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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
Stability of Service under Time-of-Use Pricing
We consider "time-of-use" pricing as a technique for matching supply and
demand of temporal resources with the goal of maximizing social welfare.
Relevant examples include energy, computing resources on a cloud computing
platform, and charging stations for electric vehicles, among many others. A
client/job in this setting has a window of time during which he needs service,
and a particular value for obtaining it. We assume a stochastic model for
demand, where each job materializes with some probability via an independent
Bernoulli trial. Given a per-time-unit pricing of resources, any realized job
will first try to get served by the cheapest available resource in its window
and, failing that, will try to find service at the next cheapest available
resource, and so on. Thus, the natural stochastic fluctuations in demand have
the potential to lead to cascading overload events. Our main result shows that
setting prices so as to optimally handle the {\em expected} demand works well:
with high probability, when the actual demand is instantiated, the system is
stable and the expected value of the jobs served is very close to that of the
optimal offline algorithm.Comment: To appear in STOC'1
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