222 research outputs found
Introduction to Queueing Theory and Stochastic Teletraffic Models
The aim of this textbook is to provide students with basic knowledge of
stochastic models that may apply to telecommunications research areas, such as
traffic modelling, resource provisioning and traffic management. These study
areas are often collectively called teletraffic. This book assumes prior
knowledge of a programming language, mathematics, probability and stochastic
processes normally taught in an electrical engineering course. For students who
have some but not sufficiently strong background in probability and stochastic
processes, we provide, in the first few chapters, background on the relevant
concepts in these areas.Comment: 298 page
Study of Queuing Systems with a Generalized Departure Process
This work was supported by the Bulgarian National Science Fund under grant BY-TH-105/2005.This paper deals with a full accessibility loss system and a single server delay system with a Poisson arrival process and state dependent exponentially distributed service time. We use the generalized service flow with nonlinear state dependence mean service time. The idea is based on the analytical continuation of the Binomial distribution and the classic M/M/n/0 and M/M/1/k system. We apply techniques based on birth and death processes and state-dependent service rates.
We consider the system M/M(g)/n/0 and M/M(g)/1/k (in Kendal notation) with a generalized departure process Mg. The output intensity depends nonlinearly on the system state with a defined parameter: “peaked factor p”. We obtain the state probabilities of the system using the general solution of
the birth and death processes. The influence of the peaked factor on the state probability distribution,
the congestion probability and the mean system time are studied. It is shown
that the state-dependent service rates changes significantly the characteristics of the queueing systems. The advantages of simplicity and uniformity in
representing both peaked and smooth behaviour make this queue attractive
in network analysis and synthesis
Optimization of polling systems with Bernoulli schedules
Optimization;Polling Systems;Queueing Theory;operations research
Adaptive TTL-Based Caching for Content Delivery
Content Delivery Networks (CDNs) deliver a majority of the user-requested
content on the Internet, including web pages, videos, and software downloads. A
CDN server caches and serves the content requested by users. Designing caching
algorithms that automatically adapt to the heterogeneity, burstiness, and
non-stationary nature of real-world content requests is a major challenge and
is the focus of our work. While there is much work on caching algorithms for
stationary request traffic, the work on non-stationary request traffic is very
limited. Consequently, most prior models are inaccurate for production CDN
traffic that is non-stationary.
We propose two TTL-based caching algorithms and provide provable guarantees
for content request traffic that is bursty and non-stationary. The first
algorithm called d-TTL dynamically adapts a TTL parameter using a stochastic
approximation approach. Given a feasible target hit rate, we show that the hit
rate of d-TTL converges to its target value for a general class of bursty
traffic that allows Markov dependence over time and non-stationary arrivals.
The second algorithm called f-TTL uses two caches, each with its own TTL. The
first-level cache adaptively filters out non-stationary traffic, while the
second-level cache stores frequently-accessed stationary traffic. Given
feasible targets for both the hit rate and the expected cache size, f-TTL
asymptotically achieves both targets. We implement d-TTL and f-TTL and evaluate
both algorithms using an extensive nine-day trace consisting of 500 million
requests from a production CDN server. We show that both d-TTL and f-TTL
converge to their hit rate targets with an error of about 1.3%. But, f-TTL
requires a significantly smaller cache size than d-TTL to achieve the same hit
rate, since it effectively filters out the non-stationary traffic for
rarely-accessed objects
Evaluation of Pareto/D/1/k Queue by Simulation
The finding that Pareto distributions are adequate to model Internet packet interarrival times has
motivated the proposal of methods to evaluate steady-state performance measures of Pareto/D/1/k queues.
Some limited analytical derivation for queue models has been proposed in the literature, but their solutions are
often of a great mathematical challenge. To overcome such limitations, simulation tools that can deal with general
queueing system must be developed. Despite certain limitations, simulation algorithms provide a mechanism to
obtain insight and good numerical approximation to parameters of queues. In this work, we give an overview of
some of these methods and compare them with our simulation approach, which are suited to solve queues with
Generalized-Pareto interarrival time distributions. The paper discusses the properties and use of the Pareto
distribution. We propose a real time trace simulation model for estimating the steady-state probability showing the
tail-raising effect, loss probability, delay of the Pareto/D/1/k queue and make a comparison with M/D/1/k. The
background on Internet traffic will help to do the evaluation correctly. This model can be used to study the long-
tailed queueing systems. We close the paper with some general comments and offer thoughts about future work
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