562 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 11, NO. 2, FEBRUARY 2012
Transactions Papers
Quality-of-Service Analysis of
Queuing Systems with Long-Range-Dependent
Network Traffic and Variable Service Capacity
Xiaolong Jin, Geyong Min, Speros Velentzas, and Jianmin Jiang
Abstract—Many high-quality measurement studies have
demonstrated that wireless network traffic exhibits the noticeable
Long-Range-Dependent (LRD) property. Moreover, the fading
nature of wireless channels can lead to variable service capacity.
Due to the inherent difficulty and high complexity of modelling
the fractal-like L RD traffic, existing analytical models of queuing
systems with LRD arrival processes have b een primarily limited
to the simplified scenarios where the service capacity is assumed
to be constant. Given the time-varying nature of wireless channels
in the real-world working environments, it is very important
and necessary to investigate system performance in the presence
of variable service capacity. To this end, this paper presents a
comprehensive analytical model for queuing systems subject to
LRD traffic and variable service capacity. We extend the appli-
cation of a Large Deviation Principle and derive the closed-form
expressions of Quality-of-Service (QoS) metrics. The accuracy
of the model validated through extensive simulation experiments
makes it a cost-effective evaluation tool for performance analysis
of communication networks. To illustrate its applications, the
model is adopted to investigate the effects of LRD trafficand
variable service capacity on the system performance and resource
configuration.
Index Terms—Quality-of-service, long-range-dependency, frac-
tional Brownian motion, variable service capacity, performance
modelling.
I. INTRODUCTION
A
Straffic scheduling plays a c rucial role in the design
and performance of communication networks, analytical
Manuscript received May 21, 2010; revised January 30 and June 19, 2011;
accepted August 22, 2011. The associate editor coordinating the review of
this paper and approving it for publication was M. L. Merani.
This work was supported by the UK EPSRC Research Grant No.
EP/C525027/1, the National Natural Science Foundation of China under
Grants No. 61100175 and No. 60933005, and the National High-Tech R&D
Program of China under Grant No. 2010AA012500.
X. Jin is with the Key Laboratory of Network Science and Technology,
Institute of Computing Technology, Chinese Academy of Sciences, Beijing,
China (e-mail: jinxiaolong@ict.ac.cn).
G. Min (corresponding author) and J. Jiang are with the School of
Informatics, University of Bradford, Bradford, BD7 1DP, UK (e-mail: {g.min,
j.jiang}@brad.ac.uk).
S. Velentzas is with the R&D Department, AdvTec Ltd., 83 Lansdown
Road, Swindon, SN1 3ND, UK (e-mail: ross@advtec.co.uk).
Digital Object Identifier 10.1109/TWC.2011.120511.100867
modelling and evaluation of queuing systems have been re-
ceiving tremendous research efforts from both academia and
industry (e.g., [1]–[4]). The innovative study reported in [5]
has revealed that the traffic in local-area networks exhibits
noticeable Long-Range-Dependent (LRD) nature and set the
groundwork for considering long-range-dependency as a key
characteristic in understanding of traffic properties, modelling
and analysis of network performance. Moreover, this study
has triggered an explosion of research on this topic [6].
Many subsequent studies have further demonstrated that long-
range-dependency is a ubiquitous phenomenon in a variety
of communicatio n networks and multimedia systems [7], [8],
including local-area n etworks, wide-area networks, metro-area
networks, world wide web, and variable-bit-rate video and
multimedia systems.
More recently, the traffic in wireless networks has also
been shown to reveal the noticeable LRD nature [7], [9]–
[12]. For instance, Liang [9] investigated the traffic in wireless
mobile ad hoc networks and revealed that such network traffic
has the noticeable characteristic of long-range-dependency.
Yin and Lin [12] further developed a mathematical model
and theoretically proved the LRD nature of mobile ad hoc
network traffic. Oliveira, Kim, and Suda [11] empirically
verified that the traffic in IEEE 802.11b wireless local-area
networks exhibits the LRD property. Ilyas and Radha [7]
studied the IEEE 802.15.4 wireless personal area networks
and again discovered the traffic long-range-dependency.
LRD network traffic manifests itself as scale-invariant
burstiness and large-lag correlation. This fractal-like traffic
behavior has significantly different theoretical properties from
those of the conventional Short-Range-Dependent (SRD) traf-
fic (e.g., Poisson or Markovian processes) and can seriously
deteriorate queuing performance and user-perceived Quality-
of-Service (QoS) [5], [13]. As a consequence, the existing
analytical models developed for queuing systems under the
assumption of SRD traffic are no longer valid in the presence
of LRD traffic. The investigation of the effects of LRD
traffic on the performance of communication networks has
emerged as an important research topic in the networking and
communication research community (e.g., [14]–[17]). Norros
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2012 IEEE