| 1. |
- Belyaev, Yu. K., et al.
(författare)
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Kolmogorov Stories
- 2021
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Ingår i: Probability in the engineering and informational sciences (Print). - : Cambridge University Press. - 0269-9648 .- 1469-8951. ; 35:3, s. 355-368
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Tidskriftsartikel (refereegranskat)abstract
- Authors of this paper were educated and have spent many years in Lomonosov Moscow State University (MSU), in the Interfaculty Laboratory of Statistical Methods (ILSM). Prof. Yu. K. Belyaev was student of Kolmogorov, and for several years his deputy in the ILSM, created and led by the great A. N. Kolmogorov. Now Prof. Yuri Belyaev is Emeritus Professor at Umea University (Sweden). Asaf Hajiyev was a PhD student in Kolmogorov's ILSM. In this paper some unusual incidents about the legendary Kolmogorov, and people around him are presented. Some stories were taken from the books and the internet (see references) dedicated to the memory of Kolmogorov; some were told by his students, and some happened with authors of this paper.
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| 2. |
- Desmarais, Colin, 1992-, et al.
(författare)
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Depths in hooking networks
- 2021
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Ingår i: Probability in the engineering and informational sciences (Print). - : Cambridge University Press. - 0269-9648 .- 1469-8951. ; , s. 1-9
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Tidskriftsartikel (refereegranskat)abstract
- A hooking network is built by stringing together components randomly chosen from a set of building blocks (graphs with hooks). The vertices are endowed with “affinities” which dictate the attachment mechanism. We study the distance from the master hook to a node in the network chosen according to its affinity after many steps of growth. Such a distance is commonly called the depth of the chosen node. We present an exact average result and a rather general central limit theorem for the depth. The affinity model covers a wide range of attachment mechanisms, such as uniform attachment and preferential attachment, among others. Naturally, the limiting normal distribution is parametrized by the structure of the building blocks and their probabilities. We also take the point of view of a visitor uninformed about the affinity mechanism by which the network is built. To explore the network, such a visitor chooses the nodes uniformly at random. We show that the distance distribution under such a uniform choice is similar to the one under random choice according to affinities.
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| 3. |
- Dimitriou, Ioannis, et al.
(författare)
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A RANDOM ACCESS G-NETWORK: STABILITY, STABLE THROUGHPUT, AND QUEUEING ANALYSIS
- 2021
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Ingår i: Probability in the engineering and informational sciences (Print). - : CAMBRIDGE UNIV PRESS. - 0269-9648 .- 1469-8951. ; 35:1, s. 111-137
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Tidskriftsartikel (refereegranskat)abstract
- The effect of signals on stability, stable throughput region, and delay in a two-user slotted ALOHA-based random-access system with collisions is considered. This work gives rise to the development of random access G-networks, which can model security attacks, expiration of deadlines, or other malfunctions, and introduce load balancing among highly interacting queues. The users are equipped with infinite capacity buffers accepting external bursty arrivals. We consider both negative and triggering signals. Negative signals delete a packet from a user queue, while triggering signals cause the instantaneous transfer of packets among user queues. We obtain the exact stability region, and show that the stable throughput region is a subset of it. Moreover, we perform a compact mathematical analysis to obtain exact expressions for the queueing delay by solving a non-homogeneous Riemann boundary value problem. A computationally efficient way to obtain explicit bounds for the expected number of buffered packets at user queues is also presented. The theoretical findings are numerically evaluated and insights regarding the system performance are derived.
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