2598 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 12, NO. 6, JUNE 2013
Modelling and Analysis of an Integrated Scheduling
Scheme with Heterogeneous LRD and SRD Traffic
Xiaolong Jin and Geyong Min
Abstract—Multimedia applications in wireless networks are
usually categorized into various classes according to their traffic
patterns and differentiated Quality-of-Service (QoS) require-
ments. The traffic of heterogeneous multimedia applications
often exhibits the Long-Range Dependent (LRD) and Short-
Range Dependent (SRD) properties, respectively. The integrated
scheduling scheme that combines Priority Queuing (PQ) and
Generalized Processor Sharing (GPS) within a hierarchical
structure, referred to as PQ-GPS, has been identified as an
efficient mechanism for QoS differentiation in wireless networks
and attracted significant research efforts. However, due to the
high complexity and interdependent relationship among traffic
flows, modelling of the integrated scheduling scheme poses
great challenges. To address this challenging and important
research problem, we develop an original analytical model for
PQ-GPS systems under heterogeneous LRD and SRD traffic.
A cost-effective flow decomposition approach is proposed to
equivalently divide the integrated scheduling system into a group
of Single-Server Single-Queue (SSSQ) systems. The expressions
for calculating the queue length distribution and loss probability
of individual traffic flows are further derived. After validating
its accuracy, the developed model is adopted as an efficient
performance tool to investigate the important issues of resource
allocation and call admission control in the integrated scheduling
system under QoS constraints.
Index Terms—Wireless multimedia, heterogeneous network
traffic, integrated scheduling, priority queuing, generalized pro-
cessor sharing, performance modelling.
I. INTRODUCTION
T
HE past decade h as witnessed a rapid increase in various
advanced multimedia applications with diverse Quality-
of-Service (QoS) requirements over wireless communication
networks. In order to efficiently support these applications,
the Differentiated Services (DiffServ) architecture has been
proposed as a scalable and coarse-grained mechanism for
managing heterogeneous wireless network traffic [14], [21],
[41]. The data packets entering a DiffServ domain are placed
into a limited number of traffic classes, which are handled in
differentiated manners, ensuring preferential treatment for the
Manuscript received December 15, 2011; revised June 20, 2012 and
November 24, 2012, and March 3, 2013, accepted March 5, 2013. The
associate editor coordinating the review of this paper and approving it for
publication was C.-F. Chiasserini.
X. Jin is with the Institute of Computing Technology, Chinese Academy
of Sciences, Beijing, China (e-mail: jinxiaolong@ict.ac.cn).
G. Min (corresponding author) is with the Department of Computing,
School of Informatics, University of Bradford, Bradford, BD7 1DP, UK (e-
mail: g.min@brad.ac.uk).
This work is supported by the National Natural Science Foundation of
China under Grants No. 61100175, No. 61232010, and No. 60933005; the
National Program on the Key Basic Research Project under Grant No.
2012CB316303, UK EPSRC Research Grant No. EP/C525027/1, and the EU
FP7-PIRSES-318939 Grant.
Digital Object Identifier 10.1109/TCOMM.2013.050313.112217
high priority traffic. In general, the DiffServ architecture can
provide low delay for real-time applications, while offering
best-effort services for non-real-time ones.
Traffic scheduling plays a key role in the design and perfor-
mance of the DiffServ architecture. The integrated scheduling
mechanism which combines different fundamental scheduling
schemes, such as Priority Queuing (PQ), and Generalized
Processor Sharing (GPS) [1] or its variants [5], [6], [18],
[39] within a hiera rchical structure, has attracted significant
research interests from both academia and industry (e.g., [16],
[24], [27]). For instance, Nikolouzou et al. [27] studied the
definition and deployment issues of DiffServ networks, where
the integrated sched uling mechanism is identified as a suitable
traffic handling scheme. Maniatis et al. [24] proposed to
adopt the integrated scheduling mechanism to d eploy QoS-
enabled end-to-end services in 3G wireless networks. More-
over, the existing studies [7], [10] have applied the integrated
scheduling schemes to investigate the issues of bandwidth
sharing, buffer allocation and QoS differentiation in IEEE
802.16/WiMAX networks. In industry, Cisco has developed
two hybrid schedulers, namely, IP Real-time Transport Proto-
col (RTP) Priority and Low Latency Qu e uing (LLQ), which
are essentially based on the PQ-GPS principle and have been
deployed on a variety of Cisco gigabit switch routers, such as,
Cisco 12000 series, Cisco 2600 and 3600 series.
In the integrated PQ-GPS scheduling system, o ne traffic
flow is ser ved with the strictly high priority. As a consequence,
this flow experiences low loss, low delay and jitter, wh ich
are actually the QoS requirements desirable for real-time
applications, e .g., the conversational applications in wireless
networks. On the other hand, other traffic flows of the low
priority in the PQ-GPS system are handled by the conventional
GPS scheduling mechanism [1], [26]. Each traffic flow in GPS
is assigned a weight in order to guarantee a minimum service
rate and provide differentiated QoS, even though other flows
may be greedy in demanding service. This property offers
forwarding assurance to individual traffic flows and prevents
them from experiencing service starvation.
Modelling and analysis of scheduling sch emes is an impor-
tant issue for efficient resource management and optimization
of communication networks. In order to obtain a proper
and deep understanding of the performance behaviors of the
integrated scheduling scheme, it is essential to take the realistic
characteristics of network traffic into account. Many high
quality measurement stu dies (e.g., [22], [4 0]) have demon-
strated that the real-world traffic in modern communication
networks with multimedia applications exh ibits heterogeneous
properties and can be categorized into two significantly dif-
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