C=20
NEW, C=30
NEW, C=40
0.06
0.04
0.02
Figure 5: User position in a cell
90% condence interval and within 5% of the sample mean. The simulated cellular system contains 100
hexagonal cells shown in Figure 4. Two integer values
x and y (1 x; y 10) are used to describe the locations of the cells. The shift parameters, si and sj ,
were set to be 3 and 2, respectively. Call arrival at
each cell was assumed to follow a Poisson process with
a mean . The hold time of a call was assumed to be
distributed based on an exponential distribution with
a mean 1= of 500 (s). The other parameters were as
follows: 1lh = 2, 1 = 2, p0 = 0:8 and cmin = 0:05C .
According to the results of [2], the call blockade probability was the lowest when the degree of coldness h was
set to 0.1. In order not to bring any bias to the LBSB
algorithm to compare it with the new algorithm, this
value was used for the LBSB algorithm. Both the algorithms used the co-channel locking scheme proposed
in this paper.
In order to determine the position of a user in a cell,
a cell is modeled as a circle with a grid of size 100x360
as shown in Figure 5. A user location is determined by
using a radial method, that is, a pair of (; ) to indicate the position of a user where denotes the distance
of the user from the center of the cell and denotes
the angle from a common reference line. It is assumed
that a user can move, with the same probability, to one
of the four directions or remain in the same position.
When a user moves to a position over 100 from the
center, a hando occurs. The location of a new user
is given at random. The cell model used in this paper
is expected to be more ecient than the other ones in
the literature since when a hando occurs the new position in the new cell is clearly determined. The time
period, , used for determining a departing user was
0.00
0.2
0.3
0.4
0.5
0.6
Load Level
0.7
0.8
0.9
1.0
Figure 6: Call blocking probability: the new algorithm
vs. the LBSB algorithm.
set to 10 time units. If a user keeps departing for at
least 5 times in the shadow region for the last period
, it is classied as a departing user. Otherwise, it is a
local user.
Figure 6 shows the call blocking probability of the
new adaptive algorithm versus the LBSB algorithm for
various values of C, the number of channels initially allocated to each cell under the xed assignment scheme.
The load level used here denotes the ratio of the call
arrival rate at one channel in a cell to the call service
rate of a channel. It was assumed that an arriving call
in a cell is served immediately if there are any channels available for use in the cell. From Figure 6, it is
shown that the value of C has strong eects on the
call blocking probability for both algorithms. It is observed as expected that, over all the range of the load
level, the new algorithm performs much better than the
LBSB algorithm. Similar to the LBSB algorithm, for a
larger C the new algorithm yields a lower call blocking
probability. It is also observed that the performance
improvement of the new algorithm over the LBSB algorithm becomes greater for a larger value of C.
Figure 7 show the call blocking probability of the new
algorithm for various values of 1lh when C = 30. A
larger 1lh yields a larger dispersion between the light
and the heavy thresholds. A channel borrowing or lending therefore does not happen easily under such a situation. For a small 1lh, on the other hand, a heavy cell
can easily nd a light cell. It is observed from Figure
7 that a relatively small 1lh yields low call blocking
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Proceedings of the 32nd Hawaii International Conference on System Sciences - 1999
Proceedings of the 32nd Hawaii International Conference on System Sciences - 1999
Further research on channel borrowing strategies is
needed. Other techniques are worth trying in order
to improve the channel utilization, besides those described in this paper. For example, a channel borrowing scheme wherein the MSC monitors the numbers of
light and heavy cells and attempts to keep the balance
between them is expected to be ecient.
0.08
0.07
Call Blocking Prob
0.06
NEW, D_lh=1
NEW, D_lh=2
NEW, D_lh=3
NEW, D_lh=4
0.05
0.04
0.03
0.02
0.01
0.00
0.2
0.3
0.4
0.5
0.6
Load Level
0.7
0.8
0.9
1.0
Figure 7: Call blocking probability: the new algorithm
with various values of 1lh.
probability.
4 Conclusion
In this paper, a new adaptive channel assignment algorithm has been proposed and evaluated in comparison
with a channel assignment strategy, the load balancing
strategy with selective borrowing (LBSB) algorithm,
in cellular systems using simulation. In contrast to the
LBSB algorithm, the new algorithm performs only one
computation for each heavy cell to borrow free channels
and therefore it is easy in implementation and ecient
in execution. It has been shown that the new algorithm
performs better than the LBSB algorithm with respect
to the call blocking probability. The reasons for this
result can be briefed as follows.
1. The new algorithm uses a two-threshold scheme
which prevents a cell from ping-pong state changes
being switched back and forth between light and
heavy.
2. The new algorithm takes into account of the states
of the co-channel cells of a lender cell when making borrowing decisions so that potential channel
borrowing loop can be avoided.
3. The new algorithm adjusts adaptively the values
of the light and the heavy thresholds according to
the system state so that better borrowing decisions
can be made.
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