Developing new mathematical methods for stochastic networks: Renovating events, networks with spatial interaction and random fluids
Lead Research Organisation:
Heriot-Watt University
Department Name: S of Mathematical and Computer Sciences
Abstract
This proposal aims at the development of new models and techniques in the area of Stochastic Networks. We propose three themes: (i) the investigation of stability via renovation events,(ii) the investigation of stability for networks with spatial interaction, and (iii) the development of performance techniques for random fluids.Stochastic networks play an important role as mathematical models of various modern complex systems, such as the Internet, mobile networks and traffic networks. Although these systems are quite different from the engineering point of view, they share common characteristics as regards the mathematical models used in describing them and, in effect, predicting their behaviour.We are seeking support for a postdoctoral research fellow for 36 months, some computing equipment, funds for research exchanges and funds for participation in scientific conferences.The research fellow is expected to contribute to the topics described below.
Organisations
Publications
Bordenave C
(2016)
A Random Multiple-Access Protocol with Spatial Interactions
in Journal of Applied Probability
Denisov D
(2010)
Conditional Limit Theorems for Ordered Random Walks
in Electronic Journal of Probability
Denisov D
(2008)
Lower Limits for Distribution Tails of Randomly Stopped Sums
in Theory of Probability & Its Applications
Denisov D
(2010)
Asymptotics of randomly stopped sums in the presence of heavy tails
in Bernoulli
Denisov D
(2012)
Limit theorems for a random directed slab graph
in The Annals of Applied Probability
Denisov D
(2008)
On lower limits and equivalences for distribution tails of randomly stopped sums
in Bernoulli
Foss S
(2012)
On Large Delays in Multi-Server Queues with Heavy Tails
in Mathematics of Operations Research
Foss S
(2016)
Stochastic Sequences with a Regenerative Structure that May Depend Both on the Future and on the Past
in Advances in Applied Probability
Sergey Foss (Author)
(2010)
Ergodicity of a Stress Release Point Process Seismic Model with Aftershocks
in Markov processes and related fields
| Description | (1) Introduced new ideas and methods for asymptotic analysis of large directed graphs, with applications to communication and other networks. (2) Developed a rigorous theory of rare events in the presence of heavy-tailed distributions, around "the single big jump phenomenon": the main cause for something unusual to happen is a single "giant" event. |
| Exploitation Route | We have developed general mathematical theory that may be used by colleagues and may be applied to a number of areas: communication networks, risk processes, etc. |
| Sectors | Education,Energy,Financial Services, and Management Consultancy,Transport,Other |
| Description | Our results have been used by researchers, cited 92 times (according to Google Scholar). Research directions started in the project have been further developed by the members of the team and many co-authors. Monograph "An Introduction to Heavy-Tailed and Subexponential Distributions" (Springer, 2011, First Edition and 2013, SEcond Edition) included results from 3 papers from the list. |
| First Year Of Impact | 2010 |
| Impact Types | Societal |