Int. J. Communications, Network and System Sciences, 2010, 3, 631-637
doi:10.4236/ijcns.2010.37085 Published Online July 2010 (http://www.SciRP.org/journal/ijcns/).
Modeling and Analysis of Bandwidth Allocation in IEEE
802.16 MAC: A Stochastic Reward Net Approach
Shanmugam Geetha, Raman Jayaparvathy
Department of EEE, Coimbatore Institute of Technology, Coimbatore, India
Received April 20, 2010; revised May 27, 2010; accepted July 2, 2010
Abstract
In this paper, we present a stochastic reward net (SRN) approach to analyse the performance of IEEE 802.16
MAC with multiple traffic classes. The SRN model captures the quality of service requirements of the traffic
classes. The model also takes into account pre-emption, priority and timeout characteristics associated with
the traffic classes under consideration. The performance of the system is evaluated in terms of mean delay
and normalized throughput considering the on-off traffic model. Our analytical model is validated by s imula-
tions.
Keywords: Wima x, IEEE 802.16, Stochastic Reward Net, Mean Delay, Throughput
1. Introduction
Over the last few years there has been tremendous in-
crease in the use of broadband access. The deployment
has boosted the usage of several multimedia applications
such as Voice over IP (VoIP), online gaming and Video
on Demand (VoD). However, in the rural and suburban
areas, deployment of traditional wired technologies is too
expensive. In such cases, broadband wireless access
(BWA) based on IEEE 802.16 provides a promising so-
lution [1,2]. One of the key features of IEEE 802.16 is that
it supports multiple applications such as HDTV, video
conference and conventional internet applications. The
challenge for BWA networks is to simultaneously provide
quality of service (QoS) to applications with very differ-
ent characteristics. Hence, a proper resource allocation
scheme for packet transmission is imperatively needed.
Performance evaluation of resource allocation me-
chanisms plays an important role in design of communi-
cation systems. Increasing complexity of networks and
the way in which they are used, has made it difficult to
construct models that are analytically tractable. SRNs are
very useful in analytical modeling of complex networks.
System operations can be precisely described by means of
a graph which translates into a markovian model. Prop-
erties such as liveness and deadlock freeness make SRN a
reliable analytical modeling tool.
SRN has been used extensively for performance mod-
eling. Performance of opportunistic and non opportunistic
schedulers was compared in [3] using analytical model
developed with stochastic Petri net (SPN). A protocol of
QoS has been developed using Petri net in [4]. The pro-
tocol has been verified for service guarantee and effec-
tive use of resources. Modeling power, analysis and veri-
fication of SPN has been discussed in [5]. Application of
Petri net (PN) in performance and availability analysis is
discussed in [6]. The authors in [7] presented a SRN ap-
proach to model IEEE 802.11 DCF with on-off traffic
model. Performance metrics such as mean delay and av-
erage system throughput have been evaluated. Reconfi-
gurable PN and their ability to model dynamic systems
have been studied in [8].
Several approaches have been used for performance
evaluation of IEEE 802.16 networks. Simulation ap-
proach has been followed in [9] for evaluating IEEE
802.16 system metrics such as mean delay and through-
put. Analytical approach to study bandwidth allocation
process has been presented in [10,11]. Packet scheduling
scheme for QoS provisioning in WiMax networks is
discussed in [12]. The proposed scheme in [12] has been
verified using simulations. In [13], authors have pro-
posed a Light WiMAX simulator (LWX) for evaluating
performance of IEEE 802.16 bandwidth allocation algo-
rithms. Simulation approach has been adopted in [14] to
compare various scheduling schemes such as round-
robin, token bucket-based and M-LWDF algorithms.
Authors in [15] have proposed an intelligent bandwidth
allocation of uplink (IBAU) for WiMax systems. IBAU
mechanism is shown to decrease delay and increase
throughput of the network. A survey on scheduling

S. GEETHA ET AL.
632
schemes in IEEE 802.16e systems has been presented in
[16]. Simulation methodologies to be adopted for MAC
and PHY layers of IEEE 802.16 are presented in [17].
In this paper, we propose a SRN approach to model and
analyze performance of the IEEE 802.16 MAC with
multiple traffic classes. The proposed model incorporates
prioritization and pre-emption of traffic classes. Packet
drop due to waiting time exceeding threshold is also
considered. We compute the average system throughput
and mean delay suffered by the first packet (i.e., the
packet in the head of line (HOL) of each queue, through
the proposed SRN formulation. Mean delay of subse-
quent packets is determined by modelling each queue as
M/G/1 queue [7]. The mean service time for the compu-
tation is obtained from the mean delay suffered by the
HOL packet. Our analytical model is validated by com-
paring the results with simulations carried out using
event based simulator.
The rest of the paper is organized as follows: Section 2
presents a brief overview of IEEE 802.16 MAC. System
model is presented in Section 3. Section 4 discusses the
performance evaluation. Results and discussion are pre-
sented in Section 5. Conclusions are drawn in Section 6.
2. IEEE 802.16 MAC
IEEE 802.16 system consists of two kinds of fixed sta-
tions: subscriber station (SS) and base station (BS). All
communication in the network is regulated by BS. Two
direction of communication path exists between BS and
SS: uplink (from SS to BS) and downlink (from BS to
SS). IEEE 802.16 MAC defines QoS signaling mechan-
isms and functions that control BS and SS data transmis-
sions. Two modes of sharing the wireless medium is
possible: Point-to-Multipoint (PMP) and Mesh. In PMP,
BS serves a set of SS in a broadcast manner. Coordina-
tion of transmissions from SSs is done by BS. In mesh
mode, organization of nodes is in ad hoc manner and
communication exists between SS. In this paper, we fo-
cus on PMP mode.
The IEEE 802.16 MAC defines four different sched-
uling service flows in order to meet the QoS requirements
of multimedia applications [9]. Unsolicited Grant Service
(UGS) is designed to support real-time applications, with
strict delay requirements which generate fixed-size packets
at periodic intervals such as T1/E1. Real-time Polling
Service (rtPS) is designed to support real-time applica-
tions with less stringent delay requirements, which gen-
erate variable size packets at periodic intervals, such as
VoIP with silence suppression. Non-real-time Polling
Service (nrtPS) support non-real-time variable bit rate
services, such as FTP. Best Effort (BE) traffic does not
have QoS guarantees, such as HTTP. Since rtPS, nrtPS
and BE traffic classes have varying bandwidth require-
ments; bandwidth allocation for these classes is per-
formed dynamically. As UGS is allocated fixed and re-
served bandwidth, dynamic reassignment of bandwidth is
not required.
SS maintains separate connection for each service
flow. The allocation of bandwidth by the BS to SS is
based on two modes: grant per subscriber station (GPSS)
and grant per connection (GPC). In GPSS, the SS obtains
aggregate bandwidth for all its individual flow and in turn
reallocates the bandwidth to each flow individually. In
GPC, the bandwidth allocation by BS is made on per flow
basic. We assume GPSS mode of operation in this paper.
3. System Model
A typical IEEE 802.16 network consists of multiple BSs.
Each BS covers several SSs. Every SS is associated with
multiple queues corresponding to different traffic classes.
We model a single SS with three queues corresponding
to rtPS, nrtPS and BE traffic classes as shown in Figure
1. The SS is assigned aggregate bandwidth by the BS.
The three queues contend for bandwidth from the SS.
The objective is to obtain the mean delay and normalized
throughput of each traffic class for varying load condi-
tions. The analytical model is required to take into ac-
count prioritization, pre-emption and dropping of packets
(with waiting time exceeding the threshold) correspond-
ing to various traffic classes.
Packets arrive at each of the queues in random epochs
of time. Data packets arriving at a queue gets buffered
till they gain access to channel. Newly arriving packets
are added to the queue on a first come first serve (FCFS)
basis. Delay of a packet is defined as the time spent by a
packet till it is successfully transmitted. Normalized
throughput of a given traffic class is defined as the ratio
of successful packets transmitted to total packets gener-
ated. Average system throughput is the sum of through-
puts of individual traffic class.
The following assumptions are made in the model.
• There are 3 different traffic classes in the system,
namely rtPS, nrtPS and BE denoted as class1, class2 and
class3 respectively.
• We consider data-only traffic with on-off traffic
model. Data bursts consist of active and idle periods.
(Practically, a data burst represents data packet of vari-
able
Figure 1. System model.

S. GEETHA ET AL.
633
length, for example an IP packet with zero idle time be-
tween finite set of consecutive packets.[7])
• Data bursts arrival at any queue follows a Poisson
process with mean arrival rate
λ
i.
• Service times of data bursts are exponentially dis-
tributed with mean 1/
µ
i seconds.
• The SSs are assumed to have negligible mobility.
4. Performance Evaluation
In this section, we present a SRN model to evaluate the
performance of the system considered in Section 3. Per-
formance metrics considered are normalized throughput
and mean delay suffered by a packets belonging to each
traffic class.
4.1. Stochastic Reward Net Model
SRN model for a SS with three queues is shown in Figure
2. The model incorporates priority, pre-emption and
timeout characteristics of the queues. Tables 1-3 lists the
various places, transitions and the meaning associated
with each of them.
Transition usri generates packets at a given rate λ
i
and deposits them into place qi. An inhibitor arc with
Table 1. List of places.
Place Meaning
cap
Total available bandwidth
usgi Number of channels currently in use
q
i
Packets in buffer
Table 2. List of timed transitions.
Timed Transition
Meaning
usri Packet arrival at rate λ
i
endi Departure of packets after service at
rate ui
time_oi
*
Removal of time out packets at rate
uto_i
*i = 1, 2
Table 3. List of immediate transitions.
Immediate Transitions
Meaning
chchki Priority transition checking
availability of channel
pre_empti,j Enable pre-emption
Figure 2. SRN model.
λ1
usr1
q1
chchk1
usg1
end1
cap
buf1
time o1
μto1
prempt13
prempt12
prempt23
usr2
λ2
buf2
q2
μto2
usg2
end2
chchk2
usr3
λ3
buf3
q3
chchk3
usg3
µ1
µ2
µ3
1
2
3

S. GEETHA ET AL.
634
cardinality bufi is needed to ensure that the number of
packets waiting to enter the current queue is finite. If all
channels are busy, the data packets are buffered in qi with
buffer size bufi.
A way to assign priority is to give each transition an
integer priority level. Transition chchki are modelled as
priority transitions. Lower integer value indicates higher
priority level. A priority transition is enabled only if no
other higher priority transition is enabled. Since, chchk1 is
assigned lowest value; class1 has highest priority to gain
access to channel, followed by class2 and class3. Firing
chchki transfers a packet from qi to usgi indicating the
packet is being served. After completion of service time,
transition endi is fired and the channel is returned to the
central pool. Note that chchki are modelled as immediate
transitions since they represent activity that does not im-
ply time dependency. Although the action of assigning a
channel implies time, the time is neglected from the point
of view of traffic modelling.
In order to model pre-emption using SRN, it is required
to check the simultaneous presence of a packet in place
usgi+1 and qi. The meaning of the above condition is that a
lower priority packet is being served, when higher priority
packet is waiting for resource. Transition prempti,j are
immediate transitions used to model pre-emption. prempti,j
is enabled when packets are available in places qi and usgj
at the same time, where subscript i and j correspond to
higher priority and lower priority traffic class respectively.
Arc connecting prempti,j indicates removal of packet from
usgj, and returning the channel to central pool of channels.
Hence, firing prempti,j pre-empts classj and enables classi
to access the resource.
The channels available in the central pool of resource
are shared by the traffic classes on arrival of data packets
and returned to the pool on completion of service. At
higher traffic loads, the available channels become insuf-
ficient to meet the bandwidth requirement. Under such
conditions, packets in buffer wait for availability of re-
source. Traffic classes, class1 and class2; belong to delay
sensitive application with maximum threshold on toler-
able delay. Packets exceeding the threshold are dropped.
Dropping of packets exceeding the delay limit is incor-
porated in the model using timed transitions time_oi.
Firing rate of time_oi is set to
µ
to_i, 1/
µ
to_i is the maximum
tolerable delay for packets belonging to traffic classi.
Firing time_oi removes a packet from qi indicating the
packet drop. Probability of packet drop depends on the
available channels, transmission rates of packets, buffer
size etc. Since, class3 traffic is not associated with any
such delay limit, we do not include time out feature for
class3.
4.2. Mean Delay and Normalized Throughput
The underlying continuous time markov chain (CTMC) of
the SRN model discussed can be obtained from extended
reachability graph (ERG) [7]. To obtain the desired per-
formance metrics, one has to solve the CTMC. Complex-
ity of CTMC increases with the size of the system. Solu-
tion of complex CTMC can be obtained by using standard
software packages such as SHARPE [18], SPNica [19] or
TimeNET [20]. The average number of packets in each
place, and hence the steady state probability of occupancy
of each state in the CTMC be determined using the soft-
ware tools. In this paper, we use SHARPE to construct the
SRN model and obtain the performance metrics.
The average throughput of a transition T is defined as
the average rate at which packets are deposited by the
transition in its output places. If
()
∧
Ot is the average
number of packets deposited by transition T in all of its
output places up to a time t, then the throughput of a
transition T,
T
η
is defined as
()
lim
∧
→∞
=
Tt
Ot
t
η
(1)
Since we consider three different traffic classes, the
throughput of traffic class i, is given by
i
i
end
i
usr
η
ηη
=
(2)
Average system throughput,
η
is given by,
3
1
i
i
ηη
=
=∑
(3)
The mean delay,
∧
H D
, experienced by a HOL packet of
traffic class i, is the sum of the mean packet holding time
and the sum of mean waiting times in places
i
q
and
i
usg
. Let the average number of packets in place P be #
P
∧
.
∧
H D
can be computed using Little’s Theorem [21] as,
( )()
## 1
∧
=++
i
ii
ii
H
usrchchk i
q usg
D
ηη µ
(4)
where i
µ
is the mean packet holding time for traffic
class i. The buffer in each queue is modelled as M/G/1
queue with mean service time
∧
i
H
D
. The mean packet
delay,
∧
D
can be determined by applying the Pol-
lackzek-Kinchine mean value formula [22] as
() ( )
2
11
21
[ ]
∧∧
=++
−
i
ii
i
b
H
iR
b
DD C
ρ
ρ
(5)
where . If delay of HOL packet is represented by random
variable, i R, then
2
2
2
∧


=
i
i
i
D
H
ER
C
D
(6)
For small loads,
2


i
ER
can be obtained as

S. GEETHA ET AL.
635
2
2
#
2
i
i
i
chchk
usg
ER
η


=
 

(7)
5. Results and Discussion
We evaluate the system performance in terms of mean
delay and normalized throughput for increasing traffic
load,
ρ
, given by
3
1i i
ρ
=
∑
, where i ρ corresponds to
traffic load of classi for
1, 23=i and
.
/=
i ii
ρ λµ
, where
i
λ
is the arrival rate and i µ is the service rate of each
traffic class. Simulation parameters are shown in Table 4.
Input traffic parameter settings are given in Table 5.
We compare the analysis and simulation results for
three traffic classes in terms of mean delay and norma-
lized throughput. From the results we find the simulation
results match with the analysis, thus validating our ana-
lytical approach. We also analyse the performance of the
system with varying buffer sizes.
Figure 3 presents a comparison of mean delay for
three traffic classes with increasing traffic load. It is ob-
served that the mean delay increases with traffic load.
Mean delay suffered by packet of class1 is least followed
by class2 and class3. The increase in mean delay is more
pronounced for class3 since class3 has the least priority
among the competing traffic classes. At higher loads,
class3 packets are starved are resources which results in
increased mean delay.
We further analyse the system with increased buffer
size. Figure 4 shows the comparison of mean delay for
buf = 15. From the figure it is observed that with increas-
ing buffer size there is no significant increase the mean
delay of class1 traffic because the packets belonging to
class1 have to wait for minimum amount of time to gain
access to the channel. Further, since class1 and class2
packets are associated with a maximum tolerable delay,
Table 4. Simulation parameters.
Cell Radius 1 km
Duplexing Schemes TDD
Ratio of Uplink slots to downlink in TDD 50%
Total available bandwidth 50 Mbps
Simulation time 500 s
Table 5. Input traffic parameters.
Traffic
Class
Latency
(ms)
Packet
Size
(Bytes)
Packet
Interval
(ms)
Traffic
load
(Kbps)
Mean
Service
Time
(ms)
rtPS
8
240
2.6
2.8-20
0.6
nrtPS
10
120
3
2-10
0.5
BE
-
120
5
2-14
0.3
Figure 3. Comparison of mean delay (buf = 1).
Figure 4. Comparison of mean delay (buf = 15).
packets exceeding the tolerable delay are dropped. Dropped
packets introduce a decrease in throughput as observed
in Figure 7.
Mean delay of class2 and class3 for varying buffer siz-
es is presented in Figures 5 and 6. From Figure 6 we
find that for a traffic load of 0.8, mean delay with buf = 1
and buf = 5 are 2.5 and 5.6 respectively resulting in 55%
increase. For the same traffic load mean delay with buf =
10 and buf =15 are 6.9 and 7.2 respectively producing
only a 4% increase. We observe that increase in buffer
size does not produce a corresponding increase mean
delay, particularly for higher values of buffer sizes. The
reason is that the available bandwidth is insufficient to
serve all packets in buffer. Hence, the number of packets
successfully transmitted, which amounts to mean delay,
does not increase significantly with increase in buffer
size. Further, existing packets in buffer prevent addition-
al packets entering the system.
Figures 7 and 8 present the normalized throughput of
the three traffic classes with buffer size 1 and 15 respec-
tively. From the graphs, it is observed that for a given
buffer size, class1 has the highest throughput followed by
class2 and class3. Further, throughput of all traffic classes
decrease with increase in traffic load. Comparing F igur es 7

S. GEETHA ET AL.
636
Figure 5. Mean delay of class2 traffic for varying buffer size.
Figure 6. Mean delay of classs3 traffic for varying buffer
size .
and 8, we find that increase in buffer size from 1 to 15
increases the throughput significantly. Decrease in through-
put of class1 traffic at higher traffic load is attributed to
insufficient bandwidth. Also, class2 and class3 traffic
suffer additional decrease in throughput due to pre-
emption.
In Figure 9, presents the throughput of class3 packets
with increasing buffer sizes. From the graph it is observed
that increasing buffer size from 1 to 5 increases the
throughput significantly. But, further increase in buffer
size from 10 to 15 does not produce any considerable
increase in throughput. Further increase in buffer size
results in saturation of the system with no further in-
crease in throughput.
6. Conclusions
We presented a SRN formulation for performance evalu-
ation of bandwidth allocation in IEEE 802.16 network
considering multiple traffic classes. The model includes
Figure 7. Comparison of normalized throughput (buf = 1).
Figure 8. Comparison of normalized throughput (buf = 15).
Figure 9. Normalized throughput of BE traffic class for
varying buffer size.
priority, pre-emption and time-out characteristics of traf-
fic classes. Performance of the system is evaluated in
terms of mean delay and normalized throughput. Our
model is validated by using simulations. The model can
be extended to include more than three traffic classes.
The model can be generalized to incorporate multiple SSs.

S. GEETHA ET AL.
637
7. References
[1] IEEE 802.16-2004, “IEEE Standard for Local and Met-
ropolitan Area Networks. Part 16: Air Interface for Fixed
Broadband Wireless Access Systems,” IEEE, October
2004.
[2] IEEE 802.16e-2005, “Amendment and Corrigendum to
IEEE Standard for Local and Metropolitan Area Networks.
Part 16: Air Interface for Fixed Broadband Wireless
Access Systems,” IEEE, February 2006.
[3] L. Lei, C. Lin, J. Cai and X. Shen, “Performance Analysis
of Wireless Opportunistic Schedulers Using Stochastic
Petri Nets,” IEEE Transactions on Wireless Communica-
tions, Vol. 8, No. 4, 2009, pp. 2076-2087.
[4] D. Lee and J. Baik, “QoS Protocol Verification Using
Petri-Net for Seamless Mobility in a Ubiquitous Envi-
ronment: A Case Study,” International Conference on
Software Engineering, Artificial Intelligence, Networking,
and Parallel/Distributed Computing, Phuket, August 2008,
pp. 617-622.
[5] P. J. Haas, “Stochastic Petri Nets for Modelling and Si-
mulation,” Proceedings of the 2004 Winter Simulation
Conference, Washington, DC, 2004, pp. 101-112.
[6] Y. Ma, J. J. Han and K. S. Trivedi, “Composite Perfor-
mance and Availability Analysis of Wireless Communi-
cation Networks,” IEEE Transactions on Vehicular
Technology, Vol. 50, No. 5, 2001, pp. 1216-1223.
[7] R. Jayaparvathy, S. Anand, S. Dharmaraja and S. Sri-
kanth, “Performance Analysis of IEEE 802.11 DCF with
Stochastic Reward Nets,” International Journal of Com-
munication Systems, Vol. 20, No. 3, 2007, pp. 273-296.
[8] M. Llorens and J. Oliver, “Structural and Dynamic
Changes in Concurrent Systems: Reconfigurable Petri
Nets,” IEEE Transactions on Computers, Vol. 53, No. 9,
2004, pp. 1147-1158.
[9] C. Cicconetti, A. Erta, L. Lenzini and E. Mingozzi, “Per-
formance Evaluation of the IEEE 802.16 MAC for QoS
Support,” IEEE Transactions on Mobile Computing, Vol.
6, No. 1, 2007, pp. 26-38.
[10] Q. Ni, A. Vinel, Y. Xiao, A. Turlikov and T. Jiang, “In-
vestigation of Bandwidth Request Mechanisms under
Point-to-Multipoint Mode of WiMAX Networks,” IEEE
Communications Magazine, Vol. 45, No. 5, 2007, pp.
132-138.
[11] Y. P. Fallah, F. Agharebparast, M. Minhas, H. M. Alnu-
weiri and V. C. M. Leung, “Analytical Modelling of
Contention-Based Bandwidth Request Mechanism in
IEEE 802.16 Wireless Networks,” IEEE Transactions on
Vehicular Technology, Vol. 57, No. 5, 2008, pp. 3094-3107.
[12] M. Sarkar and H. Sachdeva, “A QoS Aware Packet
Scheduling Scheme for WiMAX,” Proceedings of IAENG
Conference on World Congress on Engineering and
Computer Science, Berkeley, California, USA, October
2009.
[13] Y.-C. Lai and Y.-H. Chen, “Designing and Implementing
an IEEE 802.16 Network Simulator for Performance
Evaluation of Bandwidth Allocation Algorithms,” Pro-
ceedings of the 11th IEEE International Conference on
High Performance Computing and Communications, Seoul,
2009, pp. 432-437.
[14] A. Bestetti, G. Giambene and S. Hadzic, “Fair Traffic
Scheduling for WiMAX Systems,” 6th International
Symposium on Wireless Communication Systems, Tusca-
ny, September 7-10, 2009, pp. 254-258.
[15] S. Z. Tao and A. Gani, “Intelligent Uplink Bandwidth
Allocation Based on PMP Mode for WiMAX,” Proceed-
ings of the 2009 International Conference on Computer
Technology and Development, Malay s ia , 2009, pp. 86-90.
[16] C. So-In, R. Jain and A. -K. Tamimi, “Scheduling in IEEE
802.16e Mobile WiMAX Networks: Key Issues and a
Survey,” IEEE Journal on Selected Areas in Communica-
tions, Vol. 27, No. 2, 2009, pp. 156-171.
[17] R. Jai n, C. So-In and A.-K. Tamimi, “System-Level
Modeling of IEEE 802.16E Mobile Wimax Networks:
Key Issues,” IEEE Wireless Communications, Vol. 15,
No. 5, 2008, pp. 73-79.
[18] R. A. Sahner, K. S. Trivedi and A. Puliafito, “Perfor-
mance and Reliability Analysis of Computer Systems: An
Example-Based Approach Using the SHARPE Software
Package,” Kluwer Academic Publishers, Dordrecht, 1996.
[19] R. German, “Markov Regenerative Stochastic Petri Nets
with General Execution Policies: Supplementary Variable
Analysis, and a Prototype Tool,” Proceedings of the 10th
International Conference on Modeling Techniques and
Tools for Computer Performance Evaluation, Palma de
Mallorca, Spain, September 1998, pp. 255-266.
[20] R. German, C. Kelling, A. Zimmerman and G. Homel,
“TimeNET: A Toolkit for Evaluating Non-Markovian
Stochastic Petrinets,” Performance Evaluation, Vol. 24,
No. 1-2, 1995, pp. 69-87.
[21] L. Kleinrock, “Queuing Systems: Volume I, Theory,”
Kluwer Academic Press, Dordrecht, 1995.
[22] R. Jayaparvathy, S. Dharmaraja and S. Srikanth, “Sto-
chastic Petri Nets in Performance Evaluation of IEEE
802.11 WLANs,” Sixth International Conference of the
Association of the Asia Pacific Operational Research So-
cieties, New Delhi, India, December 2003, pp. 142-150.