IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 3, NO. 1, JANUARY 2004
159
A Flexible Dynamic Traffic Model for Reverse Link
CDMA Cellular Networks
Farid Ashtiani, Student Member, IEEE, Jawad A. Salehi, Member, IEEE, and Mohammad R. Aref
Abstract—In this paper, we focus on the reverse link traffic analysis of a code-division multiple-access (CDMA) cellular network in
dynamic environments. In this respect, we propose a new and flexible traffic model, which takes into account the interference-limitedness attribute of CDMA capacity as well as its soft-handoff
feature. This new traffic model is developed according to interference-based call admission control (ICAC) method and a geographical structure with three regions. The main advantage of this traffic
model is in its flexibility when we consider different traffic conditions including time-varying status of traffic in the neighboring
cells.
Index Terms—Admission control, code-division multiple-access
(CDMA), soft capacity, soft-handoff, traffic analysis, traffic model.
I. INTRODUCTION
C
ODE-DIVISION multiple-access (CDMA) scheme plays
a crucial role in third generation mobile systems. Universal mobile telecommunication system, UMTS, an important
standard for third generation mobile system, is based on wideband-CDMA (W-CDMA) as its multiple access technique [1].
CDMA has numerous attributes that distinguish it from other
techniques such as time-division multiple-access (TDMA) and
frequency-division multiple-access (FDMA). One of its distinct
attributes is soft capacity which is due to its interference-limited
behavior. This feature affects other aspects of CDMA cellular
networks such as traffic analysis. Because of stochastic nature
of interference, and thus capacity, we need a suitable method for
admission control in traffic analysis.
Ishikawa and Umeda discussed two basic methods for call admission control [2]. For the first method, namely, number-based
call admission control (NCAC), we have number of channels.
should be determined according to the whole traffic status
of the network. In this method, the resources of a network are
equivalent to the number of channels. However, in the second
method which considers interference-based call admission control (ICAC), the resources in the network are proportional to the
level of interference. Hence, ICAC method appears to be more
suitable with respect to the interference-limitedness attribute of
CDMA capacity. In this method for admitting any new arrival,
the current short-term interference is compared with a threshold.
Manuscript received December 10, 2001; revised July 1, 2002; accepted
January 3, 2003. The editor coordinating the review of this paper and
approving it for publication is L.-C. Wang. This paper was presented in part
at IEEE PIMRC’01, San Diego, CA. This work was supported in part by Iran
Telecommunication Research Center (ITRC) under Contract 7834330.
The authors are with the Department of Electrical Engineering, Sharif
University of Technology, Tehran, Iran (e-mail: ashtianimt@hotmail.com;
jasalehi@sharif.edu).
Digital Object Identifier 10.1109/TWC.2003.821197
Furthermore, due to randomness of short-term interference the
result of this comparison appears as an admission probability in
ICAC method. Therefore, for ICAC method we do not have a
restriction on the number of channels explicitly, however, transition rates diminish while the traffic states go into the higher
and higher states.
The other key feature of a CDMA cellular network is its
ability to employ soft-handoff scheme. In this scheme more than
one base station (BS) coordinate amongst themselves to provide communication services for mobile stations (MS’s) placed
in their corresponding boundary regions. Thus, in fact, for softhandoff scheme we have a transition band as opposed to a transition boundary (line) such as for hard-handoff scheme. Softhandoff has numerous benefits in view of interference optimization, capacity, and QoS enhancement ([3]–[7]) and a few disadvantages in relation to forward link such as degradation in capacity [8]. The main feature for soft-handoff process reverts to
power-control of the MS’s by the best BS. Two important criteria in this respect are signal to interference ratio (SIR) and path
loss (or equivalently, received pilot strength). Furthermore, because of a new type of region, i.e., soft-handoff region (SHR),
formed by applying soft-handoff scheme, there are more options
for designing traffic management algorithms and thus, more
flexibility and accuracy in traffic modeling and analysis, respectively.
In general, traffic analysis is performed based on a traffic
model that includes a typical region indicating a sample of the
whole network. Traffic analysis can be performed for either
immobile (users with no mobility) or dynamic (users with
mobility) cases. The basic distinguishing feature of the latter, i.e.,
dynamic, is the handoff process. Some of the previously proposed
traffic models for CDMA cellular networks, do not consider
time-varying attribute of the traffic and they focus on static
capacity [9] only, i.e., equally loaded cells without any handoff
([4], [10]–[12]). Others do not consider soft capacity feature of
CDMA cellular network and consider the network capacity like
non-CDMA cellular networks ([13], [14]). Furthermore, some
base their traffic analysis for nondynamic case only, i.e., without
considering mobility and handoff problem ([2], [9], [15]). Also,
almost all of these previous traffic models incorporate traffic
status of the neighboring cells as a stationary random variable,
and do not consider its time-varying characteristics.
In this paper, we intend to propose a flexible and dynamic
traffic model that is suitable for reverse link traffic analysis
of CDMA cellular networks. In this model we employ ICAC
method for soft capacity and we consider soft-handoff process
in our geographical configuration. Flexibility of this new traffic
model reverts to considering time-varying traffic status of the
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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 3, NO. 1, JANUARY 2004
neighboring cells and thus, its ability to analyze heterogenous
spatial traffic conditions more accurately when compared to previous traffic models. Also, this new traffic model is suitable
in designing and comparing new traffic and especially handoff
management algorithms with respect to soft-handoff process
[16].
Following this introduction we will describe issues of a general traffic model in Section II, and will propose a new reverse
link traffic model in Section III. We will conclude this paper in
Section IV.
II. GENERAL CHARACTERISTICS OF A TRAFFIC MODEL
Our main goal in proposing a traffic model is to provide
means to analyze a CDMA cellular network in reverse link
in view of evolutionary time-varying traffic for dynamic case
(users with mobility) with emphasis in soft-handoff process. In
this type of analysis increasing and decreasing the number of
users are considered step by step. One of the most important
traffic parameters which is obtained from this type of analysis
is the carried traffic, that can be viewed as dynamic capacity
of the system. In the literature, usually, the static capacity of
the network is considered with the same number of users in all
the cells ([4], [10]–[12]). Obviously, this cannot be a practical
case with respect to traffic evolution. Even for the case of the
same primary traffic parameters (such as arrival rate, average
cell sojourn time, average call duration time, etc.) for all cells,
we cannot deduce that the number of users is always the same
in different cells. Thus, dynamic traffic analysis may lead to
more practical results.
In general, typical dynamic traffic analysis of a cellular network is carried numerically and if one considers the whole network the order of computations may become very large. Thus,
a viable approach for dynamic traffic analysis is to consider a
small region representing a sample of the whole network and
consequently extending the results to the whole network [17].
With respect to soft-handoff scheme this small region usually
includes a cell (desired cell) and its neighboring overlap regions
([6], [13]). In general, we estimate some required traffic parameters related to the neighboring cells. For simplicity, we assume
the same average traffic parameters, i.e., blocking and dropping
probabilities, for the desired cell and its neighbors.
We can state that in a CDMA cellular network model we
should make decisions with respect to two basic issues, first, the
basic method of admission control and second, the geographical structure of the model with respect to soft-handoff. Obviously, our decision-based model should be such that it is flexible
enough to facilitate the analysis for different traffic conditions
and simple enough in order to be mathematically tractable. In
fact, we need a suitable tradeoff between simplicity and flexibility. For example, a flexible geographical structure enables us
to consider spatially heterogenous traffic conditions which in
turn results in more complex traffic analysis.
Another important issue with respect to a traffic model is
the corresponding probability distribution for primary traffic parameters such as new call generation process, cell sojourn time,
call duration time, orientation in different directions, etc. The
standard assumption that often simplifies the solution of the
Fig. 1.
Geographical structure of the proposed traffic model.
Markov chain corresponding to a traffic model is the memoryless property of the related distributions (like negative exponential distribution for inter-arrival time, cell sojourn time, and call
duration time).
III. PROPOSED NEW TRAFFIC MODEL
Our new model, which is based on ICAC method to include
soft capacity, considers a desired cell (cell ) and its overlap
regions (Fig. 1) in a macrocellular structure with nonsectorized
cell sites. Due to its efficiency, we compute the related parameters based on a 3-cell soft-handoff scheme [4], [18], however, for
the sake of simplicity, we consider only the two nearest cells to
the desired cell as the determining and decision-making BS’s
in SHR. This model divides the considered area into three regions (Fig. 1). The first region, inner-cell region, includes MS’s
that are power-controlled by cell and do not communicate
with any other base station. The second region (
) includes
MS’s that are placed in soft-handoff region and are power-con) includes the MS’s
trolled by cell . And third region (
in soft-handoff region that cell is not their power-controlling
BS.1 In this model, we consider path loss (equivalent to pilot
signal strength with the assumption of the same pilot strength
at all BS’s) as the criterion of power-control. And also, we assume the same target received power at the BS’s corresponding
to the desired cell and its neighboring cells. The motivation for
this geographical structure is to be able to analyze the MS’s with
various interfering effects on cell , which, will ultimately re1In
fact due to shadowing, it is possible, in practice, that some of the MS’s in
are power-controlled by cell A and some of the MS’s in SHR are not
power-controlled by cell A. However, with some minor modifications we are
able to include the effect of shadowing in this partitioning.
SHR
ASHTIANI et al.: FLEXIBLE DYNAMIC TRAFFIC MODEL FOR REVERSE LINK CDMA
161
Inverse of average call duration time;
Departure rate (due to mobility) from region u (inverse of sojourn time in region
);
Probability of an MS moving from one
subregion of region to another subregion of region (inner-cell region has
only one subregion);
Dropping probability while migrating
from region to region at ( , , )
traffic state;
Migration rate from neighboring cells’
regions (index 4) to SHR2 (index 3) of
the traffic model (Fig. 1);
Departure rate from one subregion of region ;
Dropping probability of an MS while
moving between two subregions in region at ( , , ) traffic state.
For the traffic analysis based on this model we should determine transition rates in the obtained Markov chain (Fig. 2).
The related expressions, in general, can be written as in the following:
(1)
(2)
Fig. 2. Markov chain corresponding to the proposed traffic model.
sult in different treatment of the network on the corresponding
MS’s. In fact, when we consider the movement or the migration
of an MS from inside a neighboring cell (such as cell ) toward
cell and crosses the edge of SHR, its interfering effect will become noticeable in cell . However, MS’s placed in SHR, have
various interference effect on cell . Obviously, an MS in SHR
, has less interference compared
belonging to cell , i.e.,
. Note that, with the
to ones belonging to cell , i.e.,
assumption of perfect power-control, MS’s placed in SHR that
) have the same interferare power-controlled by cell (
ence effect on cell as for MS’s placed in inner-cell region. In
this paper, we propose that for a CDMA cellular network, MS’s
should be treated differently according to their contributed interference level on cell , hence, our geographical structure enables us to analyze different traffic management policies that
have different treatment with respect to these two types of MS’s
in SHR.
In this model, we employ the standard assumption for primary traffic parameters. Hence, for the analysis of a traffic management algorithm based on the above traffic model we need
to solve a 3-dimensional Markov chain as illustrated in Fig. 2.
From this figure, ( , , ) is the state of the Markov chain such
that , , are the number of users in first, second and third regions, respectively. Also, we use the following notation for the
Markov chain equations corresponding to the proposed traffic
model in general case:
New call origination rate in the region ;
Blocking probability of a new call request in region , at ( , , ) traffic state;
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
We compute the arrival and departure rates corresponding to
different regions, and the probabilities for moving in different
directions, in Appendix A. Due to ICAC method for blocking
probability of a newly originatined call and dropping probability
due to handoff failure, at each traffic state, we need to compute
the probability that current short-term interference level exceeds
the corresponding thresholds. Interference is comprised of two
parts; intra-cell and inter-cell, and both are stochastic in nature.
With the assumption of perfect power-control, randomness of
the first part, intra-cell, is due to intermittence such as voice activity factor or burstiness in data traffic. Intra-cell interference
for the case of voice only is modeled by a bionomial random
variable. And randomness of the second part, inter-cell, is due to
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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 3, NO. 1, JANUARY 2004
propagation channel (especially shadow fading), intermittence,
and variant locations of the neighboring MS’s. We need a suitable distribution for inter-cell interference and with respect to
[2] and [10], and in case of voice only traffic gamma distribution appears to be a proper choice with the assumption of uniform spatial traffic distribution in the neighboring cells. Hence,
in applying this distribution at any ( , , ) traffic state, we
require the mean and variance of the interfering effects of the
neighboring cells’ users at that state. But we have a large number
of states corresponding to various traffic status of the neighboring cells and each state leads to a specific mean and variance, or equiavalently a specific inter-cell interference distribution. Hence, we are obliged to limit ourselves to a few number
of these states in order to be able to track the related equations
mathematically and this will lead to an approximate solution
for our traffic analysis. One of the main advantages of our geographical structure reverts to its flexibility to include limited
traffic states corresponding to neighboring cells. To simplify our
analysis further, we focus on the first tier of neighboring cells’
users as the dominant interfering users on the desired cell. Thus,
for our traffic model we need only the traffic parameters of the
desired cell (cell ) and first tier of interfering cells (like cell
).
In order to simplify the related traffic equations, the limiting
scheme used for our traffic model is to estimate the number
of dominant inter-cell interfering users, i.e., network-admitted
users in the first tier of interfering cells, at each ( , , ) traffic
state by an estimation which takes into account , the number of
. For the sake of simplicity, we employ linear esusers in
timation that is justified with the assumption of uniform spatial
traffic distribution at each neighboring cell. In this methodology,
we are able to evaluate the mean and the variance, or equivalently distribution, of inter-cell interference for the desired cell
at each traffic state distinctly. Due to lack of sufficient information corresponding to first tier of interfering cells, especially
the traffic status of their neighbors (e.g., second tier with respect
to cell ), we are obliged to employ average traffic parameters
corresponding to these cells. Thus, we need to estimate the corresponding average traffic parameters at the onset that leads to
an iterative approach in solving the related equations. In fact,
after solving the related equations we are able to compute the respective average traffic parameters corresponding to the desired
cell, which are then considered as new estimates for the respective average traffic parameters corresponding to the neighboring
cells. Obviously, iterations should be continued until the corresponding average traffic parameters for the desired cell converge to the respective estimates, since in our scheme we assume
that the estimates obtained for various average traffic parameters of the first tier of neighboring cells correspond to the same
average traffic parameters of the desired cell. However, in the
case of discrepency between some of the primary traffic parameters (such as new call arrival rate) at cell and its neighbors,
such assumption can be justified by suitable setting of corresponding thresholds at the neighboring cells. Also, to simplify
further, we assume the same conditions for various traffic status
and parameters for all the first tier of neighboring cells, however, this assumption can be removed by proper changes in the
traffic equations.
With respect to above discussions, we can compute the mean
and the variance of interfering effects of the neighboring cells
as follow:
(12)
(13)
where
is inter-cell interference distribution (gamma distribution), is the normalized real-valued number of inter-cell interferers (it is equal to the ratio of inter-cell interference on the
interference of an intra-cell user), is the voice activity factor,
is the estimate of the number of inter-cell interferers
and
will
in each neighboring cell and for uniform estimation
equal to multiplied by the ratio of the area of one cell to the
. Furthermore, ,
are coefficient factors asarea of
signed to the mean and the variance of the interference due to
active users in the neighboring cells. Their values are assumed
constant in all traffic states, and are similar to those used in [2].
The blocking (inner-cell blocking) and dropping probabilities
at each traffic state (i.e., conditional probabilities) with respect
to current short-term interference level and using the above assumptions, will be computed as follows:
(14)
where the subscript
corresponds to blocking (dropping)
and
is the threshold corresponding to blocking
corre(dropping) a new (handoff) call request. And
sponds to the probability of interfering (active) users with
connected users in the desired cell. The first term of the
argument of in (14), i.e.,
, indicates intra-cell
interference and the second term, i.e., the integral term, represents the inter-cell interference at ( , , ) traffic state. The
blocking and dropping probabilities in each region should be
computed according to a specific traffic management policy.
In order to obtain average blocking (dropping) probabilities
and other traffic parameters we need to solve global balance
equations (GBE) corresponding to the Markov chain in Fig. 2
(see Appendix B).
to evaluate stationary probabilities,
Thus, we have some average traffic parameters as follow:
(15)
(16)
(17)
ASHTIANI et al.: FLEXIBLE DYNAMIC TRAFFIC MODEL FOR REVERSE LINK CDMA
where
163
Handoff rate at each ( , , ) traffic state with the assumption
of uniform spatial traffic distribution at neighboring cells will be
as follows:
(A.3)
(18)
defines the quality loss at ( , , ) traffic state,
i.e., it indicates the average fraction of time that the active MS’s
will confront degradation in their QoS due to large interference
[2].
is the maximum allowable realIn the above equations
valued number of interfering users with respect to required value
of SIR, and can be obtained by [2]:
We observe that we consider handoff arrival rate from neighboring cells as a traffic load dependent rate. This is one among
the flexibilities of the proposed traffic model, since in most of
the previous traffic models, a fixed average handoff rate is considered.
We assume the probability of moving in different directions
according to border line length at each direction. Also, we consider these movements in each subregion. Therefore we will
have:
(19)
where pg is the processing gain,
is the bit energy,
is the
acceptable maximum total interference power density, and
(
is the thermal noise power density). We, usually,
. In the above equations for
normalize the thresholds to
computational purposes we limit the number of users in each
region, however, this limit should not be the limiting factor in
soft capacity due to ICAC modeling (see Appendix B).
IV. CONCLUSION
In this paper we discussed two important features of the
CDMA cellular network, i.e., soft capacity and soft-handoff,
and their effect on the traffic analysis and modeling. We
then discussed traffic analysis of the CDMA cellular network
especially with respect to interference-limitedness attribute of
its capacity. After describing the important issues of a traffic
model for such a network we proposed a new and flexible
reverse link traffic model. This traffic model is built upon
ICAC method for soft capacity consideration and includes
time-varying traffic status of the neighboring cells in computing
inter-cell interference and handoff rate by using triple regions
in its geographical structure. Also, this model is suitable for
analysis and especially for comparison of traffic and handoff
management algorithms in dynamic environments.
(A.4)
APPENDIX B
In this appendix we discuss the global balance equations
(GBE) used for solving our Markov chain. For computational
reasons we need to limit for the number of users in three
,
, and
. Because of accepting
regions as
ICAC method for our traffic model, these numbers should not
be the dominant factors in limiting the number of channels.
In the analysis, we can determine these numbers such that the
blocking and dropping probabilities exceed a threshold equal
to 0.9 (by increasing this threshold we should not observe any
noticeable change in the results). Obviously, these limits are
determined adaptively, so, the number of states are reduced
and the speed of numerical analysis is increased. The GBE in
general is as in the following:
APPENDIX A
Computing average sojourn time in different regions is performed according to [13, appendix A]. Also, we compute new
call origination rate and departure rate for different regions as
follow:
(A.1)
(A.2)
where
is the area of region and
is the area of one
subregion of region . These equations have been written with
the assumption of the same primary traffic parameters at cell
as well as its neighbors. However, this assumption can be
removed in the case of heterogenous traffic intensities for the
concerning cells.
(B.1)
In the general equation, some of the terms may be removed
depending upon the specific ( , , ) traffic state, if the corresponding indices exceed the adaptive computed maximum or
become negative.
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ACKNOWLEDGMENT
The authors would like to thank Dr. M. Hakkak and Dr. M.
Beik-Zadeh for their support of this project.
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Farid Ashtiani (S’02) was born in 1973 in Tehran,
Iran. He received the B.S. degree from Shahid
Beheshti University, Tehran, Iran, in 1994, the M.S.
degree from K. N. Toosi University of Technology,
Tehran, Iran, in 1997, and the Ph.D. degree from
Sharif University of Technology, Tehran, Iran, in
2003, all in electrical engineering.
From 1995 to 1999 he was partly working in
Power Research Center (P.R.C.) and Niroo Research
Institute (N.R.I.) of Iran. From 1999 to 2001 he
was a member of research staff with Advanced
Communication Science Research Laboratory at Iran Telecommunication
Research Center (I.T.R.C.), Tehran, Iran. His research interests include traffic
analysis and modeling in CDMA cellular networks, soft-handoff management
policies, mobility modeling and radio resource control.
Jawad A. Salehi (S’80–M’84) was born in Kazemain, Iraq, on Dec. 22, 1956. He received the B.S.
degree in electrical engineering from the University
of California, Irvine, in 1979, and the M.S. and Ph.D.
degrees from the University of Southern California
(USC), Los Angeles, in 1980 and 1984, respectively.
From 1981 to 1984, he was a full-time Research
Assistant at Communication Science Institute at
USC engaged in research in the area of spread
spectrum systems. From 1984 to 1993, he was a
Member of technical staff with the Applied Research
Area at Bell Communications Research (Bellcore), Morristown, NJ. From
February to May 1990, he was with the Laboratory of Information and Decision
Systems at the Massachusetts Institute of Technology (MIT), Cambridge, as
a Visiting Research Scientist conducting research on optical multiple-access
networks. Currently, he is a Professor of Electrical Engineering Department at
Sharif University of Technology, Tehran, Iran. From fall 1999 till fall 2001 he
was the head of Mobile Communications Systems group and Co-Director of
Advanced and Wideband CDMA Lab at Iran Telecom Research Center (ITRC)
conducting research in the area of advance CDMA techniques for optical
and radio communications systems. His current research interests are in the
areas of optical multi-access networks, in particular, optical orthogonal codes
(OOC), fiber-optic CDMA, femtosecond or ultra-short light pulse CDMA,
spread time CDMA, holographic CDMA, wireless indoor infrared CDMA, and
applications of EDFA in optical systems. His work on optical CDMA resulted
in ten U.S. patents.
Dr. Salehi is a recipient of the Bellcore’s Award of excellence. He assisted,
as a member of the organizing committee, to organize the first and the second
IEEE Conference on Neural Information. In May 2001, he was appointed to
serve as Editor for Optical CDMA of the IEEE TRANSACTIONS ON COMMUNICATIONS.
Mohammad R. Aref was born in Iran in 1951. He received his B.Sc. in 1974
from Tehran University, his M.Sc. in 1975 and his Ph.D. in 1979 from Stanford
University, Stanford, California, all in electrical engineering.
From 1994 to 1999 he was the Chancellor of Tehran University. He is now a
Professor of electrical engineering at Sharif University of Technology in Tehran,
Iran, and has published numerous technical papers on communications theory
in international journals and conference proceedings.