Study of Guard-Channel-Based Call Admission Control Schemes for 4G
Cellular Networks
Faisal Iradat
Center for Computer Studies, Institute of Business Administration, Karachi
firadat@iba.edu.pk
Dr. Sayeed Ghani
Center for Computer Studies, Institute of Business Administration, Karachi
sghani@iba.edu.pk
Abstract
The success of next generation mobile and
wireless networks will significantly depend
on the performance of Call Admission
Control (CAC) schemes which contributes
to the overall network performance. Due to
the limited availability of resources,
mobility of users, and quality of service
(QoS) provisioning for applications whose
demand
and
nature
are
highly
heterogeneous, CAC schemes now play a
more central role in QoS provisioning for
next generation mobile and wireless
networks such as 3G, B3G, WLAN,
WiMAX and others. In this paper, we
briefly review existing CAC schemes and
examine the analytical methods employed
by
these
schemes
for
computing
new/handoff
call
blocking/dropping
probabilities. The normalized approach for
determining
the
new/handoff
call
blocking/dropping probabilities for the NewCall Bounding Scheme is further
investigated in terms of the expected number
of new/handoff call packets in the system in
steady state. A performance comparison of
these techniques is carried out via simulation
and compared with analytical results.
On the basis of this study we also suggest
that the performance evaluation of an
“effective holding time” approach of the
guard-channel (GC) based CAC scheme be
reexamined/addressed in a 4G cellular
network. This is due to the higher efficiency
and lower computational complexity of the
said approach, as compared to other
traditional and normalized approaches to the
guard channel based CAC schemes.
I.
Introduction
With the rapid advancement in the next
generation of mobile and wireless networks,
future telecommunication networks are
targeted at providing a rich set of new
wireless data and multimedia services along
with the support of traditional voice service.
The designers of these telecommunication
networks face significant challenges due to
the strict quality of service (QoS)
requirements. These challenges are further
exasperated due to the typical mobile and
wireless issues such as limited availability of
resources, user mobility, fading, shadowing,
noise etc.
In order to cope with these challenges, the
next generation of wireless technologies will
have to incorporate radio resource
management (RRM) mechanisms that
efficiently utilize the available resources.
RRM plays a critical role in the provisioning
of QoS in wireless systems. The
performance of these schemes in turn affects
the overall network performance. Many
researchers have proposed several radio
resource management techniques but later
on discovered through analysis and
simulation that a sub area within RRM,
called call admission control (CAC) is to be
addressed more critically than RRM [1,2].
1
Traditionally arriving new/handoff calls are
either accepted or denied access to the
network by the CAC scheme based on call
handoff dropping probability or cell
overload probability [3]. A CAC scheme
controls the amount of traffic entering the
network by either managing the number of
call connections into the network or
reducing the overall network load thus
enabling the network to provide the desired
QoS to new/handoff call connections.
Various CAC schemes have been proposed
in the past for different types of networks.
Following are some of the prominent
schemes that have been proposed for 3G,
beyond 3G (B3G) and Asynchronous
Transfer Mode (ATM) networks.
For cellular networks such as 3G and B3G
systems, several CAC schemes have been
proposed such as the distributed call
admission control [3], handoff density [4],
two-dimensional Markov approximation
approach [5], Hoeffding Bounds [6],
Tangent at Peak [7], Tangent at Origin [7],
Measure CAC[7], and Aggregated traffic
envelops [7] in order to reduce the call
handoff probability or cell overload
probability.
Whereas Non-statistical allocation, Peak
bandwidth allocation, and statistical
allocation call admission control schemes
have been proposed for Asynchronous
Transfer Mode (ATM) networks [8].
In the above networks, CAC schemes are
only concerned with accepting or rejecting
calls based on QoS requirements. On the
other hand in upcoming wireless
infrastructures such as the 4G ubiquitous
wireless
systems,
there
will
be
heterogeneous wireless access networks
such as wireless local area network
(WLAN), wireless metropolitan area
network (WiMAX) etc. Congestion control
techniques for these sort of wireless systems
are expected to be far more complex than
traditional cellular network systems in the
sense that the proposed CAC scheme should
now be capable of also selecting the best
access network and at the same time
supporting QoS requirements and user
mobility.
For such heterogeneous networks, several
solutions have recently been studied such as
the WLAN voice manager [9], ranking
schemes [2], call admission and rate control
scheme (CARC) [10], Distributed Call
Admission Control scheme for non-uniform
traffic [11], thinning schemes [12],
Differentiated Treatment to Multimedia
Traffic at Link Layer Framework [13],
Dynamic Programming Based Approach in
Polynomial Time [14], and Stable Dynamic
CAC (SDCA) [15] for call admission
control purposes.
Future telecommunications networks such as
the 4G cellular networks aim to provide
differentiated services such as traditional
voice, data, and multimedia with the desired
QoS to service providers. From the call
management perspective, in such type of
networks normally handoff calls are
assigned higher priority over new calls as
call dropping (which occurs when the
network is unable to provide resources to a
call for it to be handed off to another cell) is
more intolerable to mobile users than call
blocking.
Handoff priority-based CAC schemes is the
area where most of the recent research on
CAC for wireless networks has been studied
in depth in the recent past as compared with
other schemes
discussed
previously
[5,12,16,17]. In this paper we explore these
CAC schemes briefly and examine the
analytical methods employed by these
2
schemes for computing new / handoff call
blocking / dropping probabilities. The
normalized approach for determining the
new/handoff
call
blocking/dropping
probabilities for the New-Call Bounding
Scheme is further investigated in terms of
the expected number of new/handoff call
packets in the system in steady state [En(L)
& Eh(L)].
Finally, suggest that the performance
evaluation of the “effective holding time”
approach of the guard-channel based CAC
scheme be reexamined / addressed in a 4G
cellular network.
The rest of this paper is organized as
follows. In Section II we briefly present the
different Guard-Channel (GC) schemes.
Next, in section III we study the
performance of the New-Call Bounding
Scheme in detail. Results of simulation and
analysis are presented in this section. In
section IV we review the “effective holding
time” approach of the guard-channel based
CAC scheme. Finally section V summarizes
our findings and discusses future research
areas.
II.
Brief Overview of Guard-Channel
Based CAC Schemes
In a wireless mobile / cellular network
environment, call dropping is more
intolerable than call blocking from the
mobile users aspect. As a result most of the
CAC schemes proposed, give higher priority
to handoff calls than to news calls. Handoff
priority-based CAC schemes proposed in
[5,12,16,17], are classified in two broad
categories, as described below.
1. Guard Channel (GC) schemes:
In guard channel based schemes some
channels are reserved for handoff calls.
Following are the four different types:
New Call Bounding Scheme [5]:
In the new call bounding scheme, a
threshold is enforced on the number of
new calls accepted into the cell. If the
number of new calls in a cell is less than
a threshold K than a new call will be
admitted.
Cutoff Priority Scheme [18,19,20]:
In the cutoff priority scheme, new calls
are admitted only if the number of busy
channels is less than a threshold m.
Fractional GC Scheme [17]:
This is also called as the Thinning
Scheme, in which new calls will be
selectively blocked when the cell traffic
increases. More specifically, new calls
are admitted with probability  i when
the number of busy channels is i. Based
on this probability a new call is either
admitted or blocked.
By assigning different values to  i this
scheme can be reduced to the cutoff
priority scheme [17] that has been
discussed earlier. As this scheme is quite
similar to cutoff priority scheme, it will
not be presented in detail, in this paper.
 n c 1 h 

 q(c  1)  cq(c)
h 
 n
c=1,….,C
(1)
Here q(c) denotes the equilibrium
channel occupancy probability when
exactly c channels are occupied in a cell
and h , h and n , n are the arrival and
departure rates for handoff calls and new
calls respectively. c is the number of
occupied channels in a cell.
Rigid Division Based Scheme [21]:
In this scheme all channels are divided
into two groups: one for common calls
and the other for handoff calls. This
scheme does not efficiently utilize the
available resources and mentioned for
reference only.
3
2. Queuing Priority (QP) schemes:
In these schemes if channels are free
than calls will be accepted. When all
channels are busy either new calls are
queued and the handoff calls are
blocked, or new calls are blocked and
handoff calls are queued, or all arriving
calls
are
queued
with
certain
rearrangements
in
the
queue
[22,23,24,25,26].
These schemes are restrictive to the GC
schemes
presented
earlier
[17].
Secondly, they cannot be compared with
other GC schemes as the protocol is
quite different [17].
In recent research [5,17] the above
mentioned GC based CAC schemes were
examined using the Markov chain models.
In a traditional circuit switched network, the
one-dimensional Markov chain model was
used under the assumption that all arrivals
are modeled as Poisson and the channel
holding time and channel residence time are
modeled as exponential with predetermined
channel bandwidth [27,28]. However with
the rapid evolution of cellular networks, the
Markov chain model used for obtaining
blocking/dropping
probabilities
for
new/handoff calls becomes more complex as
the new and handoff calls may have
different average holding times and worse,
different distributions. This problem may be
solved with use of multidimensional Markov
chain model but these suffers from the curse
of dimensionality thus making them much
more complex as compared with the onedimensional Markov chain models [29].
Many researchers attacked this problem with
the assumption that the channel holding
times for new/handoff calls are identically
distributed with the same average values.
However this assumption is inappropriate as
new and handoff calls may have quite
different distributions and average holding
times [30,31].
To avoid such complexities associated with
multidimensional Markov chain models,
approximations have been used that have
high accuracy and low computational
complexity with the condition that the
approximation is based on a onedimensional Markov chain model with
exponentially distributed holding times for
new / handoff calls however with different
average values [5,17].
III.
Performance of New Call
Bounding Scheme using
Simulation and Analysis
In this section we will briefly discuss the
performance of the new call bounding
scheme using the traditional and the
normalized analytical methods proposed in
[5,17]. The assumptions made are that the
arrival process of the new/handoff calls are
modeled as Poisson, and the average
channel holding times are different, and are
exponentially distributed. Resulats of a
simulation written in C++ are given and
compared to analytical results as well.
In
the
traditional
approach,
the
blocking/dropping probabilities are derived
for new/handoff calls with the assumption
that the new/handoff calls have the same
average values and channel holding time
distributions. This system is approximated
as one-dimensional Markov chain model
with a fixed channel holding time for the
total cell traffic [5].
In the normalized approach [5], the results
are improved by normalizing the average
service times for new/handoff calls to unity
rather than equal average channel holding
time.
The performance of the new call bounding
4
scheme is discussed as follows:
As presented earlier in section II, if we use
the call admission control scheme given in
section II for the new call bounding scheme,
Handoff calls (n2)
we get the following transition diagram (Fig.
1) which is modeled by a two-dimensional
Markov chain model (Please refer to
appendix A for nomenclature).
New
Calls
(n1)
Fig. 1. State transition diagram for the new call bounding scheme (Source [5])
The steady state probability p(n1, n2) can be
determined as given below (2) by solving
the global balance equations from the state
transition diagram as shown in Fig. 1. n1 and
n2 represents new calls and handoff calls.
p(n1 , n2 ) 
Where  n 
nn hn
1
2
n1! n2!
p(0,0)
(2)
n

and  h  h represents the
n
h
traffic intensities for new/handoff calls
(please refer to appendix A for
nomenclature).
Due to the inherent complexity associated
with the two-dimensional Markov chain
model, in the normalized approach the
new/handoff
calls
blocking/dropping
a
probabilities (  nb
and
 a nh ) are
determined under the assumption that the
service rate of new/handoff calls equals to 1
(please refer to appendix B for
blocking/dropping probabilities of the new
call bounding scheme for the normalized
approach) [5,17]. Whereas, the traditional
approach uses fixed average channel holding
time  av for total cell traffic is given by:
1
n 1
h 1  n   h



(3)
av n  h n n  h h n  h
1
1
By replacing
and
in the formulas for
n
h
new/handoff
call
blocking/dropping
probabilities of the normalized approach
(please refer to appendix B for
blocking/dropping probabilities of the new
call bounding scheme for the normalized
approach) we get the traffic intensities for
new/handoff calls in the resulting onedimensional Markov chain model for the
traditional approach (please refer to
appendix
B
for
blocking/dropping
5
probabilities of the new call bounding
scheme for the traditional approach).
In order to compare the normalized versus
traditional approaches a simulation was also
conducted, written in C++. The simulation
made the same assumptions as noted above
for traffic and call admission control.
Results of the simulation and analytical
expressions are discussed below.
When the new call bounding scheme is
investigated under fixed handoff holding
times and varying new call holding times
(K=15, C=30, 1/λn=30, 1/µn=changes from
200 to 600, 1/λh=30, 1/µh=450), it is
apparent from Fig. 2 that the traditional
approach overestimates the normalized
approach when handoff call traffic load is
higher than new call traffic load whereas the
traditional approach underestimates handoff
call blocking probability of the normalized
approach as shown in Fig. 3. Figure 4 shows
the graph of average number of new/handoff
calls in a cell in steady state for different
new call traffic loads (  n ).
Fig. 4. Average number of New/Handoff calls in
a cell in steady state *
* N and T denotes the Normalized and
Traditional Approaches, n and h denote
new/handoff, S and A denote Simulation /
Analytical
On the other hand when the new call
bounding scheme is investigated under
varying handoff holding times and fixed
new call holding times (K=20, C=30,
1/λn=30, 1/µn=300, 1/λh=30, 1/µh= changes
from 100 to 1200), it is observed from Fig. 5
and Fig. 6 that the new call blocking
probability and handoff call blocking
probability are similar in value. This makes
sense because due to the heavy traffic load
incurred from handoff calls the new calls
will not be able to reach a bound. However,
the traditional approach is close but not the
same as the normalized approach. . Figure 7
shows the graph of average number of
new/handoff calls in a cell in steady state for
different handoff traffic loads (  h ).
Fig. 2. New call blocking probability in the new
call bounding scheme*
Fig. 5. New call blocking probability in the new
call bounding scheme *
Fig. 3. Handoff call blocking probability in the
new call bounding scheme*
6
chain model. All that is required is a better
approximation method.
Fig.6. Handoff call blocking probability in the
new call bounding scheme *
N and T denotes the Normalized and
Traditional Approaches, n and h denotes
new/handoff, S and A denotes Simulation /
Analytical
*
In the “effective holding time approach”,
equation (1) is simplified by replacing the
average holding times for new/handoff calls
with the average channel holding time for
the total traffic also referred to as average
1
effective channel holding time
. In this
 eff
case we would replace
1
 eff
rather than
1
 avg
1
n
N and T denotes the Normalized and
Traditional Approaches, n and h denotes
new/handoff, S and A denotes Simulation /
Analytical
*
Review of the “effective holding
time” approach of the guardchannel based CAC scheme
From the results presented in the previous
section we can determine that the
normalized approach performs better than
the traditional approach [17]. However in
order to further improve the results while
keeping the complexity low, a new approach
called the “effective holding time approach”
was proposed which produced better results
when compared with the existing
approaches discussed earlier [17].
IV.
To keep the computational complexity low it
is useful to reduce the two-dimensional
Markov chain model to a one-dimensional
1
h
with
as in the traditional
approach. We cannot use the
Fig. 7. Average number of New/Handoff calls in
a cell in steady state *
and
1
 avg
average
since the average channel holding times for
total cell traffic have different blocking
probabilities for new / handoff calls. The
1
average is obtained from the idea
 eff
proposed in [29] which is also referred to as
the knapsack problem approach (please refer
to appendix B for locking/dropping
probabilities of the cutoff priority scheme
for the “effective holding time” approach)
[17].
In order to evaluate the performance, the
numerical results obtained from this scheme
i.e. the “effective holding time approach”
was compared with those obtained from the
existing traditional approach, normalized
approach, and the direct approach. The exact
method that is used for determining the
actual values of a multidimensional Markov
chain model using the “LU decomposition”
is referred to as the direct approach [17].
Through the comparison (Fig. 8 and Fig. 9)
it was observed that the traditional approach
and
normalized
approaches
deviate
significantly from the direct and the
“effective holding time approach”. The
7
“effective holding time approach” results are
very close to the actual results obtained from
the direct method and seem as the best fit as
a future GC based CAC scheme for wireless
network.
Fig. 8. New
call blocking probability in the
effective holding time approach [17].
call blocking probability in
the effective holding time approach [17].
Fig. 9. Handoff
In summation, the traditional approach
overestimates whereas the normalized
approach
underestimates
the
direct
approach.
V.
Summary and Future Work
In this paper we critically reviewed existing
guard-channel
based
CAC
schemes
proposed in [5,17] in order to determine the
approach that gives more accurate results
when compared with other approaches. It
was learnt that the two-dimensional Markov
chain model solves the problem when the
average channel holding times for the new
and handoff calls are significantly different.
However as the dimensions of the Markov
chain model increase due to distinct traffic
type’s e.g. video, voice, and packetized data,
the computational complexity increases and
at times becomes virtually impossible to
analyze exactly due to, the asymmetric
nature of the states in a Markov chain
transition diagram. Hence it was noted that it
is useful to attempt reducing/approximating
the two-dimensional Markov chain model
with a one-dimension Markov chain model.
All GC scheme approximate a twodimensional Markov chain model with a
one-dimensional Markov chain model using
different approaches referred to as the
traditional approach, normalized approach,
and the effective holding time approach.
It has been shown that the “effective holding
time approach” outperforms the traditional
and normalized approaches in terms of
accuracy and low computational complexity.
Hence in order to evaluate CAC schemes for
a 4G network environment, which will
require handling of multiclass services we
suggest that the “effective holding time”
approach be used and further studied.
References
[1] Hossam Ahmed, “Call Admission
Control in wireless Networks: A
Comprehensive Survey”, IEEE
Communications Survey & Tutorials,
Volume 7, No. 1, First Quarter 2005.
[2] Robert Achieng and H. Anthony Chan,
“A QoS Enabling Queuing Scheme for
4G Wireless Access Networks”, ACM –
IWCMC, July 2006.
[3] M. Naghshineh, and M. Schawrtz,
“Distributed Call Admission Control in
Mobile/Wireless Networks”,
International Symposium on Personal
Indoor Mobile Radio Communications,
IEEE, September 1995.
[4] Q. Gao and A. Acampora, “Performance
Comparison of Admission Control
Strategies for Future Wireless
Networks”, Proc. IEEE wirelss
Communication and Network
Conference, WCNC2002, vol. 1, Mar.
2002, pp. 317-21.
8
[5] Y. Fang and Yi Zhang, “Call Admission
Control Schemes and Performance
Analysis in Wireless Mobile
Networks”, IEEE Trans. Veh. Technol.,
Vol 51, no. 2, pp. 371-382, Mar. 2002.
[6] G. Razzano and A. Curcio,
“Performance Comparison of Three
Call Admission Control Algorithms in a
Wireless Ad Hoc Network”, Proc. Int’l
Conf. Commun. Tech. (ICCT 2003),
vol. 2., Apr. 2003, pp. 1332-36.
[7] L.Breslau and S. Jamin, “Comments on
the Performance of Measurement-Based
Admission Control Algorithms”, Proc.
IEEE INFOCOM 2000, vol. 3, Mar.
2000, pp. 1233-41.
[8] H. G. Perros, and K. M. Elsayed, “Call
Admission Control Schemes: A
review”, IEEE Communications
Magazine, Nov. 1996, vol. 34., no. 11,
pp. 82-91.
[9] Yi Qian, Qingyang Hu, Hsiao-Hwa
Chen, “A Call Admission Control
Framework for Voice over WLANS”,
IEEE wireless communications,
February 2006.
[10] H. Zhai, X. Chen, and Y. Fang, “A Call
Admission and Rate Control Scheme
for Multimedia Support over IEEE
802.11 Wireless LANs”, QSHINE 04,
2004.
[11] J. Kim, E. Jeong, and J. Cho, “Call
Admission Control for Non-uniform
Traffic in Wireless Networks”,
Electronic letters, January 2000.
[12] Y. Fang, “Thinning Schemes for Call
Admission Control in Wireless
Networks”, IEEE transactions on
Computers, Vol. 52, No. 5, May 2003.
[13] R. Jayaram, S. K. Das, S. K. Sen, “A
Call Admission and Control Scheme for
Quality of Service (QoS) Provisioning
in Next Generation Wireless
Networks”, Baltzer Journal, 2000.
[14] S. Ganguly, B. Nath and N. Goyal,
“Optimal Bandwidth reservation
Schedule in Cellular Networks”, IEEE
INFOCOM 2003, 2003.
[15] S. Wu, K. Wong, and B. Li, “A
Dynamic Call Admission Policy with
Precision QoS Guarantee using
Stochastic Control for Mobile Wireless
Networks”, IEEE Transactions on
Networking, Vol 10, No. 2, April 2002.
[16] I. Katzela and M, Naghshineh,
“Channel assignment schemes for
cellularmobile telecommunication
systems: A comprehensive survey”,
IEEE Personal Commun., vol. 3, pp. 1031, June 1996.
[17] A. Yavuz and C. M. Leung,
“Computationally efficient method to
evaluate the performance of GuardChannel-Based call admission control
in cellular networks”, IEEE Trans. on
Veh. Techno.., vol. 55, no. 4, July 2006.
[18] R. A. Guerin, “Queuing–blocking
system with two arrival streams and
guard channels,” IEEE Trans.
Commun., vol. 36, no. 2, pp. 153–163,
Feb. 1988.
[19] D. Levine, I. Akyildiz, and M.
Naghshineh, “A resource estimation and
call admission algorithm for wireless
multimedia networks using the shadow
cluster concept,” IEEE/ACM Trans.
Netw., vol. 5, no. 1, pp. 1–12, Feb.
1997.
[20] C. Oliveira, J. B. Kim, and T. Suda,
“An adaptive bandwidth reservation
scheme for high-speed multimedia
wireless networks,” IEEE J. Sel. Areas
Commun., vol. 16, no. 6, pp. 858–874,
Aug. 1998.
[21] M. D. Kulavaratharasah and A. H.
Aghvami, “Teletraffic performance
evaluation of microcell personal
communication networks (PCN’s) with
prioritized handoff procedures,” IEEE
Trans. Veh. Technol., vol. 48, no. 1, pp.
137–152, Jan. 1999.
9
[22] R. A. Guerin, “Queuing–blocking
system with two arrival streams and
guard channels,” IEEE Trans.
Commun., vol. 36, no. 2, pp. 153–163,
Feb. 1988.
[23] E. D. Re, R. Fantacci, and G.
Giambene, “handover queuing
strategies with dynamic and fixed
channel allocation techniques in low
earth orbit mobile satellites systems”,
IEEE Transc. Commun., vol. 47, no. 1,
pp. 89-102, 1999.
[24] C. H. Yoon and C. K. Un,
“Performance of personal portable radio
telephone systems with and without
guard channels”, IEEE J. Select. Areas
Commun., vol. 11, no. 6, pp. 911-917,
1993.
[25] C. Chang, C. J. Chang, and K. R. Lo,
“Analysis of a hierarchical cellular
system with reneging and dropping for
waiting new calls and handoff calls,”
IEEE Trans. Veh. Technol., vol. 48, no.
4, pp. 1080–1091, Jul. 1999.
[26] V. K. N. Lau and S. V. Maric,
“Mobility of queued call requests of a
new call queuing technique for cellular
systems,” IEEE Trans. Veh. Technol.,
vol. 47, no. 2, pp. 480–488, May 1998.
[27] R. Guerin, “Equivalent capacity and its
application to bandwidth allocation in
high-speed networks,” IEEE J. Sel.
Areas Commun., vol. 9, no. 7, pp. 968–
981, Sep. 1991.
[28] Q. Ren and G. Ramamurthy, “A realtime dynamic connection admission
controller based on traffic modeling,
measurement, and fuzzy logic control,”
IEEE J. Sel. Areas Commun., vol. 18,
no. 2, pp. 184–196, Feb. 2000.
[29] A. Gersht and K. J. Lee, “A bandwidth
management strategy in ATM
networks,” GTE Laboratories,
Waltham, MA, 1990. Tech. Rep.
[30] Y. Fang and I. Chlamtac, “Teletraffic
analysis and mobility modeling for PCS
networks,” IEEE Trans. Commun., vol.
47, no. 7, pp. 1062–1072, Jul. 1999.
[31] Y. Fang, I. Chlamtac, and Y. B. Lin,
“Channel occupancy times and handoff
rate for mobile computing and PCS
networks,” IEEE Trans. Comput., vol.
47, no. 6, pp. 679–692, Jun. 1998.
Appendix – A
C
Number of channels in a cell.
c
Number of occupied channels in a cell.
K
Threshold for new call bounding
scheme.
m
Threshold for the cutoff priority scheme.
Arrival rate for new calls.
n
h
1 n
Arrival rate for handoff calls.
Average channel holding time for new
calls.
1 h
Average channel holding time for
handoff calls.
1  eff Average effective channel holding time.
n
h
Traffic intensities for new calls.
Pnb
Phb
Blocking probability for new calls.
Traffic intensities for handoff calls.
Dropping probability for handoff calls.
a
nb
P
Blocking probability for new calls from
the normalized approximation.
Phba
Dropping probability for handoff calls
from the normalized approximation.
Pnbt
Blocking probability for new calls from
the traditional approximation.
Phbt
Dropping probability for handoff calls
from the traditional approximation.
Pnbeff
Blocking probability for new calls from
the effective holding time approximation.
Phbeff
Dropping probability for handoff calls
from the effective holding time approximation.
Admission probability for new calls in
i
fractional guard channel (GC) scheme
q (c ) Equilibrium occupancy probability.

q (c ) Approximate equilibrium occupancy
probability.
10
Appendix – B
1. New Call Bounding Scheme
Normalized Approach
 nK  hK
C K
Pnba 
 K!
K 1

n2 !
n2  0
n1  0

K
 hC  n
1
1
n1! (C  n1 )!
n1 C  n1
n
 hn
n2  0
2
 n!  n !
n1  0
K
Pnba 
 nn
 nn
1
2
 hC  n
 n ! (C  n )!
1
n1  0
1
K

1
n1 C  n1
n

1
n2
h
 n!  n !
n1  0
1
n2  0
2
Traditional Approach

n

n  n 
( n   h )
 av n  h

n 
h
n

( n   h )
 av n  h
Replace the given traffic intensities in the
equations for normalized approach (new call
bounding approach) given above (1.1) to get
the probabilities for the traditional approach.
2. Effective Holding Time Approach
C 1

n . j .q ( j )

Pnbeff  1  j  0C

 n .q ( j )
j 0
C 1
Phbeff  1 

  . .q ( j )
j 0
C
h
j

  .q ( j )
j 0
h
11