0469224 20250225145348.320170117235959.9 85018260342 000430374200006 14 s. P cav_un_epca*03780591980-0436132 (2016)1151-1164Instituto Nacional de Matematica Pura e Aplicada (I M P A) Self-organized criticality Gabrielli and Caldarelli queueing model Barabasi queueing model email communication cav_un_auth*0316935 50 Formentin Marco UTIA-B Stochastická informatika Department of Stochastic Informatics SI SI Department of Stochastic Informatics IT Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0217893 50 Swart Jan M. UTIA-B Stochastická informatika Department of Stochastic Informatics SI SI Department of Stochastic Informatics CZ Ústav teorie informace a automatizace AV ČR, v. v. i. http://library.utia.cas.cz/separaty/2016/SI/swart-0469224.pdf cav_un_auth*0291241 GAP201/12/2613 GA ČR We study a model for email communication due to Gabrielli and Caldarelli, where someone receives and answers emails at the times of independent Poisson processes with intensities λin > λout . The receiver assigns i.i.d. priorities to incoming emails according to some atomless law and always answers the email in the mailbox with the highest priority. Since the frequency of incoming emails is higher than the frequency of answering, below a critical priority, the mailbox fills up ad infinitum. We prove a theorem about the limiting shape of the mailbox just above the critical point, linking it to the convex hull of Brownian motion. We con- jecture that this limiting shape is universal in a class of similar models, including a model for the evolution of an order book due to Stigler and Luckock. BA 10000 10100 10101 2017 2 RVO:67985556 http://hdl.handle.net/11104/0268911 S RIV/67985556:_____/16:00469224!RIV17-AV0-67985556 191870799 Doplnění UT WOS RIV/67985556:_____/16:00469224!RIV17-GA0-67985556 191876831 Doplnění UT WOS 2 Article Statistics Probability STATISTICS&PROBABILITY 0.630 0.114 4.9 0.0017 0.717 185 1.053 Q2 0.342 35 Q4 48.171 5.2 Q3 Q2 5.242 2016 85018260342 SCOPUS PUBMED 000430374200006 WOS cav_un_epca*0378059 Alea (Rio de Janeiro) 1980-0436 Roč. 13 č. 2 2016 1151 1164 Instituto Nacional de Matematica Pura e Aplicada (I M P A)