Packet Loss in Real-Time Services:
Markovian Models Generating QoE Impairments
Oliver Hohlfeld
Multimedia Communications Lab
Darmstadt University of Technology
Merckstr. 25, D-64283 Darmstadt, Germany
hohlfeld@kom.tu-darmstadt.de
Ru¨diger Geib, Gerhard Haßlinger
T-Systems
Deutsche-Telekom-Allee 7
D-64295 Darmstadt, Germany
{ruediger.geib, gerhard.hasslinger}@t-systems.com
Abstract—Real-time Internet services are gaining in popularity
due to rapid provisioning of broadband access technologies.
Delivery of high Quality of Experience (QoE) is important for
consumer acceptance of multimedia applications.
IP packet level errors affect QoE and the resulting quality
degradations have to be taken into account in network operation.
We derive the second order statistics of the number of packet
losses in finite Markov models over several relevant time scales
and adapt them to loss processes visible in wired and wireless
transmission channels.
Higher order Markov chains offer a large set of parameters to
be exploited by complex fitting procedures. We experience that
the 2-state Gilbert-Elliott model already captures a wide range of
observed loss pattern appropriately and discuss how such models
can be used to examine the quality degradations caused by packet
losses.
I. INTRODUCTION
The transfer of real-time data for multimedia services over
the Internet and channels in heterogeneous packet networks is
subject to errors of various types which will affect the QoS
and QoE. On wireless and mobile links temporary and long
lasting reductions in the available capacity frequently occur
and even in fixed and wired network sectors packets may be
dropped at routers and switches in phases of overload. Lost
information will affect the perceived quality by impairing the
multimedia content. The QoE degradation not only depends on
the amount of lost packets, but also on the semantic of the lost
information at the application layer. In video streams, a lost
intra predicted I-Frame that is referenced by subsequent inter
predicted P- and B-Frames may cause a much stronger visual
impact due to error propagation than a lost inter predicted
frame.
In this work, we focus on packet loss on Internet links
with most traffic controlled by TCP superposed with a con-
siderable contribution of real-time traffic without flow control.
The impact of packet loss on the user’s perception of real-
time services can be investigated starting from measurement
traces of traffic or generated by finite-state stochastic models,
which have been adapted to the characteristics observed in
the measurement and thus produce statistically similar traces.
Using model based generators for loss processes has several
advantages:
• the amount of necessary storage capacity is reduced
significantly from several gigabyte to a set of model
parameters,
• stochastic models usually include a set of parameters with
a clear interpretation, which can be adapted to meet the
demands of a considered scenario in which the model
is used (e.g. a certain packet loss rate) and makes them
more flexible than a measurement trace,
• the length of the generated sequence is independent of
the measurement trace used for training,
• stochastic models produce random but statistically con-
sistent sequences.
Both, using real data loss traces—e.g. captured in backbone
links—and model generated loss traces have their benefits. The
main disadvantage of using model generated loss traces is that
statistical properties may not fit to the statistical properties of
a measured trace as they are likely to be biased by model
limitations. As measurement traces show characteristics on
multiple time scales, we derive the second order statistics of
finite Markov models to be used as a parameter estimation
technique to adapt the model to the second order statistics of
the amount of packet losses observed in a given traffic trace
on multiple time scales by moment matching. We focused
on 2-state Markov models in [10]. The present paper gives a
generalised view on finite Markov models and discusses how
these models can be used in the study of QoE impacts on
video streams. The aim is to provide a generator for packet
loss pattern to be used in the estimation of the degradation in
the Quality of Experience (QoE) for Internet services.
Section II will describe the trace evaluation as the basis
for further investigations. The traffic variability and packet
loss patterns observed in multiple time scales will be dis-
cussed in Section II. Section III will introduce Markov chains
as stochastic models to capture statistical properties of the
training traces and produce artificial traces as output. Besides
the general definition of finite-state Markov models, two
commonly used models will be introduced and related work
on Markov modelling will be discussed. From the definition of
finite Markov chains, the second order statistics on multiple
time scales will be derived in Section IV. In Section V, a
comparison of different parameter estimation techniques for
2-state Markov models shows that simple Markov processes