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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 51, NO. 1, JANUARY 2002
Unified Approach of GOS Optimization for Fixed
Wireless Access
Nathan Blaunstein, Ran Giladi, Avraham Freedman, Senior Member, IEEE, and Moshe Levin
Abstract—We present analytical and simulation models that obtain the minimum number of required communication channels for
subscriber units and their allocations so as to increase the level of
the grade of service (GOS) per user of fixed wireless access communication systems (FWA or WACS). On the basis of the proposed
analytical and simulation models, a new methodology of using user
radio ports (RPs) is introduced for evaluating the optimal number
of RP systems, their allocation policy, and their spatial distribution for different configurations. This methodology enables us to
increase the efficiency of FWA services on the basis of GOS maximization.
Index Terms—Balanced and unbalanced link matrix, controlled
resources search, fixed wireless access, grade of service, predefined
order search, random search.
I. INTRODUCTION
IXED wireless access (FWA) communication systems are
considered to be part of the personal communication services (PCS) as a replacement for and enhancement of traditional
wireline services. FWAs are also often called wireless access
communication systems (WACSs) and radio or /wireless in the
local loop (RLL or WLL, respectively). Standard organizations
are currently involved in establishing and investigating various
technical solutions for FWA [1]–[9].
These systems are useful in places where wireline telephone
access solutions are impractical, expensive, or temporary. More
and more manufacturers and operators are considering FWA in
order to enhance regular services (mainly bypass operators) and
to provide better, cheaper, and more flexible services. The main
principle of these systems is to connect end users to the telephone network via wireless radio links, which are allocated to
them when required. This is in contrast to regular wireline end
users, where the reserved wireline to the end user guarantees a
free channel to each end user. FWA therefore performs a kind
of resource switching by allocating channels (lines) to end users
per request, rather than by providing all users with resources to
access the network.
FWA systems, however, create problems in establishing reliable, accessible links between the end users and the public
switched telephone network (PSTN), in contrast to common
wireline systems. The design of these systems must take into
account user traffic intensity and the probability that the system
F
Manuscript received June 10, 1998; revised August 16, 2001.
N. Blaunstein and R. Giladi are with the Department of Communication Systems Engineering, Ben Gurion University, 84105 Beer-Sheva, Israel (e-mail:
natanb@cse.bgu.ac.il).
A. Freedman and M. Levin are with InnoWave-ECI Telecom, Tel-Aviv, Israel
(e-mail: avif@hexagonltd.com).
Publisher Item Identifier S 0018-9545(02)00437-1.
cannot establish a call-for interconnection, which relates to the
grade of service (GOS), i.e., the probability of a blocked system
that causes the unavailability of telephone lines to customers.
Until recently, an FWA infrastructure was designed by using
the Erlang loss function [10]. The number of required channels was calculated as a function of user traffic intensity and
desired GOS (generally smaller than 1%). The use of Erlang’s
formula is justified only in cases where all users have access
to all resources of the system (i.e., lines), a situation referred
to as a full availability system [see Fig. 1(a)], and where there
is a large number of end users using the available lines. In the
case of a wireless system, various obstacles, as well as wave
attenuation, require that the system components be deployed
in a proper geographical distribution, so that users can access
resources in a distributed way. This is referred to as a limited
availability system [see Fig. 1(b)]. In other words, not all the
lines are available to all the users (some users have access to
some lines, while others can access another set of lines). The
limited availability problem has been encountered in the design
of telephone exchanges [10, Ch. 6], [11, Ch. 4], where a source
has access to only a part of the channels provided. The actual
switching problem was solved by grading (see [10] and [11]).
However, the limited availability problem we describe in this
paper is different. The resource availability is determined by the
propagation conditions and cannot always be as well balanced
as is achieved by grading within the exchange. To estimate the
average probability of blocking the carried traffic, approximate
formulas have been developed [e.g., the Palm Jacobaeus (PJ)
and modified PJ formulas]. However, because the model we are
using is a simple one, we chose to use the exact solutions of the
state equations in order to estimate the probability of blocking.
The formulas described can, in some cases, be used for more
complex problems.
The problem of limited availability has an effect on any
cellular wireless system, be it mobile or fixed access, and
should be taken into account in the cellular network design.
There is a large variety of algorithms of resource allocations
(or channel allocation, as the spectrum is the scarcest resource
in a wireless system) among the various users. Reference [12]
provides a very thorough and extensive description of fixed
channel allocation and dynamic channel allocation algorithms.
None of the algorithms, however, takes limited availability
explicitly into account. Generally, a balanced load assignment
(as in fixed channel allocations) or an optimal approach (like,
e.g., [13]) may overcome this problem.
Here, we demonstrate the limited availability problem for relatively simple cases. This paper is organized as follows. In Section II, we build a model that enables us to calculate the min-
0018-9545/02$17.00 © 2002 IEEE
BLAUNSTEIN et al.: UNIFIED APPROACH OF GOS OPTIMIZATION FOR FIXED WIRELESS ACCESS
(a)
201
(b)
Fig. 1. (a) Full and (b) limited availability.
imum number of required channels and their allocation in order
to achieve a predetermined GOS per user. Analytical evaluation
of the model is described in Section III, with a methodology for
carrying out the numerical simulations presented in Section IV.
Section V describes the simulation results, followed by an analysis of the simulations. The results obtained in Section V are
very similar to those of load balancing algorithms, as described
in [14] and [15]. Section VI discusses the similarities and differences of the two problems. Section VII presents a brief summary
and some conclusions.
II. MODEL DEFINITION
A fixed wireless system is composed of shared telephone
lines that are potentially offered to a fixed population of end
users. This system is composed of antennas (radio ports, noted
in Fig. 1 as RPs). These devices link the fixed PSTN to the end
users’ devices (subscriber units, noted in Fig. 1 as SUs). RPs are
“intelligent” devices that can allocate telephone lines to a large
number of users (typically tens of SUs). The number of channels
that the RP can allocate depends on the frequency bandwidth of
the air transmission (each channel requires a certain frequency
bandwidth).
Given the users’ placement in a certain area, the objective is
to deploy the minimum number of RPs in order to save costs
while simultaneously achieving a predefined GOS per user. It is
important to note that the optimal criterion here is the GOS that
each user receives, and not, for instance, some other optimal criterion like the average GOS of all the users. In fact, the system
must provide a sufficient level of service for each connected
user. In other words, we face a min-max problem. The deployment of the RPs must also take into account geographical and
topological constraints. Some zones are forbidden completely
(military or private areas), while others are not convenient for
installation (terrain accidents).
For every RP deployment, the link loss between each RP
and each SU is computed, resulting in numbers between zero
and one that define the quality of the connections. These numbers are rounded to zero when they are smaller than a certain
threshold and to one when they are larger than this threshold.
They are stored in a matrix called the link matrix
. Rows in
this link matrix represent the SUs, and columns represent the
RPs. Thus, a “1” in row and column indicates a physically
possible connection between the th SU and the th RP, while
a “0” means that no physical connection is possible. Note that
when a physical connection is possible, one can always cancel
this connection in order to achieve better results in the optimization of the GOS (as we will see further on).
and
Each user is supposed to have a fixed calling rate
. In fixed wireless systems, one must give each
holding time
user an allocation policy for his connection to the system. The
different policies that we considered are as follows.
method): each user
1) Random search (denoted as the
chooses randomly from among his available RPs (with
“1” in the corresponding row of the link matrix) for his
first attempt to get a connection. If the chosen RP has at
least one free channel, the user will receive and use it, and
will speak for an exponential time (with parameter ). If
the chosen RP is occupied (all its channels are currently
busy), the user randomly chooses another RP amongst the
other RPs available to him, and so on. At the end of the
process, the user that did not receive a connection gets
a blocked call and tries again after an exponential time
(with parameter ).
2) Predefined order search (denoted as the method): each
user chooses the order of the successive connection trials
to his corresponding RPs from a predefined order given
in advance and stored in a database. The predefined order
of size
. It provides
search is defined by a matrix
the order of the successive connection trials for each user
when attempting to connect to its RP. The th row of
will be completed with zeros if the th user does not have
access to all the deployed RPs in the area. For instance
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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 51, NO. 1, JANUARY 2002
and
mean that the first user will try only RP (from
, we
see that it is in fact the only possibility), the second user
will try only RP , and the third user will try RP and, in
case of a failed attempt, will try RP . For each given link
matrix, there are many possibilities of a predefined order
search, but in each case the results will be presented with
optimized (noted as
, which means achieving the
best min-max (GOS) for a given link matrix.
3) Controlled resources search (denoted as the method):
each user will know at any moment the availability of
all its allowed RPs. He will use the RP with the highest
number of free channels.
We define a user-RP-balanced link matrix as a matrix representing a situation where each user can get connected to and
use the same number of RPs, and each RP can get connected
to and be used by the same number of SUs. We specify a
user-RP-balanced link matrix with customers and RPs by
matrix
, where
total number of users
an
and
total number of RPs
in the area.
For instance
is a balanced 2
matrix, while
is not balanced because the second user can get connected to and
use two RPs while the first user can only get connected to and
use the first one. Note that a full “ ” matrix is always balanced
[and is an
matrix], being in fact the full availability case
[presented in Fig. 1(a)], where the Erlang B formula is applicable [6]. This formula can be used instead of the Engset distriis infinite,
bution [6] for the case when the number of SUs
whereas the number of channels per RP is finite.
We further define an RP-balanced link matrix as one where
each RP can get connected to and be used by the same number
of SUs. Note that every user-RP-balanced matrix is also an
RP-balanced matrix. For instance
(a)
(b)
Fig. 2. (a) Predefined order search state diagram. (b) Random search state
diagram.
then by using a random search. We use two user groups with a
link matrix that describes their connections to the servers as
(a nonbalanced link matrix). The analysis is based on two typical situations of SU-RP connections presented in Fig. 1(b). The
state diagrams of these two servers in the two serving policies,
i.e., the predefined order and the random searches, are shown in
. specifies that
Fig. 2(a) and (b). Each state is marked
the first server is occupied by a user from the first group (1) or
the second group (2), or is free (0); specifies how the second
server is occupied in the same manner.
In the case of a predefined order search [state diagram in
Fig. 2(a)], a user from the first group can use server RP , and if
it is occupied he can use server RP (if it is free; if not, he leaves
the system without service, which is a “blocked” situation). A
user from the second group can use only RP , if it is free. If it
is not, he is blocked (he leaves the system without service). The
predefined search matrix is therefore
is an RP-balanced link matrix, where each RP is connected to
two users (RP to user 1 and 3 and RP to user 2 and 3).
III. ANALYTICAL EVALUATION
In the analytical model and, subsequently, in the numerical
and use the Erlang B
simulations, we assume that
formula [6] since in our approach the parameter is independent
of the number of customers or servers in use. Below we analyze
two server systems, first by using a predefined order search and
The probability of the system’s being in state
is
state transition equilibrium equations are given by
. The
(1a)
(1b)
(1c)
(1d)
BLAUNSTEIN et al.: UNIFIED APPROACH OF GOS OPTIMIZATION FOR FIXED WIRELESS ACCESS
(1e)
(1f)
(1g)
After deriving system (1a)–(1g), we can obtain the probability
of the event that a user of the first group gets an occupied system
by the following equation:
GOS
(2)
The probability that a user of the second group gets an occupied
system can also be obtained from system (1a)–(1g) as
GOS
(3)
The case of a random search is slightly different. The state
diagram of this service is presented in Fig. 2(b). For this case,
the state transition equilibrium is given by the following system:
(4a)
(4b)
(4c)
(4d)
(4e)
(4f)
(4g)
From system (4a)–(4g), one can obtain the probability that a
user of the first group gets an occupied system
GOS
(5)
203
. As can be seen from the illustration, the difference is
. In the case of the
limited to a value of about 0.015 for
second group of users, however, the situation is the opposite.
The random search GOS is larger than the predefined order
search GOS , which means that in terms of the second group
of users, it is advisable to adopt the predefined order search.
The difference, GOS (random) GOS (predefined) from (3)
and (6), is presented in Fig. 3(b) as a function of the value of
. As can be seen, there are
utilization in the range
. The
large differences in GOS in the range
better search policy, in terms of maximal GOS for all the users,
is obviously the predefined order search (users of group 2 show
much higher differences in GOS). The better search policy,
in terms of average minimal GOS for all the users, could be
evaluated by calculating
GOS (predefined) GOS (random)
GOS (predefined) GOS (random)
(7)
is the number of users
where is the total number of users,
is the number of users in the second
in the first group, and
group
. The random search policy is better when
(7) is positive, etc. The precise calculated difference is
GOS
(8)
This leaves us with the problem of comparing these search
policies to the controlled resource search, as well as the problem
of comparing policies with bigger link matrices. As can be seen
from the graph depicted in Fig. 3(c), the distance between the
two differences presented in Fig. 3(a) and (b) for in the range
, which is (7) for case
, suggests that the predefined order search is still the best search policy.
IV. METHODOLOGY
Because an analytical description for the general case is impossible, we used simulations of the model presented above. We
assumed that there are two groups of users connected to two
RPs, as in Fig. 1(b), and used the structures of matrices defined
above. To check how the structure of the matrix and the allo2
cation policy affect the GOS, we ran simulations using
matrices in the general form
and the probability that a user of the second group gets an occupied system
—
—
GOS
(9)
(6)
It is worthwhile to compare the two search methods in this case.
It turns out that the predefined order search GOS is slightly
larger than the random search GOS , which means that in terms
of the first group of users, it is advisable to adopt the random
GOS (random)
search. The difference, GOS (predefined)
,
from (2) and (5), depends on the value of utilization,
as follows from the graph [Fig. 3(a)] for values in the range
—
—
rows of (1,0),
rows of (0,1), and
rows
where there are
. This -matrix defines three
of (1,1), where
users that can
classes of users: the first class is composed of
only use RP ; the second class is composed of users that can
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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 51, NO. 1, JANUARY 2002
(a)
(b)
(c)
Fig. 3.
The difference in GOS for users of (a) group 1 and (b) group 2. (c) Average random GOS and average predefined GOS.
only use RP ; and the third class is composed of
users that
can use both RP and RP , as in Fig. 1(b).
The general form of this presentation enables us to check a
variety of situations, such as a user-RP-balanced matrix, where
and
(so we get an ( 2,1) balanced
and
(so we get an ( ,2) balmatrix) or
anced matrix). We can also check an RP-balanced matrix, when
, varying from a slightly user-RP-unbalanced
or
) to a severely
link matrix (when
user-RP-unbalanced link matrix (when
or
). To optimize the number of RPs and their location in
the area, we ran simulations with different configurations of the
BLAUNSTEIN et al.: UNIFIED APPROACH OF GOS OPTIMIZATION FOR FIXED WIRELESS ACCESS
link matrix. We began with the balanced configuration and then
gradually added links to degrade this balanced situation. Then
we compared different allocation policies for all cases.
The user load is assumed constant, conforming to data that we
obtained from experimental situations composed of incoming
and outgoing calls symmetrically distributed. The main parameters assumed in the simulations are as follows: user load equals
, and the number of
0.0625, the size of the population
.
channels per RP (available lines from each RP)
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TABLE I
GOS RESULTS OF A DIVERTED
USER-RP-BALANCED LINK MATRIX
V. SIMULATION RESULTS
Using simulations, we examined the behavior of the maximal
GOS , in terms of two
value of the grade of service, i.e.,
main parameters:
1) the structure of the connections between RP and SU;
2) the allocation policy, i.e., the method used by each user to
establish his connection to the system.
In the following section, we analyze these results for the case of
two different link matrices.
A. The User-RP-Balanced Link Matrix
We start with balanced situation (
, where
the matrix
and the predefined search order is
2,1). The simulation uses
and
,
Fig. 4. GOS results of a diverted user-RP-balanced link matrix.
configuration:
predefined search order will now be
—
. The
—
(11)
—
—
—
—
(10)
—
—
(which is the only possibility in this case).
The maximum GOS of all the users, for each of the three
and , which are the same in this particular
methods (
case), is 2.98% maxgosR, 2.94% maxgosP, and 2.98% maxgosF,
respectively. In fact, in this case, the Erlang B formula [6] is
users and the last
users form
applicable because the first
two independent user teams (they have their own independent
servers [RP and RP , as follows from Fig. 1(b)]. The Erlang
B formula yields GOS 2.94 % and the Engset formula yields
GOS 3.01%. These results are in accordance with our results.
On this basis, we assume that the results of the simulation should
be closer to those obtained by the Engset formula; however, in
, the Erlang B and the Engset approaches
our case with
are almost the same. Again, in this particular case, we find that
the expected theoretical GOS result is identical for every user
and does not depend on the policy given to users.
Now, we diverge from the user-RP-balanced link matrix
by gradually adding
-type users to the
Note that this is the optimal order and is intuitively determined;
RP serves more possible users than RP [Fig. 1(b)], so it is
sensible to permit the third class of users to try RP first. The
and ) are
results of simulation for the three methods (
presented in Table I and graphically in Fig. 4. Note that when
is zero, we are dealing with two independent groups—half
the users are in the first group using RP and the other half are
increases up to 20, we
in the second group using RP . When
transfer users from the second group (that uses RP ) to a new
group, a third one, that allows the use of both RP and RP .
is 20, we are in a situation where half the users are
When
in the first group, using RP , and the other half are in the third
group, using both RP and RP .
In this case, the predefined order method is the best of the
three methods, and adding links (until half of the users
get connected to RP and RP ) makes matters worse; disconnecting links to establish a balanced situation
might even be advisable. This is, of course, true with
respect to the maximal GOS of all the users. This kind of conin
figuration makes life easier for users in the new group
terms of their GOS.
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Fig. 5.
IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 51, NO. 1, JANUARY 2002
Fig. 6. GOS results of the RP-balanced link matrix.
GOS results of diverting to a full availability link matrix.
In the next cases, we check what happens if we shift the balwith even more supplementary connections,
anced matrix
getting closer to the full availability case
. The predefined search order is
TABLE II
GOS RESULTS OF DIVERTING TO A FULL AVAILABILITY LINK MATRIX
matrix
will have the configuration:
and the predefined search order matrix
—
,
—
(12)
—
—
—
—
—
—
—
—
Note that this is the optimal order, intuitively determined; RP is
granted first to the first team who can access only one RP, while
the second team tries RP first. The results of simulation for the
three methods are presented in Table II and graphically in Fig. 5.
Note again that we are essentially continuing the previous case.
After the second group was emptied, we started to move users
from the first group to the third one. In this situation, when
, we are approximately in the same situation as the last phase
in the previous example, i.e., half the users are in the first group,
using RP , and the other half are in the third group, using both
increases, and more users are moved from
RP and RP . As
the first group to the third one, we end up with
. This is
the most efficient situation since almost all users are in the third
group and are using both RP and RP . From the histograms
presented in Fig. 5, we see that in this case, the predefined order
to
method is again the best of the three methods. For
, the maxgosP (2.91% to 0.54%, respectively) becomes
smaller than the balanced situation [( 2,1) with 2.94%]. Note
, we reach the full availability case [Fig. 1(a)],
that for
which we can predict by the Erlang B formula [6] GOS
% . This is the ( ,2) balanced matrix case that achieves
the best level of service.
B. The RP-Balanced Matrix
We start by examining how the GOS behaves in the RP-balanced matrix case for the three methods ( , , and ). The link
where the last two partitions of
belong to the third class of
users and the number of
rows is equal to the number of
). Note that
is intu(2,1) rows (and equal to
itively optimized by equalizing the load on each RP. The results
of simulation for the three methods are presented in Table III
and graphically in Fig. 6.
In this situation, we are starting with two independent groups,
each being served by a separate RP. Half the customers are in
increases, we
the first group and the rest in the second. As
take users from the two groups and move them to a new third
is 20, then
group being served by both RP and RP . When
a quarter of the users are in the first group, being served by
RP ; another quarter are in the second group, being served by
RP ; and half are in the third group, using both RP and RP .
approaches 38, almost all users are in the third group,
When
using both RP and RP . The histograms presented in Fig. 6
reveal a strange phenomenon: using the and methods and
adding more links from the balanced situation ( 2,1) to the
GOS (in the
pseudobalanced situation only increases the
method, we get a degradation of the
GOS from 2.99%
BLAUNSTEIN et al.: UNIFIED APPROACH OF GOS OPTIMIZATION FOR FIXED WIRELESS ACCESS
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TABLE III
GOS RESULTS OF THE RP-BALANCED LINK MATRIX
to 3.28%, and for the method from 2.99% to 3.33%). The
method behaves in the opposite way: the
GOS decreases from 2.87% to 1.11%. The GOS in the balanced situation (from the Erlang B formula [6]), as mentioned earlier, is
equal to 3.01%. Thus, the and methods are never worthwhile, but using the
method always improves the GOS in
comparison with the balanced situation.
C. Analysis
From the simulation results presented in Tables I–III and
Figs. 4–6, it follows that for the case of a user-RP-balanced link
matrix, the maximum GOS of all users for the three methods
of the search is 3.0%, and it degrades as links are added (the
maximum GOS increases) in non-RP-balanced configurations.
is the best of
Moreover, the predefined search order method
the three methods for different non-RP-balanced configurations
of link matrices.
In the case of the RP-balanced link matrix for various kinds
of configurations, only the controlled resources search
method improves the GOS level, decreasing it from 2.87%
to 1.11% as we move from one user-RP-balanced situation
( 2,1) (two separate groups) to a second user-RP-balanced
situation ( ,2) (full availability case). The other two methods
GOS : The -search increase is from 2.99%
increase the
to 3.28% and the -search from 2.99% to 3.33%.
We also notice that going from one user-RP-balanced
situation to another [( 2,1) to ( ,2)], the link matrix can
reach many configurations, including RP-balanced link matrix
configurations. When the configuration is not an RP-balanced
link matrix case, it is better to use the -search method in
order to achieve the best (minimal) maximum GOS. However,
if an RP-balanced situation does not exist, links can be added
or deleted, so that it can be configured to the nearest balanced
configuration, an effect that depends on the degree of nonbalancing of the link matrix. After a certain point, when links
are disconnected in order to return to the balanced situation, a
GOS can be achieved using the -search method.
better
This point depends on the ratio of the links to the size of
population and RP number.
In the RP-balanced situation, the -search method allows
us to obtain the correct solution to the SU and RP optimization problems. When using the nonbalanced link matrix, the
-search is best in terms of maximal GOS, but the -search
gives us a good alternative as well, in comparison with the
and search methods.
In practice, the main parameters might be different from those
presented in the numerical simulation. In fact, a typical size of
might be in the hundreds, and the number
the population
of deployed RPs might be about ten. Fortunately, in the case
of RP-balancing, the -policy gives us the correct solution to
the optimization problem. In other cases (where the -matrix is
severely nonbalanced), the predefined search order
method
is optimal, but might not be so easy to calculate. In these cases,
the -search method still provides a good alternative.
VI. COMPARISON TO OTHER APPROACHES
The results of the analysis suggest that balancing the load on
each RP gives the optimal solution of the problem. Load balancing has been treated extensively, mainly in the context of
networks; however, it is not identical to the problem described
above. On the other hand, the similar solutions might suggest
that some of the methods and algorithms described in the context of load balancing can be applied for the case of limited
availability.
Work in [14] introduces an algorithm for rehoming in
order to balance the load of mobiles on mobile switching
centers (MSCs). The home MSC handles call-related network
activities, such as mobile termination and call delivery, and
inter–visitor location register (VLR) registration activities,
which load the MSC and can be balanced by moving a group
of mobiles to another MSC. The algorithm suggested therein
is doing the rehoming process according to the criterion of
maximum benefit to the load standard deviation ratio, where
benefit is expressed in the terms of maximal load reduction.
This algorithm could be applied to the limited availability case
if there is an overlap of coverage area of more than two RPs.
The measure of the benefits and costs would depend on the
characteristics of the system in question.
Work in [15] formulates the load balancing problem as an
optimal control problem and shows that variants of the “least
loaded routing” policy is asymptotically optimal for large call
arrival rates. The problems descirbed in [15] are very similar
to the problem described above, especially the “basic dynamic
model” given in Section III. However, the cost function chosen
in [15] does not reflect the real cost for an FWA system, which
aims to minimize the probability of blocking of the user located
in the worst location. In [15], on the other hand, the cost function
was a quadratic function of the load, which is not at all identical.
The least loaded routing algorithm studied in [15] is the algorithm suggeted above, which was shown here to be the best
choice in most cases.
VII. SUMMARY
This paper presents a new methodology that is based on three
different search methods by the user/subscriber unit, whose
purpose is to optimize the number of RPs and their spatial
, predefined order
, and controlled
allocation: random
. For each of these methods, we carried out
resources
simulations for two different configurations of link matrices:
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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 51, NO. 1, JANUARY 2002
the user-RP-balanced and RP-balanced matrices. The grade
of service was evaluated for two variants of communication
channel service policies. The simulated results resembled those
of the traditional approach based on Erlang’s canonical formula. Generally, the controlled resource approach was proven
to be the optimal policy, in terms of GOS, as the simulations
showed. In some cases, however, the predefined order approach
was preferred. Both analytical and numerical analysis enabled
us to predict the maximal GOS level and to obtain the optimal
number of radio ports and their effective allocation with
subscriber units for wireless access communication systems.
Similar results were obtained in studies of the load-balancing
problems, although the problem by itself is not identical.
Load-balancing algorithms can thus be applied, at least on a
first trial basis, for the limited availability problem as well.
Ran Giladi received the B.A. degree in physics and the M.Sc. degree in biomedical engineering from The Technion, Haifa, Israel, and the Ph.D. degree in computers and information systems from Tel-Aviv University, Tel-Aviv, Israel.
He is the President and CEO of InfoCyclone Inc., a company he cofounded
in October 2000. He previously was the Founder and Head of the Department
of Communication Systems Engineering, Ben-Gurion University of the Negev,
Beer Sheva, Israel (1992–2000). He taught at the Business School and at the
Electrical Engineering Department of Tel-Aviv University (1987–1993). He cofounded Ramir Ltd., which was later acquired by Adacom, and served as Vice
President of R&D in both companies (1984–1986). Prior to that, he was an R&D
Manager with Fibronics and System Programmer in the computer center of The
Technion. He also founded the Israeli Consortia for research on network management systems and served as the Chairman of the Consortia Board of Directors. His research interests include computer and communications systems performance, data networks and communications, and network management systems.
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[5] “Wireless local loop,” European Radio Communications Office (ERO),
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[6] “Wireless access local loop,” International Telecommunication Union
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[7] “Fixed service trends post-1998,” European Radio Communications Office (ERO), Copenhagen, Denmark, May 1998.
[8] C. V. Macario, Cellular Radio, London, U.K.: Macmillan, 1993.
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[10] R. Syski, Introduction to Congestion Theory in Telephone Systems, 2nd
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[11] J. R. Boucher, Voice Teletraffic System Engineering, 2nd ed. Norwood,
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[12] I. Katzela and M. Naghshinen, “Channel assignment schemes for
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[13] S. Papavassiliou and L. Tassiulas, “Joint optimal channel base station
and power assignment for wireless access,” IEEE/ACM Trans. Networking, vol. 4, pp. 857–872, Dec. 1996.
[14] W. Yuan et al., “Load balancing in Wireless Networks,” in Proc.
GLOBECOM, 1997, pp. 1616–1620.
[15] M. Alanyali and B. Hajek, “On simple algorithm for dynamic load balancing,” in Proc. IEEE INFOCOM, vol. 1, 1995, pp. 230–238.
Nathan Blaunstein received the B.Sc. and M.Sc.
degrees in radiophysics and electronics from Tomsk
University, Tomsk, Russia, in 1972 and 1976,
respectively, and the Ph.D. and D.Sc. degrees in
radiophysics and electronics from the Institute
of Geomagnetism, Ionosphere, and Radiowave
Propagation (IZMIR), Academy of Science USSR,
Moscow, Russia, in 1985 and 1991, respectively.
From 1979 to 1984, he was an Engineer, a Lecturer, and then, from 1984 to 1992, a Senior Scientist, an Associate Professor, and a Professor at Moldavian University, Beltsy, Moldova, former USSR. From 1993 to 1995, he was
a Researcher in the Scientific “Shapira” Program, Ben-Gurion University of the
Negev, Beer Sheva, Israel. Since 1995, he has been a Senior Scientist with the
Department of Electrical and Computer Engineering and a Visiting Professor in
the Wireless Cellular Communication Program at Ben-Gurion University, where
he is now a Professor. His research interests include problems of radiowave
propagation, diffraction, and scattering in various media for purposes of radio
location, mobile-satellite and terrestrial communications, and cellular and mobile systems performance and services.
Avraham Freedman (M’87–SM’98) received the
B.Sc., M.Sc., and Ph.D degrees from Tel-Aviv
University, Tel-Aviv, Israel, in 1974, 1985, and 1993,
respectively, all in electrical engineering.
Between 1980 and 1993, he was with the Israel
Defense Forces and with Elta Electronic Industries,
Ashdod, Israel. Between 1993 and 1996, he was a Research Fellow with the Valley Forge Research Center,
School of Electrical Engineering, University of Pennsylvania, Philadelphia, and was involved in development and research of communication, antenna, and
radar systems. Between 1996 and 2000, he was with Inno Wave—ECI Wireless
Systems, Petach-Tikva, Israel, as a member of the Business Research Group,
and involved in the research and planning of present and future FWA systems.
He was CTO of Hexagon System Engineering, a consulting firm specilizing in
tools for cellular systems planning and deployment, where he is still involved
and consults. He is currently with the Electronic Systems Department, Faculty
of Engineering, Tel-Aviv University. He has published more than 20 papers in
the fields of radar and communication systems. He is active in ETSI, IEEE, and
other standardization bodies in defining and developing standards for FWA systems.
Moshe Levin received the B.S. degree in electrical engineering in from The
Technion—Israel Institute of Technology, Haifa, Israel, in 1981. He received
the M.A. degree in electrical engineering, the Ph.D. degree in radar signal processing, and the Ph.D. degree in business administration (strategic planning)
from Tel-Aviv University, Tel-Aviv, Israel in 1986, 1989, and 2000, respectively.
From 1981 to 1992, he worked in the defense industry, mainly in research and
development of signal-processing algorithms. From 1992 to 1998, he was with
Tadiran Telecommunications as the Vice-President of Research and Planning
and as the Chief Scientist of the Wireless Systems Division. Currently, he is
President and CEO of Hexagon System Engineering Ltd., a fixed wireless access
consulting firm. He is the author of more than 40 papers covering various aspects
of wireless local-loop systems.