Big Jobs Arrive Early: From Critical Queues to Random Graphs

Published Online:https://doi.org/10.1287/stsy.2019.0057

References

  • Abramowitz M, Stegun IA (1964) Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables (Dover Publications, New York).Google Scholar
  • Addario-Berry L, Broutin N, Goldschmidt C (2012) The continuum limit of critical random graphs. Probability Theory Related Fields 152(3–4):367–406.Google Scholar
  • Aldous D (1997) Brownian excursions, critical random graphs and the multiplicative coalescent. Ann. Probability 25(2):812–854.Google Scholar
  • Bet G (2018) An alternative approach to heavy-traffic limits for finite-pool queues. Preprint, submitted November 23, https://arxiv.org/abs/1811.09576.Google Scholar
  • Bet G, Selen J, Zocca A (2020) Weighted Dyck paths for nonstationary queues. Preprint, submitted February 9, https://arxiv.org/abs/2002.03424.Google Scholar
  • Bet G, van der Hofstad R, van Leeuwaarden JSH (2017) Finite-pool queueing with heavy-tailed services. J. Appl. Probab. 54(3):921–942.Google Scholar
  • Bet G, van der Hofstad R, van Leeuwaarden JSH (2019) Heavy-traffic analysis through uniform acceleration of queues with diminishing populations. Math. Oper. Res. 44(3):821–864Google Scholar
  • Bhamidi S, Budhiraja A, Wang X (2014) The augmented multiplicative coalescent, bounded size rules and critical dynamics of random graphs. Probability Theory Related Fields 160(3–4):733–796.Google Scholar
  • Bhamidi S, Sen S, Wang X (2017) Continuum limit of critical inhomogeneous random graphs. Probab. Theory Related Fields 169(1–2):565–641.Google Scholar
  • Bhamidi S, van der Hofstad R, van Leeuwaarden JSH (2010) Scaling limits for critical inhomogeneous random graphs with finite third moments. Electronic J. Probability 15:1682–1702.Google Scholar
  • Bhamidi S, van der Hofstad R, van Leeuwaarden JSH (2012) Novel scaling limits for critical inhomogeneous random graphs. Ann. Probability 40(6):2299–2361.Google Scholar
  • Bollobás B, Janson S, Riordan O (2007) The phase transition in inhomogeneous random graphs. Random Structures Algorithms 31(1):3–122.Google Scholar
  • Dhara S, van der Hofstad R, van Leeuwaarden JSH, Sen S (2017) Critical window for the configuration model: finite third moment degrees. Electron. J. Probab. 22(2017):Paper No. 16.Google Scholar
  • Dhara S, van der Hofstad R, van Leeuwaarden JSH, Sen S (2016) Heavy-tailed configuration models at criticality. Preprint, submitted December 2, https://arxiv.org/abs/1612.00650.Google Scholar
  • Duquesne T, Le Gall J-F (2005) Random trees, Lévy processes and spatial branching processes. Preprint, submitted September 23, https://arxiv.org/abs/math/0509558.Google Scholar
  • Durrett R (2010) Probability—Theory and Examples (Cambridge University Press, MA).Google Scholar
  • Ethier SN, Kurtz TG (1986) Markov Processes: Characterization and Convergence (Wiley, New York).Google Scholar
  • Goldschmidt C, Stephenson R (2019) The scaling limit of a critical random directed graph. Preprint, submitted October 29, https://arxiv.org/abs/1905.05397.Google Scholar
  • Honnappa H, Ward AR (2014) On transitory queueing. Preprint, submitted December 7, https://arxiv.org/abs/1412.2321.Google Scholar
  • Honnappa H, Jain R, Ward AR (2015) A queueing model with independent arrivals, and its fluid and diffusion limits. Queueing Systems 80:71–103.Google Scholar
  • Joseph A (2014) The component sizes of a critical random graph with a given degree sequence. Ann. Appl. Probability 24(6):2560–2594.Google Scholar
  • Kendall DG (1951) Some problems in the theory of queues. J. Roy. Statist. Soc. B 13(2):151–185.Google Scholar
  • Klenke A (2008) Probability Theory: A Comprehensive Course (Springer, London).Google Scholar
  • Le Gall J-F (2005) Random trees and applications. Probability Survey 2:245–311.Google Scholar
  • Limic V (2001) A LIFO queue in heavy traffic. Ann. Appl. Probability 11(2):301–331.Google Scholar
  • Luczak T (1990) The phase transition in the evolution of random digraphs. J. Graph Theory 14(2):217–223.Google Scholar
  • Luczak T, Seierstad TG (2009) The critical behavior of random digraphs. Random Structures Algorithms 35(3):271–293.Google Scholar
  • Martin-Löf A (1998) The final size of a nearly critical epidemic, and the first passage time of a Wiener process to a parabolic barrier. J. Appl. Probability 35(3):671–682.Google Scholar
  • Takács L (1988) Queues, random graphs and branching processes. J. Appl. Math. Simulation 1(3):223–243.Google Scholar
  • Takács L (1993) Limit distributions for queues and random rooted trees. J. Appl. Math. Stochastic Anal. 6(3):189–216.Google Scholar
  • Takács L (1995) Queueing methods in the theory of random graphs. Dshalalow JH, ed. Advances in Queueing: Theory, Methods and Open Problems (CRC Press, Boca Raton, FL), 45–78.Google Scholar
  • van der Hofstad R (2016) Random Graphs and Complex Networks (Cambridge University Press, MA).Google Scholar
  • van der Hofstad R, Janssen A, van Leeuwaarden JSH (2010) Critical epidemics, random graphs, and Brownian motion with a parabolic drift. Adv. Appl. Probability 42(4):1187–1206.Google Scholar
  • van der Hofstad R, Kliem S, van Leeuwaarden JSH (2018) Cluster tails for critical power-law inhomogeneous random graphs. J. Statist. Physics 171(1):38–95.Google Scholar
  • van der Hofstad R, van Leeuwaarden JSH, Stegehuis C (2016) Mesoscopic scales in hierarchical configuration models. Preprint, submitted December 8, https://arxiv.org/abs/1612.02668.Google Scholar
  • Whitt W (2002) Stochastic-Process Limits: An Introduction to Stochastic-Process Limits and Their Application to Queues (Springer, New York).Google Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.