Stochastic Networks

URL study guide

Omschrijving

This course covers a broad variety of stochastic models which all have in common that their stationary distribution can be written as a product form.  These stochastic networks arise in various situations, from small networks such as repair shops with only three employees to large data centers with thousands of servers that have to process enormous incoming volumes of requests.

The main part of the course focuses on the classical product-form theory where continuous-time Markov chains like Jackson networks, multi-class queueing networks with Markovian routing and loss networks are discussed.  The product-form distributions make the stochastic networks amenable to analysis, yielding convenient expressions for performance measures such as mean queue lengths or the probability of excessive delays.  Besides the analytical results, numerical schemes for calculating these performance measures will be considered.

The second part of the course is devoted to load balancing and routing problems, i.e. how to divide incoming service requests among servers, as well as scheduling and resource allocation problems, i.e., how to allocate shared resources among various queues.  Remarkably, quite often the strategies for both kinds of problems also give rise to product-form distributions.

Doelstellingen

• Obtaining an overview of classical and modern stochastic models for large-scale networks.
• Gaining knowledge about the important roles these models play in real-life applications, like communication networks, data centers, supply chains, transportation systems.
• Understanding fundamental network concepts at a sufficient level to apply them in practical situations.
• Applying the models and numerical algorithms to solve realistic assignments.

Beoordelingsmethode