Performance Modeling of a Wireless 4G Cell under a GPS Scheme with Hand Off
Demetres Kouvatsos, Irfan Awan and Yue Li
Networks and Performance Engineering Research Group
University of Bradford, Bradford BD7 1DP,
West Yorkshire, UK
Email:(D.D.Kouvatsos, I.Awan)@scm.bradford.ac.uk Y.Li5@bradford.ac.uk
Abstract
performance evaluation and prediction of complex mobile
networks with ever increasing volumes of multimedia traffic with different quality-of-service(QoS) guarantees.
A analytic framework is devised, based on the principle of maximum entropy (ME), for the performance
modelling of a wireless 4G cell with bursty multimedia traffic with hand off under an efficient MAC protocol
with a buffer threshold-based generalized partial sharing (GPS) traffic handling scheme. In this context, an open
queueing network model (QNM) is proposed consisting
of three interacting multiclass GE-type queueing and delay systems, namely a GE/GE/c1 /c1 loss system of IP voice
calls, a GE/GE/c2 /N2 /FCFS/CBS(Tl , Th ) queueing system of streaming media packets with low (Tl ) and high
(Th ) buffer thresholds and a GE/GE/1/N3 /PS delay system with a discriminatory PS transfer rule. Analytic ME solutions for the state probabilities of these systems are
characterized, subject to appropriate GE-type queueing and delay theoretic constraints and new closed form
expressions for the aggregate state and blocking probabilities are determined. Typical numerical examples are included to validate the ME performance metrics against
Java-based simulation results and also to study the effect of bursty multiple class traffic upon the performance of
the cell.
Earlier performance models for 2G wireless networks
are based on the Global System for Mobile (GSM) telecommunications for the transmission of voice calls (e.g., [1])
and its extension based on the General Packet Radio Service (GPRS) which allows data communication with higher
bit rates than those provided by a single GSM channel (e.g.,
[2-5]). Furthermore, the introduction of the wireless third
generation (3G) multi-service Universal Mobile Telecommunication Systems (UMTS) for multimedia traffic flows,
such as voice calls, streaming media and data packets, has
been of major interest for mobile network providers and
has received widespread attention in the literature (e.g., [69]). More recently, fourth generation mobile systems have
been proposed, broadly as a collection of different radio networks, which have access to IP based services and where
roaming is envisaged to be seamless.
The general industrial trend to migrate the 4G network
towards an IP based solution is one of the most popular topics. This allows for easy and cost effective service creation
through reuse of application software as well as straight forward interpretability with existing Internet services. In addition IP is technology independent and can thus work on
any underlying access technology. As such it represents an
efficient interface amogst the different radio networks. A
network that uses the Internet Protocol to combine different radio access network is hereafter referred to as 4G network.[16] Moreover, to support multimedia packet traffic
flows with better QoS, wireless 4G cell architectures have
been proposed based on medium access control (MAC) protocols composed on both time-division and code-division
statistical multiplexing (e.g., [10,11]). For multimedia communications, the MAC protocol is expectd to accommodate
packets with different QoS requirements. Although these
views have been adopted by the mobile research community, nevertheless mobility management and performance
modelling and prediction of 4G network architectures still
Key words: Wireless 4G Cell, Internet protocol (IP),
medium access control (MAC) protocol, quality-of-service
(QoS), generalized partial sharing (GPS) scheme, firstcome-first-served (FCFS) rule, processor share (PS) rule,
complete buffer sharing (CBS) scheme, performance evaluation, queueing network model (QNM), generalized exponential (GE) distribution, maximum entropy (ME) principle.
1. Introduction
Cost-effective algorithms for queueing and delay network models under various traffic handling schemes are
widely recognized as powerful and realistic tools for the
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(QNM) is proposed consisting of three interacting multiclass generalised exponential (GE)-type queueing and
delay systems with multiple servers and finite capacities, namely a GE/GE/c1 /c1 loss system of IP voice calls,
a GE/GE/c2 /N2 /FCFS/CBS(Tl , Th ) queue of streaming media packets with low (Tl ) and high (Th ) buffer
thresholds, first-come-first-served (FCFS) scheduling discipline and complete buffer sharing (CBS) scheme and a
GE/GE/1 /N3 /PS delay system with discriminatory processor sharing (PS) transfer rule. Analytic solutions are characterised, subject to appropriate GE-type queueing and delay theoretic mean value constraints and new closed form
expressions for the state and blocking probability distributions are determined. Typical numerical experiments
are included to verify the credibility of the ME solutions against simulation results at 95% confidence intervals
and also investigate the effect of bursty multiple class traffic upon the performance of the cell.
Some preliminary remarks on the GE-type distribution and the ME formalism are included in Section 2.
The performance modelling and evaluation of a wireless 4G cell under GPS scheme with hand off is described in Section 3. An overview of the ME analysis of the
GE/GE/c/N/FCFS/CBS(Tl , Th ) and GE/GE/1/N/PS building block systems for the solution of the open QNM is
highlighted in Section 4. Typical experiments are devised in Section 5. Concluding remarks follow in Section
6.
remain two of the critical issues requiring further consideration.
Recent performance evaluation studies for wireless cells
are very often based on simulation modelling and the numerical solution of Marcov models [e.g., 2-4,6-10]. Simulation modelling is an efficient tool for studying detailed
system behaviour but it becomes costly, particularly as the
system size increases. Markov models on the other hand
provide greater flexibility. However, associated numerical
solutions may suffer from several drawbacks, such as restrictive assumptions of Poisson arrival process and/or state
space explosion, limiting the analysis to small mobile systems. Note that an application of the information theoretic
principle of maximum entropy (ME) [12, 13] to the performance analysis of a wireless GSM/GPRS cell with generalised exponential(GE) bursty traffic subject to partial sharing (PS) scheme can be seen in [5].
In this paper, an extended ME analytic framework is devised for the performance modelling and evaluation of a
4G cell with bursty multiple class flows of IP voice calls,
streaming media packets and data packets in conjunction
with multimedia hand off traffic classes subject to an efficient MAC protocol with a buffer threshold-based generalised partial sharing (GPS) traffic handling scheme. In
escence, the GPS scheme assigns priorities to multimedia
users, as appropriate, and utilizes buffer threshold based information for the efficient transmission of packets in the
time slots of each transmissonn frame. In this way, channel
usage can be maximized for multiple access subject to QoS
constraints. A generic visualation of a multimedia wireless
4G cell under GPS with hand off can be seen in Fig. 1.
2. Preliminary remarks
2.1. GE-Type Distribution
The GE-type distribution is of the form [c.f., 5, 13]
F (t) = P (X ≤ t) = 1 − τe−τ vt , τ = 2/(1 + C 2 ), t ≥ 0
(1)
where
X
is
an
interevent
time
random
variable
and
ª
©
1/v, C 2 are the mean and squared coefficient of variation (SCV) of the interevent times, respectively.
Hand off classes
Multimedia Traf ic
Ordinary classes
WIRELESS
CELL WITH
BUFFER
THRESHOLDS
(GPS)
The GE distribution has a counting compound Poisson process (CPP) with geometrically distributed batch
sizes with mean 1/τ. It may be meaningfully used to
model the interarrival times of bursty multiple class mobile connections with different minimum capacity demands. Note that an IP packet length distribution is
known to be non-exponential and should at least be described by the mean, 1/v, and SCV, C 2 . This is because
IP packets are restricted by the underlying physical network, such as Ethernet and ATM, and thus, they have different packet lengths, typically 1500 bytes and 53 bytes, respectively.
Figure 1. A generic 4G cell with ordinary and
hand of f tr affic classe s u nd er GPS
In this context, an open queueing network model
http://www.unik.no/personer/paalee/
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The GE distribution may also be employed to model
short range dependence (SRD) traffic with small error. For example, an SRD process may be approximated
by an ordinary GE distribution whose first two moments of the count distribution match the the corresponding
first two SRD moments. This approximation of a correlated arrival process by an uncorrelated GE traffic process
may facilitate (under certain conditions) problem tractability with a tolerable accuracy and, thus, the understanding
of the performance behaviour of external SRD traffic in the interior of the network. It can be further argued
that, for a given buffer size, the shape of the autocorrelation curve, from a certain point onwards, does not
influence system behaviour (c.f., [4]). Thus, in the context of system performance evaluation, an SRD model
may be used to approximate accurately long range dependence (LRD) real traffic.
mance metrics, as appropriate. Hence, the principle of ME
may be applied to characterize useful information theoretic approximations of performance distributions of queueing/delay systems and related networks.
The ME solution for the joint state probability distribution of an arbitrary open network with queueing and delay stations, subject to marginal mean value constraints, can
be interpreted as a product-form approximation. Thus, entropy maximization implies a decomposition of a complex network into individual station each of which can
be analyzed separately with revised inter-arrival and service times. Moreover, the marginal ME state probability
of a single station, in conjunction with suitable formulae for the estimation of flow moments in the network, can
play the role of a cost-effective analytic building block towards the computation of the performance metrics of
the entire network. Further information on ME formalism and queueing networks can be found in Kouvatsos
[13].
2.2. Maximum Entropy (ME) Formalism
The principle of ME (c.f., Jaynes [12]) provides a
self-consistent method of inference for characterizing, under general conditions, an unknown but true probability distribution, subject to known (or, known to exist)
mean value constraints. The ME solution can be expressed in terms of a normalizing constant and a product
of Lagrangian coefficients corresponding to the constraints. In an information theoretic context, the ME solution is associated with the maximum disorder of system
states and, thus, is considered to be the least biased distribution estimate of all solutions satisfying the system’s
constraints. Major discrepancies between the ME distribution and an experimentally observed (c.f., [12])
or stochastically derived (c.f., [13]) distribution indicate that important physical or theoretical constraints have
been overlooked. Conversely, experimental or theoretical agreement with the ME solution represents evidence
that the constraints of the system have been properly identified.
3. Performance Modelling of a 4G Cell under
GPS Scheme with Hand Off
An open QNM of a wireless 4G cell under GPS scheme
can be seen in Fig. 2. The compound Poisson process with
geometrically distributed batch sizes (or, equivalently, GEtype interarrival times) is used to represent arrival process
of multiple class bursty traffic consisting of IP voice calls,
steaming media and data packets together with corresponding hand off traffic flows, respectively, which are assumed
to be aggregated into single special classes, as appropriate.
Moreover, GE distributions are employed to describe the
IP voice traffic durations as well as the channel transmission times of streaming media/data packets. In the context
of the proposed QNMs, only up link traffic is considered.
Note that the proposed QNM is of robust nature enabling
the inclusion of some essential application functions envisaged to to be present in a 4G mobile network. More specifically, it does not only support all IP based multimedia traffic
flows but also incorporates GPS traffic handling scheme towards efficient bandwidth management.
The open QNM can be clearly decomposed into three interacting GE-type building block queueing and delay system as follows: A number of bufferless channels may be allocated to multiple classes of IP voice calls each of which
requiring the assignment of a single channel for its entire duration. Clearly, the transmission resource for IP
voice calls can be modelled by a GE/GE/c1 /c1 loss system with c1 channels. Moreover, a multiple class streaming media traffic is packet based and each connection will
attempt to use the complete available bandwidth. The associated channels may, therefore, be seen as c2 ’servers’
In the field of systems modelling, expected values performance distributions, such as those relating to the marginal
and joint state probabilities (i.e., number of jobs at an individual queue or a network) may be known to exist and
thus, they can be used as constraints for the characterization of the form of the ME solution. Alternatively, these
expectations may be often analytically established via classical queueing theory in terms of some moments of the
inter-arrival time and service time distributions. An efficient analytic (exact or approximate) implementation
of the ME solution clearly requires the a priori estimation of the Lagrangian coefficients via exact or asymptotic
expressions involving basic system parameters and perfor-
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packets reach threshold low, Tl , the fixed number of common channels will be released to support the partition of the
data packets. Subsequently, the transmission capacities of
both partitions for data packets and streaming media packets are progressively reduced or increased, as appropriate.
1
Hand off classes
Voice classes in the cell
GE/GE/c/c loss system
2
c
Acquire
Rlease
4. ME Analysis of GE/GE/c/N/FCFS/CBS
(Tl ,Th ) and GE/GE/1/N/PS systems
Hand off classes
Data classes in the cell
GE/GE/1/N/PS/CBS
delay system
Acquire
Threashhold high
TH
1
Hand off classes
2
Streaming
classes in
the cell
Threashhold low TL
This section presents an overview of the ME analysis
of the GE/GE/c/N/FCFS/CBS(Tl ,Th ) and GE/GE/1/N/PS.
Note that the multiple class GE/GE/c/c loss system is a special case of the GE/GE/c/N/FCFS/CBS(Tl ,Th ) with c = N .
Notation For each class i (i = 1, 2, . . . , R, R > 1) let
2
2
}, {1/µi , Csi
} be the mean and squared coeffi{1/λi , Cai
cient of variation (SCV ) of the interarrival and service time
distributions, respectively. Note that µi (i = 1, 2, . . . , R)
under PS rule are defined subject to discrimination weights.
Let c be a generic number of servers for either queueing or
delay systems. Moreover, let
Rlease
GE/GE/c/N/FCFS/CBS
queueing system
c
Figure 2. An open QNM of a wireless 4G cell
under GPS
of a GE/GE/c2 /N2 /FCFS/CBS(Tl , Th ) queueing system with a maximum capacity, N2 , serving streaming media packets under a first-come-first-served (FCFS) and
a complete buffer sharing scheme (CBS) subject to low
and high buffer thresholds (Tl and Th ). These thresholds can be used to stipulate efficient channel sharing under
the GPS scheme of the MAC protocol. Finally, all admitted interactive/background data packet connections
will share the available bandwidth according to the priority for each data class. Physically, a wireless 4G cell should
be capable of allocating all available channels to one connection (subject to some battery restrictions) [14]. Thus,
the transmission queue for these data packets can be modelled by a GE/GE/1/N3 /PS delay system with a multiple
class of interactive and background data packets under discriminatory PS rule and finite capacity N3 . Note that N
may represent the maximum number of connections sharing simultaneously the available data bandwidth according
to assigned priorities.
Given the open QNM displayed in Fig. 2, the GPS traffic
handling scheme can be described as follows: At any given
time, free IP voice calls and a fixed number of common
channels of the streaming media packets belonging to the
GE/GE/c1 /c1 and GE/GE/c2 /N2 /FCFS/CBS(Tl , Th ) systems, respectively, may be released to increase the transmission capacity of the GE/GE/1/N3 /PS delay system. However, new arrivals of IP voice calls, which have higher priority, will cause the immediate release of some or all acquired IP voice channels, as appropriate, of the loss system.
Moreover, when the streaming media packet flow reaches
threshold high, Th , all the released streaming media channels to the partition of the data packets are returned back to
the queueing system. When the number of streaming media
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ni be the number of entities of class i (i = 1, 2, . . . , R);
n = (n1 , n2 , . . . , nR ) be a joint system state (n.b., 0 =
(0, . . . , 0));
Ω be the set of all feasible joint states {n};
P(n) , n ∈ Ω, be the joint state probability;
πi be the blocking probability that an arrival of class i will
find the system at the full capacity.
4.1. ME Solutions of GE/GE/c/N/FCFS/CBS
(Tl ,Th ) and GE/GE/1/N/PS systems
The form of the ME joint state probabilities
{P (n), ∀n ∈ Ω} of the GE/GE/c/N/FCFS/CBS(Tl ,Th )
and GE/GE/1/N/PS building block queueing and delay systems, where ni is the number of class i entities representing IP voice calls or data packets in either systems, as appropriate, can be determined, subject to appropriate marginal (class) mean value constraints. These constraints are based on the class utilisations
{Ui , i = 1, 2, . . . , R} for GE/GE/1/N/PS (T) delay sysP
tem and {Uik = 1 − k−1
n=1 Pi (n), i = 1, 2, . . . , R;
k = 1, 2, . . . , c} for GE/GE/c/N/FCFS/CBS(Tl , Th ) queueing system, and for each system, mean number of entities per class {Li , i = 1, 2, . . . , R} and the full buffer
state probabilities {φi , i = 1, 2, . . . , R} for GE/GE/1/N/PS
(T) and {φik , i = 1, 2, . . . , R; k = 1, 2, . . . , c} for
GE/GE/c/N/FCFS/CBS(Tl , Th ) queueing system, with a
class i entity in service satisfying the flow balance equations(c.f., [3])
λi (1 − πi ) = µi Ui , i = 1, . . . , R,
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where Ui is the marginal utilization of class i, i =
1, 2, ..., R. By employing Lagrange’s method of undetermined multipliers, the ME steady state joint probability
P (n) can be expressed by
P (n) =
½
1
Z Γ1 Γ2 Γ3 Γ4 ,
1
Z Θ1 Θ2 Θ3 ,
GE/GE/c/N/FCFS/CBS(Tl ,Th );
GE/GE/1/N/PS (T);
(3)

QR−1 ¡n−nl ¢
nl+1


, ¶
 Γ1 = l=0Rn−c
µ
QR
n − nl
with

l=1

nl+1

Θ1 =
,
Rn−1
Γ3 =
Θ3 =
Γ4 =
QR
³Q
ki
hik (n) fik (n)
yik
i=1
k=1 gik
QR
nj
j=1,j6=i xj .
R−1
Y
PR
nR −E(n)+
xni i −ki xR
n=0
i=1
´
ki
,
,
(5)
(6)
QR nQE(n)
i=1
h (n) f (n)
k=1
o
X n−1 ,
ri
ri (1−σi )+σi , δi (n)
= 1 (∀n > 0), and
if n = 0,
if 0 < n < c
if c ≤ n ≤ N.
4.2. Weighted Performance Measures under PSS
All performance metrics of interest for the QNM of
Fig. 2 can be determined by making use of weighted
averages taking probabilistically into account the dynamic increase/decrease of the transmission capacity
of IP voice calls and streaming media packets, respectively. More specifically, data packets will receive under GPS variable transmission capacity depending on
the availability of free IP voice call and streaming media channels. To this end, an average performance statistic for data packets (DP) of discriminatory (under PS) class
i
, of the GE/GE/1/N3 /PS delay system can be dei, say SDP
fined by the weighted average measure:
(7)
i
=
SDP
c2
c1 X
X
Ξ1 Ξ2 , i = 1, 2, . . . , R
(11)
l1 =0 l2 =0
l1 ,l2 ,i
where Ξ1
=
SDP
PV C (n1
=
l1 ) and
Ξ2 = PSM (n2 = l2 ) with PSM (.) being the aggregate streaming media (SM) packets steady state probability
of the GE/GE/c2 /N2 /FCFS/CBS(Th , Tl ) queueing sysl1 ,l2 ,i
, l1 = 0, 1, 2, . . . , c1 , l2 = 0, 1, 2, . . . , c2 }
tem and {SDP
i
corresponding at
are estimated values of statistic SDP
each stage to the maximum available mean data packets transfer rates. These rates under the GPS scheme are
given by {µiDP + (c1 − l1 )µV C + (c2 − l2 )µSM , l1 =
0, 1, 2, . . . , c1 , l2 = 0, 1, 2, . . . , c2 } with {µV C ,µiSM ,
,


Tl < n < Th




c
. n ≥ Th


 2
for GE/GE/c/N/F CF S/CBS(Tl , Th )
(8)
The aggregate probability P(n) can be obtained by unconditioning the joint probability P(n) over all classes and
is determined by:
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n⊆An

 c
max(0, c − n)
L=

0

n, n ≤ c1




c


·1 , n ≤ Tl
¸


 (n−[ c2 −c1 ])c1 +(n+[ c2 −c1 ])c2
2
P
gikik yikik
GE/GE/c/N/FCFS/CBS(T
³P
´ l ,Th );
fi (n)
G(n)
1
X n−1 ,
i=1 gi xi yi
Z
GE/GE/1/N/PS(T).
where δi (0) =
where Z = 1/P (0), {hik (n), fi (n), fik (n) n ∈ Ω}
are suitable auxiliary functions and {xi , gik , yik , ∀i, n} are
Lagrangian coefficients for GE/GE/c/N/FCFS/CBS(Th , Tl )
queueing system and {gi , xi , yi , i = 1, 2, . . . , R} are the
Lagrangian coefficients for GE/GE/1/N/PS delay system
corresponding to the aforementioned constraints, (Uik or
Ui , Li , φik or φi , i=1,2,. . . ,R). These Lagrangian coefficients can be determined by making asymptotic connections to the corresponding infinite capacity systemP
and usR
ing flow balance equations (1) [3]. Moreover, n = i=1 ni
and E(n) is auxiliary function given by
E(n) =





1
Z
(9)
PR
whereZ = 1/P (0), X = i=1 xi , An = {n : n =
PR
i=1 ni , 0 ≤ ni ≤ N }. Subsequently, focusing on a
tagged either streaming media packet or data packet, as appropriate, within an arriving bulk and applying GE-type
probabilistic arguments, the blocking probability per class
πi , (i = 1, 2, . . . , R) can be approximated by
 PN
N−n
P (n),

n=0 δi (n)(1 − σi )

 GE/GE/1/N/P
S(T );
PR PN
πi =
(10)
L
N−n

P (n),

j=1
n=0 δi (0)(1 − σi )

GE/GE/c/N/F CF S/CBS(Th , Tl ),
(4)
½
Q ¡E(n) ¢¡n−E(n) ¢ ¾

PR
PE(n) R−1

ki
ni −ki
l=1

¡n−n
¢
QR−1
Γ
=
,

2
ki =1
i=1
l


n
l+1
l=0

¶
µ

n − ni − 1
P
n

i+1 − 1
R
 Θ2 =
µ
¶ gi yi xni i −1 ,


i=1 Q

n
−
n
R
l


l=1
nl+1
(
P (n) =






2
2n
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It can be seen that the ME analytic results are very
comparable to those obtained via simulation whilst the interarrival time SCV has an adverse effect on the performance metrics of the service classes (c.f., Figs. 3-10). More
specifically, it can be observed in Figs. [9,10] that the
analytically established mean number of streaming media
and data packets deteriorate rapidly with increasing external interarrival-time SCVs (or, equivalently, average batch
sizes) beyond a specific critical value of the buffer size
which corresponds to the same mean number of data packets for two different SCV values. It is interesting to note,
however, that for smaller buffer sizes in relation to the critical buffer size and increasing mean batch sizes, the mean
number of data packets steadily improves with increasing values of the corresponding SCVs. This ‘buffer size
anomaly’ can be attributed to the fact that, for a given arrival rate, the mean batch size of arriving bulks becomes
larger as the SCV of the interarrival time increases, resulting in a greater proportion of arrivals being blocked (lost)
and, thus, a lower mean effective arrival rate; this influence
has much greater impact on smaller buffer sizes.
Note that additional numerical experiments can be seen
in [15].
µiDP } being the initially allocated aggregate class i transfer rates to the IP voice calls (VC) GE/GE/c1 /c1 loss system, the streaming media GE/GE/c2 /N2 /FCFS/CBS(Tl , Th )
queueing system and the data packets GE/GE/1/N3 /PS delay system, respectively.
Futher details on the mathematical proofs associated
with key analytic GE-type results can be seen in [15].
5. Numerical Results
This section presents typical numerical experiments using the proposed open QNM of Fig. 2 in order to evaluate the credibility of the performance approximations of
the ME methodology against simulation results produced
in Java programming language at 95 % confidence intervals. To this end, both analytic and simulation experiments
on the QNM are based on the same underlying assumptions and parameterizations. Moreover, the section demonstrates the applicability of ME solutions, as simple and costeffective performance evaluation tools, for assessing the effect of bursty multimedia traffics upon the performance of
the proposed wireless 4G cell.
Numerical results are presented in Figs. 3-10 involving
two classes of IP voice calls and a hand off class, three
classes of streaming media with 300KBytes , 62.5KBytes
corresponding to a hand off class on streaming media and
three classes of data packets having different mean sizes
given by 12.5KBytes (class 1, e.g., voice mail), 62.5KBytes
(class 2, e.g., web browsing) and a hand off class. In this
context, fixed arrival rate and SCV relating service rate
and SCV can be assumed some virtual parameters such
like 1.0/0.6 for arrival rate and 3.0 for service rate on IP
voice calls experiments. It is assumed that the IP voice calls,
streaming media and data packets partitions consist of one
frequency providing total capacity of 171.2 Kbps. The following fixed input data are used: {λ11 = 1.0, λ12 = 0.6,
µ11 = µ12 = 3.0, c1 = 2, Ca212 = 5, Cs211 = 5, Cs212 = 5}
for IP voice call, {λ21 = 2.0, λ22 = 1.2, λhandof f = 0.6,
µ21 = µ22 = µhandof f = 6.0, Ca221 = Cs221 = 5, Cs222 =
5, Cahandof f = Cshandof f = 2 c2 = 2, N2 = 10}
for streaming media packets and {λ31 = 1.0, λ32 = 0.5,
λhandof f = 0.2, µ3 = 9.0, PS service discrimination
weight = 1/3, (µ31 = 1/3µ3 , µ32 = 1/3µ3 ), µhandof f =
1/3µ3 , Ca231 = 5, Ca232 = 2, Ca2handof f = 2, Cs231 = 5,
Cs232 = 5, Cs2handof f = 5, N3 = 20} for data packets.
Without loss of generality, the comparative study focuses on
marginal performance metrics of mean number of streaming media and data packets per class as well as the aggregate blocking probabilities of voice calls, streaming media
packets and data packets, respectively. Note that the numerical tests make use of varying traffic values of the interarrival times SCVs, Ca211 and Ca222 .
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6. Conclusions
This paper focuses on the performance modelling and
evaluation of a wireless 4G cell architecture subject to GPS
traffic handling scheme with hand off, as a cost-effective resource sharing MAC protocol, in support of multiple voice
calls, streaming media and data packet service classes. An
open QNM is proposed and analysed using the principle of
ME, subject to GE-type queueing and delay theoretic constraints, as well as simulation programmes developed in
Java. New analytic ME solutions for the joint state probabilities of these systems are characterized, subject to appropriate GE-type queueing and delay theoretic constraints.
Moreover, closed form expressions for the aggregate state
and blocking (per class) probabilities are determined and
play the role of simple and robust analytic building block
tools for the performance modelling and prediction of the
proposed 4G wireless cell. Typical numerical tests validate
the credibility of the ME solutions against simulation at
95% confidence intervals and also verify the adverse effect
of traffic variability upon the enhanced 4G network performance.
References
[1] K.Al-Begain, G. Bolch and M. Telek, Scalable Schemes for
Call Admission and Handover Handling in Cellular Networks with Multiple Services. Journal on Wireless Personal Communications, Volume 15, No. 2, Kluwer Academic Publishers, 2000a, pp. 125-144.
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[2] R. Litjens and R. Boucherie, Radio Resource Sharing in
GSM/GPRS Network.
em ITC Specialist Seminar on Mobile Systems and Mobility, Lillehammer, Norway, March 22 - 24, 2000. pp. 261274.
[3] Y-R. Haung, Y-B. Lin and J-M. Ho, Performance Analysis
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NGI 2005
IP voice calls hand off class ME
IP voice calls hand off class SIM
IP voice calls class ME
IP voice calls class SIM
−0.5
Marginal mean number of
IP voice calls per class
10
−0.6
10
0
10
5
15
20
SCV of incoming IP voice calls, Ca2
25
30
22
Figure 3 . Effect of tra ffic varia bili ty on the
marginal mean number of IP voice calls for
a multiple class GE/GE/c/c loss system
Marginal mean number of
streaming media packets per class
0.5
0.45
0.4
0.35
Streaming media hand off class ME
Streaming media hand off class SIM
Streaming media class 1 ME
Streaming media class 1 SIM
Streaming media class 2 ME
streaming media class 2 SIM
0.3
0.25
0.2
0.15
0
5
10
15
20
25
SCV of incoming streaming media packetet, Ca222
30
Figure 4 . Effect of tra ffic varia bili ty on the
marginal mean number of steaming media for
a multiple class GE/GE/c/N/FCFS/CBS (Tl , Th )
queueing system
Marginal blocking probability of
streaming media packets per class
0.045
Streaming
Streaming
Streaming
Streaming
Streaming
Streaming
0.04
media
media
media
media
media
media
hand off class ME
hand off class SIM
class 1 ME
class 1 SIM
class 2 ME
class 2 SIM
0.035
0.03
0.025
0.02
0.015
0.01
0
5
10
15
20
25
SCV of incoming streaming media packets, Ca222
30
Figure 5. E ffec t of tr affic varia bili ty
the marginal blocking probability of
steaming media for a multiple class
GE/GE/c/N/FCFS/CBS (Tl , Th ) queueing system
418
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Aggr. Mean No. of Stre. Media
3.5
Marginal mean number of
data packets per class
3
2.5
2
Data
Data
Data
Data
Data
Data
1.5
packets
packets
packets
packets
packets
packets
hand off class ME
hand off class SIM
class 1 ME
class 1 SIM
class 2 ME
class 2 SIM
1
0.5
Ca2 = 1
Ca2 = 5
Ca2 = 10
2
Ca = 15
2
Ca = 20
2
Ca = 25
1
0.9
0.8
0.7
0.6
0.5
0.4
0
0
5
10
15
20
SCV of incoming IP voice calls & stre. media,
25
Ca2 ,
11
Ca2
22
30
0.3
0.2
0
20
Figur e 6. Ef fe ct of traffic variability o n t he
marginal mean number of steaming media for
a multiple class GE/GE/1/N/PS delay system
0.22
Data
Data
Data
Data
Data
Data
Marginal blocking probability of
of streaming media per class
0.2
0.18
packets
packets
packets
packets
packets
packets
40
5
SCV , Ca22
10
15
20
30
25
Capacity of GE/GE/c/N/FCFS/CBS, N
2
Figure 9. E ffec t of traffic var iability o n t he aggregate mean number of streaming media for
a multiple class GE/GE/c/N/FCFS/CBS (Tl , Th )
queueing system under PSS (Experiment 11Input Data: {λ21 = 2.0, λ22 = 1.2, λ23 = 0.6,
µ21 = µ22 = µ23 = 6.0, Ca221 = Cs221 = 5,
Cs222 = 5, Ca23 = Cs23 = 2 c2 = 2, } for streaming media packets).
hand off class ME
hand off class SIM
class 1 ME
class 1 SIM
class 2 ME
class 2 SIM
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0
5
10
15
20
25
30
SCV of incoming IP voice calls & stre. media, Ca2 , Ca2
11
22
Figur e 7. Ef fe ct of traffic variability o n t he
marginal blocking probability of steaming
media for a multiple class GE/GE/1/N/PS delay system
Aggr. Mean No. of Data Packets
0.02
10
2
Ca
2
Ca
2
Ca
2
Ca
2
Ca
2
Ca
9
8
=
=
=
=
=
=
1
5
10
15
20
25
7
6
5
4
3
2
1
0
10
20
30
0
10
2
SCV, Ca3
−1
Aggregate blocking probability
10
5
10
15
20
25
30
Capacity of GE/GE/1/N/PS, N3
−2
10
IP voice call, π1
Streaming media, π
2
Streaming media, π (TH)
2
Data packets, π3
Figure 10. Ef fect of traffic var i ability o n t he
aggregate mean number of data packets
for a multiple class GE/GE/1/N/PS(T) queueing system under PSS (Experiment 12-Input
Data: {λ31 = 1.0, λ32 = 0.5, λ33 = 0.2,
µ
3 = 9.0, PS service discrimination weight =
SCV of incoming IP voice calls & stre. media, Ca , Ca
1/3, (µ31 = 1/3µ3 , µ32 = 1/3µ3 ), µ33 = 1/3µ3 ,
Ca2 = 5, Ca2 = 2, Ca233 = 2, Cs231 = 5,
Figur e 8 . Ef fect of traffic varia bil ity on t he ag- Cs231 = 5, Cs2 32
32
33 = 5, } for data packets).
gregate blocking probability under GPS
−3
10
−4
10
−5
10
−6
10
−7
10
0
5
10
15
20
25
2
11
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2
22
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