An efficient model for reducing soft blocking probability in wireless cellular networks

International Journal of Wireless & Mobile Networks (IJWMN) Vol. 6, No. 4, August 2014
AN EFFICIENT MODEL FOR REDUCING
SOFT BLOCKING PROBABILITY IN
WIRELESS CELLULAR NETWORKS
Edem E. Williams1 and Daniel E. Asuquo2
1Department of Mathematics/Statistics and Computer Science
University of Calabar, PMB 1115, Calabar-Nigeria
2Department of Computer Science
University of Uyo, PMB 1017, Uyo-Nigeria
ABSTRACT
One of the research challenges in cellular networks is the design of an efficient model that can reduce call
blocking probability and improve the quality of service (QoS) provided to mobile users. Blocking occurs
when a new call cannot be admitted into the network due to channel unavailability caused by limited
capacity or when an ongoing call cannot be continued as it moves from one base station to another due to
mobility of the user. The proposed model computes the steady state probability and resource occupancy
distribution, traffic distribution, intra-cell and inter-cell interferences from mobile users. Previously
proposed models are reviewed through which the present model is built for use in emerging wireless
networks so as to obtain improved QoS performance. The developed model is validated through simulations
in MATLAB and its equations implemented using Java Programming Language. The results obtained
indicate reduced call blocking probability below threshold.
KEYWORDS
Call Blocking Probability Reduction, Cellular Networks, Quality of Service & Computer Simulations
1. INTRODUCTION
In cellular mobile networks, call blocking can occur as either new call blocking or handoff call
blocking. The former refers to blocking of a new call request due to lack of available channel
while the later refers to blocking of a call in the new cell as the mobile moves from its originating
base station (BS) to a new BS. Ideally, during handoff or handover, the distributed mobile
transceivers move from cell to cell during an ongoing continuous communication and switching
from one cell frequency to a different cell frequency is done electronically without interruption
and without a BS operator or manual switching. Typically, a new channel is automatically
selected for the mobile unit on the new BS which will serve it. The mobile unit then automatically
switches from the current channel to the new channel and communication continues. The two
kinds of arriving calls to a cell site are shown in figure 1. Call blocking probability is one of the
quality of service (QoS) parameters for performance evaluation in wireless cellular networks.
According to [1], for better QoS it is desirable to reduce the call blocking probability. Call
blocking is perceived negatively by users because it results to degradation in required QoS and
developing an efficient model to reduce its probability in cellular networks is a growing research
aimed at improving overall cellular system performance.
DOI : 10.5121/ijwmn.2014.6407 85

86
Figure 1: The two kinds of arriving calls to a cell site
The existing Visafone network suffers more of call blocking causing more calls to be rejected due
to channel unavailability, as shown in figure 2. It indicates that only a few of its BSs within the
region under study were able to carry traffic load beyond 400 Erlang per cell. This is definitely
not a good characteristic of a reliable and efficient network. The key Performance Indicators
(KPIs) usually measured by the regulatory bodies or commissions include Call Setup Success
Rate (CSSR), Call Completion Rate (CCR), Standalone Dedicated Control Channel and
Handover Success Rate (SDCCH), Call Data Rate (CDR) and Traffic Channel Congestion with or
without Handover (TCHCon). The network operators could be rated on excellent, good,
improvement, fluctuation, poor, slight decay and mostly steady below threshold on the KPIs. It is
important to note that a rating of improvement does not mean the target key performance
indicator is met. Rather, it means that the trend to reach the threshold is progressing towards the
set target of the indicator, taking into consideration the challenges the operators are facing daily.
It is therefore important that the operators continue working towards meeting the set target by
adopting improved architectures despite challenges faced in infrastructure, upgrade, and service
delivery.
Carried traffic Vs Days
1200.00
1000.00
800.00
600.00
400.00
200.00
0.00
Day1
Day3
Day5
Day7
Day9
Day11
Day13
Day15
Day17
Day19
Day21
Day23
Day25
Day27
Day29
Figure 2: Visafone BS’s Carried Traffic Load for 30 days
Erlang Traffic per cell
Several proposed models or techniques for reducing call blocking probability exist in literature
either for reducing new call blocking [2], or reducing handoff blocking [3,4,5] or reducing both
[6, 7, 8]. Whatever the case, there is a tradeoff between reducing handoff probability and new call
blocking probability. A proposed method which attempts to optimally reduce handoff failures in
mobile networks without significant increase in blocking probability of originating calls within a
cell is highly desirable. However, call blocking model could either be said to be hard or soft. In
hard call blocking models, the blocking probability is evaluated with fixed-valued parameters
regardless of the channel and traffic conditions. In a Code Division Multiple Access (CDMA)-
based network, the interference-limited nature makes it difficult to achieve accurate admission

control. Because of the co-channel interference, the amount of resources (power, bandwidth)
required by each user is dependent on the number of users in the system, their geographical
locations, and physical channel conditions. In soft blocking models, the blocking probability is
evaluated taking note of interference nature of the CDMA network. This work develops and
implements a soft blocking probability reducing model for new call request in the uplink of a
CDMA cellular network. A well established CDMA network named Visafone is studied in the
South-South Zone of Nigeria’s Niger Delta region.
The rest of this paper is organized as follows: section 2 reviews existing literature on call
blocking probability estimation for both hard and soft blocking while section 3 presents the
system design for the proposed model for reducing soft blocking probability with the developed
algorithm. In section 4, the pseudo code for the developed algorithm is presented, the model’s
accuracy is validated through computer simulations in MATLAB and the equations implemented
in Java. Section 5 presents the simulation results and conclusion giving direction for future
works.
2. LITERATURE REVIEW
In a wireless network composed of several BSs serving some mobile users, user’s power is
limited to some given maximal value. The same frequency spectrum is available to all BSs (i.e.,
the frequency reuse factor is unity, 1). For a CDMA network, the interference of single user
detection is regarded as noise. MSs and BSs are both assumed to be uniformly and randomly
distributed on an infinite plane, but with different terminal densities (coverage areas). Blocking
occurs in a network when due to limited capacity at least one link on the route is not able to admit
a new call. Thus, such a user will not be able to subscribe to a particular channel. The following
section discusses the two types of call blocking for CDMA BSs.
2.1 Hard Call Blocking
Hard blocking occurs when arriving calls to a network are blocked due to lack of available
channels irrespective of the traffic characteristic and channel conditions [2, 5].
2.1.1 Erlang-B Model
The Erlang-B formula in equation (1) is used to compute hard blocking as a function of the
number of available channels and the offered load. The equation is based on analytical probability
theory and can be used when the following assumptions are satisfied.
87
i. All call attempts are Poisson distributed with exponential service time
ii. Blocked calls are cleared (BCC) in the system and that the caller tries again later

(1)
In equation (2.3), = probability of blocking,
= offered traffic in Erlang,
= number of channels in the cell, and
i = number of busy channels
Thus, there is no queuing and no retry for unsuccessful calls with the Erlang-B model.
2.1.2 Extended Erlang B Model
The Extended Erlang B Model uses the same formula and assumptions as Erlang-B model except
that a percentage of callers retry their calls until they are serviced. This model is commonly used

International Journal of Wireless Mobile Networks (IJWMN) Vol. 6, No. 4, August 2014
for standalone trunk groups with a retry probability such as a MODEM pool. The model is as
expressed in equation (2).
88
=

(2)
Where, k is the number of busy channels, N is the number of servers (trunks), A is the traffic
density in Erlang, and is the blocking probability.
The Extended Erlang B traffic model is used by telephone system designers to estimate the
number of lines required for public switch telephone network connections (trunks) or private wire
connections and takes into account the additional traffic load caused by blocked callers
immediately trying to call again if their calls are blocked. It therefore, allows retry of
unsuccessful calls and assumes infinite population of callers (sources). This traffic model may be
used where no overflow facilities are available from the trunk group being designed.
2.1.3 Erlang-C Model
In the Erlang C Model, the system is designed around the queuing theory. The caller makes one
call and is held in a queue until answered, so the formula expresses the waiting probability. Just
as the Erlang B formula, Erlang C assumes an infinite population of sources, which jointly offer
traffic of A Erlangs to N servers. However, if all the servers are busy when a request arrives from
a source, the request is queued. An unlimited number of requests may be held in the queue in this
way simultaneously.
This formula calculates the probability of queuing offered traffic, assuming that blocked calls stay
in the system until they can be handled. This formula is used to determine the number of agents or
customer service representatives needed to staff a call centre a specified desired probability of
queuing. The blocking probability or the delay probability (waiting probability) is given in
equation 3.

(3)
where,
A is the total traffic offered in units of erlangs
N is the number of servers; i is the number of busy servers
PW is the probability that a customer has to wait for service
It is assumed that the call arrivals can be modeled by a Poisson process and that call holding times
are described by a negative exponential distribution. A common use for Erlang C is modeling and
dimensioning call center agents in a call center environment. It can also be used to determine
bandwidth needs on data transmission circuits.
2.1.4 Engset Formula
The Engset formula is used to determine the probability of congestion occurring within a
telephony circuit group. It deals with a finite population of S sources rather than the infinite
population of sources that Erlang assumes. The formula requires that the user knows the expected
peak traffic, the number of sources (callers) and the number of circuits in the network.
Engset's formula given in equation (4) is similar to the Erlang-B formula; however one major
difference is that the Erlang's equation assumes an infinite source of calls, yielding a Poisson
arrival process, while Engset specifies a finite number of callers. Thus Engset's equation should

be used when the source population is small. But for population sources greater than 200 users,
extensions or customers, it becomes similar to Erlang-B model [9, 10].
=
89
!

$ (4)
!

#
where,
A = offered traffic intensity in Erlangs, from all sources
S = number of sources of traffic
N = number of circuits in group
Pb = probability of blocking or congestion
In the traditional flat cellular networks, the Erlang-B model is generally used to describe the
limitation in physical resources independent of the quality experienced on the radio interface (i.e.
hard blocking). With the increasing complexity of CDMA cellular networks, the required
assumptions are no more valid and the Erlang-B formula is found to overestimate the capacity.
Thus, to properly account for the quality of service experienced at the BS, soft blocking should be
modeled and evaluated.
2.2 Soft Call Blocking
Soft blocking is related to the amount of interference in a network. There may be plenty of
channels available at a BS but since there are many users in the same cell already, the interference
level is such that adding an additional user would increase the interference above a predetermined
threshold. The call is therefore denied. Modeling soft blocking due to interference is important
and is considered a major aspect of this paper.
In [11], three explicit analytical models (single random trials (SRT), repeated random trials
(RRT), and least busy fit (LBF)) were developed for evaluating the request blocking probability
of movie files in video-on-demand (VoD) systems under three server selection schemes. The
authors reported that the choice of server selection schemes can significantly affect the blocking
probability performance of the system, and validated the accuracy of the analytical models
through simulation.
A rapid and accurate method for evaluating the quality of service (QoS) perceived by the users in
the uplink of wireless cellular networks was proposed in [2]. In doing so, the author aimed at
accounting for the dynamics induced by the arrivals and the departures of users. The evaluated
QoS was in terms of the blocking probability for streaming users and the throughput for elastic
calls. The blocking probability of streaming users was evaluated using the Kaufman-Roberts
algorithm as in [12, 13], whereas the throughput of elastic calls was evaluated using a multi-class
processor sharing model. The research in [14] modeled soft blocking in multi-cell CDMA
systems as an independent birth and death process at each cell. The model predicts the
distribution of the number of calls connected to a base station.
In [15], the authors presented an analytical model for the estimation of the blocking probability as
a function of the offered traffic per user in a cellular environment, where capacity is determined
by hard blocking and the average number of users per cell is small. Using statistical model, they
concluded that the number of mobiles audible to a base station with the strongest signal has a
Poisson distribution, which mean is given in terms of the mean densities of mobile and base
stations and the parameters of the attenuation law. The model does not represent a tool for
detailed network planning.
In [16], the outage probability is considered a performance measure for real-time traffic in
wireless networks. They observed that the blocking and outage probabilities do not have closed-form
expressions as they strongly depend on the traffic characteristics (call duration, bit rate
requirement, etc.), the radio conditions (fading, shadowing, noise, interference, etc.), the

considered admission and outage policies. They assumed that the admission and outage policies
satisfy a certain monotonicity property. Their results are applied to the uplink and the downlink of
CDMA networks. In [17], a wireless network with beam-forming capabilities at the receiver is
considered. They derived the blocking probabilities for calls in the system, under different traffic
policies. For a set of co-channel transmitters, their success probabilities for being captured by
separate antenna beams are computed. These success probabilities are taken into account in the
queuing model of the system. Their analytical and numerical results show that adaptive beam-forming
at the receiver reduces the blocking probability of calls and increases the total carried
traffic of the system.
In [18], a new resource-dimensioning concept based on both the allowable noise-rise and traffic
statistics is presented. The soft blocking probability based on outage probability and the
assumption of the Poisson arrival and exponential services time are first derived, with a consistent
view on traffic dimensioning. The relationship between outage probability, soft blocking
probability and hard blocking probability is discussed. The authors in [19] focused on the call
blocking probabilities calculation in a WCDMA cell with fixed number of channels and finite
number of traffic sources. They proposed the use of the Engset Multi-rate Loss Model (EnMLM)
in the uplink direction, which incorporates local blockings. The call admission depends on the
availability of the required channels. To analyze the system, they formulated an aggregate one-dimensional
90
Markov chain.
The work in [4] studied the QoS in terms of blocking and dropping probabilities, but the
interference between the users was not taken into account explicitly. The work in [20] studied the
QoS in wireless local area and sensor networks whereas this work focuses on wireless cellular
networks. Certain models for soft blocking evaluation assumes that there is a constant number of
users in the cell, power control is perfect, and each user requires the same signal bit energy to
noise spectral density %. From the above review, it appears studies on soft blocking have not
considered interference under imperfect power control which this work considers by extending
the Kaufman-Roberts algorithm under the assumption that in reality, none of these assumptions
holds. The reason is that the number of active users in a cell is Poisson distributed with mean
arrival and exponential service time ' (. Furthermore, due to voice activity, each user is ON with
probability, ) and OFF with probability * + ) and each user requires a different % to
achieve a desired bit error rate or communication signal quality.
3. PROPOSED MODEL FOR REDUCING CALL BLOCKING
PROBABILITY
In CDMA systems, signals of each MS can be modeled as interfering noise for the others, leading
to degradation in service. Adopting imperfect power control in CDMA wireless networks is to
regulate the transmission power levels of MS such that each user obtains a satisfactory QoS. This
goal is more precisely stated as to achieve a certain SINR regardless of channel conditions while
minimizing the interference and battery usage, and hence improving the overall performance.
Modeling the uplink system interference involves taking into consideration the cell model, path
loss model, power control, and simulation parameters. The proposed system design is shown in
figure 3 and implemented in six algorithmic stages. The stages are:
(i) modeling the state of a cell
(ii) Computation of total uplink interference
(iii) Computation and comparison of maximum effective cell load with threshold
(iv) Computation of soft blocking probability when cell load threshold is exceeded
(v) Blocking or accepting new call based on computed probability
(vi) Storage of generated results and updated system parameters

91
Figure 3: Proposed System Design for Soft Blocking Probability Evaluation
Stage1: Modeling the State of a Cell
Cell Model: In our model, each cell blocks newly arriving calls with a state dependent probability
illustrated using Markov Chain in figure 3. The state of a cell is the number of users currently in
that cell. Other cells simply contribute interference which causes blocking with some probability,

which is assumed to depend on the state , of the current cell. We model the state of a cell as
a birth and death process and showed that the arrival rate is thinned by the blocking probability,
'* +
!, while the departure rate is ,-.
Stage 2: Computation of Total Uplink Interference
CDMA systems consider soft blocking taking note of interference from mobiles in own cell and
other cells. Therefore in the uplink, the interference experienced by a certain mobile is related to
the load distribution within the network. The total interference is computed considering own-cell

interference, other-cell interference, and interference due to an empty system referred to as
thermal noise i.e .//01 2 .3 4 ./567 4 . This is represented in figure 3 in the hexagonal 3-
cell structure. The more users are active at the BS, the larger is the multi-access interference at the
BS and the higher are the transmit powers required by mobiles to fulfill their %
requirements.
SINR Calculation: The signal-to-interference-noise ratio 8.9 of each and every connection in
the uplink depends on the power emitted by mobile users, own-cell interference .3, other-cell
interference ./567, thermal noise #, and multi user detection factor, : as given in equation 5.
8.9; 2
92
=?@AB?@CDEF
(5)
where the received signal, 8= + GHIJ + K/L + K7L, and is the transmit signal power, K/L
is the transmitting antenna gain, K7L is the receiving antenna gain and J is the path loss
propagation (attenuation) model from MS-BS.
Path Loss Model: Considering a BS antenna height MNof 15metres and log-normally
distributed shadowing (logF) with standard deviation of 10dB, the path loss is calculated based on
equation (6) as in [21] as follows:
J 2 OP* + O Q *PRMN STUV + *WSTUMN+21Q STUX 4 WP (6)
J = *YZW 4 [Z STUV 4 STU] 2 *[ZW 4 [Z STUV (7)
where V is the MS-BS separation in kilometers.
Users connect to the BS per cell and each mobile connecting to one BS only at any given time.
The ,/5 mobile transmits with a nonnegative uplink power level of P ^
^ _0L `
, where
_0Lis a sufficiently large upper-bound imposed for technical reasons. The received power at the
a/5 BS, b
1 , is the attenuated version of the transmitted power level, b
1 2 N
1
, where the
quantity N
1 P c N
1 c * represents the slow-varying channel gain (excluding any fading).
Stage 3: Computation and Comparison of Maximum Effective Cell load with Threshold
Power Model: When a call arrives to the cell, the noise rise is estimated and if it exceeds a
maximum predefined threshold, the call is blocked and lost. Noise rise is the ratio of total
received power at the BS, .//01, to the thermal noise power, given in equation (8) as:
9=?C@Cde
@
=?@AB?@CDEF@
@
(8)
The cell load f, is defined as the ratio of the received power from all active users to the total
received power as given in equation (9). The cell load threshold must not be exceeded for call
admission at any given state of the cell.
f= ?@AB?@CDEF
?@AB?@CDEF@
(9)
The noise rise is related to the cell load given in equation (10) as follows:
9=
?C@Cde
@
?@AB?@CDEF@
=
@
=
=
@
g@ABhg@CDEFh@
=
=
= g@CDEFh@
g@ABhg@CDEFh@
=
=
=3
(10)
Thus, instead of using noise rise, the cell load can be used to determine call admission.

93
Stage 4: Computation of Soft Blocking Probability when Cell load Threshold is Exceeded
Simulation Model: In CDMA network, the cell load, f is interpreted as shared resource and the
load per cell (loading factor), J as resource requirement. The application of the Kaufman-
Roberts algorithm postulates a discrete shared resource and discrete service requirements. Thus,
in order to calculate the new call blocking probabilities of different service classes, we make
discrete the loading factor and the cell load by introducing a cell load unit i of which f_0L is an
integer multiple. This will help us determine the system state probabilities. Thus, the resulting
capacity and resource requirements are:
j =
3kdl
m
and n = round
m
Since a state corresponds to the resources occupied when all users are active. We denote by
o 2f3i as the number of occupied resources by the active users and introduce a random
variable for the number of occupied resources. Still assuming no local blocking occurs, the
probability pqr that c resources are occupied in state r (bandwidth occupancy) is computed
from equation (11):
pq,=
, s
= tup + vwq, + vw 4 * + upq, + vwx (11)
for , 2 *yzy ,_0L and o ^ ,, where ,_0L is the highest reachable system state.
The resource occupancy distribution is computed according to equation (11). So, using the
theorem of total probability we derive the local blocking probability (blocking factor) as in [8] as:
y,=

pq,
{# yo (12)
Again, we denote by,, the probability that the system is in state , or the probability that state
, is reached by a new call of service | or the probability that state , is reached from state , + n as
follows:
,=
}
7=~y
7€
F

(13)
where,
},=‚
*yXƒn, 2 P

}, + n * + y, + n s
= „
7

Xƒn, 2 *yzy j
Py…a†…
‡ (14)
This probability depends on }, + n and y, + n which are known for all states owith
o c ,. „,ny},, y,are the parameters of the model with infinite number of sources. Still
observing the steady state probabilities given in equation (14), we obtain the total (soft) blocking
probability for a service-class | as the sum of all state probabilities , multiplied with the
blocking probabilities y,, for all reachable states as shown in equation (15):
=

kdl y,

# ˆ, (15)

94
Stage 5: Blocking or Accepting New Call based on Computed Probability
The developed model is aimed at enhancing the acceptance of more user calls into the system to
improve overall utilization of scare network resources. Thus, a call is blocked when the blocking
probability value is greater than the predefined threshold of 0.01given in [15] or at worst 0.02,
otherwise, it is accepted, assigned a channel with needed QoS requirement and the channel
released on call completion.
In [22], an intelligent CAC scheme was developed where fuzzy logic technique was adopted in
the admission decision. Calls admissions were termed strongly accepted, weakly accepted,
weakly rejected and strongly rejected depending on the output value of the multi-criteria
parameters in the input to the call admission controller. Their results show the capability of fuzzy
logic to improve system performance by accepting more user calls.
Stage 6: Storage of Generated Results and Updated System Parameters
At this stage, the result obtained from the computed soft blocking probability which is used to
determine the acceptance or blocking of the new call is stored. Similarly, system parameters
generated are also stored in the database so that the next state of a cell can be determined from
parameters from the previous state. The objective is to improve battery live, reduce inter-cell
interference, maintain desired service quality, and maximize utilization of network resource for
improved system performance.
4. MODEL IMPLEMENTATION
Figure 4 shows the pseudo code for the developed algorithm. The model was validated through
simulations in MATLAB and its equations were implemented in Java programming language.
The results obtained are as shown in figures 5-7 for the three performance measures listed below.
Table 1 indicates the simulation parameters.
Performance Measure 1 (‰vs. „ at different 9 values): The impact of data rates on soft
blocking for given offered load.
Performance Measure 2 (‰vs. „ at different % values): The impact of signal energy
per bit to noise spectral density for given offered load.
Performance Measure 3 (‰vs. „ at different ./567 values): The impact of other-cell
interference on soft blocking for given offered load.
In figure 5, the developed system accepts input parameters and runs numbers of simulations for
performance measure 1(i.e. model 1). The result obtained indicates that at different traffic data
rates for given offered load to the system, the soft blocking probability values are higher for
services that require higher data rates and vice versa. Nevertheless, the overall performance of the
system is improved as the soft blocking probability values obtained are less than 0.02 showing
significant reduction.
In figure 6, the system evaluates the impact of each user’s signal energy per bit to noise spectral
density % on soft blocking since in reality, it value cannot be fixed for all service classes in a
CDMA network. This parameter is sometimes used to ascertain the user’s QoS requirement. For
different values of % input for performance measure 2 (i.e. model 2), the soft blocking
probability is reduced significantly indicating that more user calls are admitted into the system for
resource sharing.
In figure 7, the impact of other-cell interference ./567 on soft blocking probability is simulated
for given traffic load considering performance measure 3 (i.e. model 3). The results indicate that
though the soft blocking probability values obtained are higher for higher values of ./567

indicating the negative effect of inter-cell interference on CDMA networks, the values are
significantly reduced thus allowing lower blocking rates.
95
01 while (connection request is from a new user) {
02 do
03 initiate new call request;
04 if (.//01 ^ ._0L c ./5)
05 accept new call request;
06 elseif (f 4 J ^ f_0L)
08 else
09 { compute ‰|;
10 if ‰| ^‘’“”
12 else
Fig. 2: Pseudo code for the Developed Algorithm
13 Block new call request; } }
14 Ignore connection request; // it’s a handoff request
15 End
Figure 4: Pseudo code for the developed algorithm
Table 1: Simulation parameters
Parameter Value
Chip rate, W 5MHz
BS thermal noise, -174dBm
Data rate, 9 144Kbps,253Kbps,384Kbps
Voice activity factor, u 0.65, 1
Signal bit energy over noise spectral density, % 3 - 7dB
Multi user detection factor, : 0.78
Transmitting antenna gain, K/L 11dBi
BS antenna height, MN 15m, omnidirectional
MS transmitted power signal 21-30dBm
Maximum cell load, f_0L 0.8
Values of other-cell interference, ./567 Š…=‹Œ - 6…=ŽŒ
Offered load, „ 0.2 – 2.0 Erlang
Loading factor, J 0.05, 0.1, 0.15, 0.2, 0.25
Maximum number of states, ,_0L 4
Number of service class, | 3

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