Heavy-Traffic Analysis Through Uniform Acceleration of Queues with Diminishing Populations

Published Online:https://doi.org/10.1287/moor.2018.0947

References

  • [1] Abramowitz M, Stegun IA (1964) Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables, vol. 55 (Dover Publications, Mineola, NY).Google Scholar
  • [2] Aldous D (1997) Brownian excursions, critical random graphs and the multiplicative coalescent. Ann. Probab. 25(2):812–854.CrossrefGoogle Scholar
  • [3] Bhamidi S, van der Hofstad R, van Leeuwaarden JSH (2010) Scaling limits for critical inhomogeneous random graphs with finite third moments. Electron. J. Probab. 15(54):1682–1702.CrossrefGoogle Scholar
  • [4] Bhamidi S, van der Hofstad R, van Leeuwaarden JSH (2012) Novel scaling limits for critical inhomogeneous random graphs. Ann. Probab. 40(6):2299–2361.CrossrefGoogle Scholar
  • [5] Billingsley P (2009) Convergence of Probability Measures (John Wiley & Sons, Hoboken, NJ).Google Scholar
  • [6] Bollobás B (2001) Random Graphs (Cambridge University Press, Cambridge, UK).CrossrefGoogle Scholar
  • [7] Bollobás B, Janson S, Riordan O (2007) The phase transition in inhomogeneous random graphs. Random Structures Algorithms 31(1):3–122.CrossrefGoogle Scholar
  • [8] Britton T, Deijfen M, Martin-Löf A (2006) Generating simple random graphs with prescribed degree distribution. J. Statist. Phys. 124(6):1377–1397.CrossrefGoogle Scholar
  • [9] Caccavale MV, Iovanella A, Lancia C, Lulli G, Scoppola B (2014) A model of inbound air traffic: The application to Heathrow airport. J. Air Transp. Management 34:116–122.CrossrefGoogle Scholar
  • [10] Chung F, Lu L (2006) Complex Graphs and Networks (American Mathematical Society, Providence, RI).CrossrefGoogle Scholar
  • [11] David HA, Nagaraja HN (2003) Order Statistics (John Wiley & Sons, Hoboken, NJ).CrossrefGoogle Scholar
  • [12] Ethier SN, Kurtz TG (1985) Markov Processes: Characterization and Convergence (John Wiley & Sons, Hoboken, NJ).Google Scholar
  • [13] Grenander U (1956) On the theory of mortality measurement: Part II. Scandinavian Actuarial J. 1956(2):125–153.CrossrefGoogle Scholar
  • [14] Groeneboom P, Hooghiemstra G, Lopuhaä HP (1999) Asymptotic normality of the L1error of the grenander estimator. Ann. Statist. 27(4):1316–1347.Google Scholar
  • [15] Guadagni G, Ndreca S, Scoppola B (2011) Queueing systems with pre-scheduled random arrivals. Math. Methods Oper. Res. 73(1):1–18.CrossrefGoogle Scholar
  • [16] Hassin R, Mendel S (2008) Scheduling arrivals to queues: A single-server model with no-shows. Management Sci. 54(3):565–572.LinkGoogle Scholar
  • [17] Honnappa H, Rahul J (2015) Strategic arrivals into queueing networks: The network concert queueing game. Oper. Res. 63(1):247–259.LinkGoogle Scholar
  • [18] Honnappa H, Jain R, Ward AR (2014) On transitory queueing. Working paper, Purdue University, West Lafayette, IN.Google Scholar
  • [19] Honnappa H, Jain R, Ward AR (2015) A queueing model with independent arrivals, and its fluid and diffusion limits. Queueing Syst. 80(1–2):71–103.CrossrefGoogle Scholar
  • [20] Iglehart DL, Whitt W (1970) Multiple channel queues in heavy traffic. I. Adv. Appl. Probab. 2(1):150–177.CrossrefGoogle Scholar
  • [21] Iglehart DL, Whitt W (1970) Multiple channel queues in heavy traffic. II. Adv. Appl. Probab. 2(1):355–369.CrossrefGoogle Scholar
  • [22] Jacod J, Shiryaev AN (2003) Limit Theorems for Stochastic Processes (Springer, New York).CrossrefGoogle Scholar
  • [23] Janson S, Łuczak T, Rucinski A (2000) Random Graphs (John Wiley & Sons, Hoboken, NJ).CrossrefGoogle Scholar
  • [24] Joseph A (2014) The component sizes of a critical random graph with pre-described degree sequence. Ann. Appl. Probab. 24(6):2560–2594.CrossrefGoogle Scholar
  • [25] Keller JB (1982) Time-dependent queues. SIAM Rev. 24(4):401–412.CrossrefGoogle Scholar
  • [26] Klenke A (2007) Probability Theory: A Comprehensive Course (Springer, New York).Google Scholar
  • [27] Louchard G (1994) Large finite population queueing systems. The single-server model. Stochastic Process. Appl. 53(1):117–145.CrossrefGoogle Scholar
  • [28] Mandelbaum A, Massey WA (1995) Strong approximations for time-dependent queues. Math. Oper. Res. 20(1):33–64.LinkGoogle Scholar
  • [29] 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. Probab. 35(3):671–682.CrossrefGoogle Scholar
  • [30] Massey WA (1982) Non-stationary queues. PhD thesis, Princeton University, Princeton, NJ.Google Scholar
  • [31] Massey WA (1985) Asymptotic analysis of the time dependent M/M/1 queue. Math. Oper. Res. 10(2):305–327.LinkGoogle Scholar
  • [32] Newell GF (1968) Queues with time-dependent arrival rates I, II and III. J. Appl. Probab. 5(3):436–451.CrossrefGoogle Scholar
  • [33] Newell GF (1982) Applications of Queueing Theory (Springer, New York).CrossrefGoogle Scholar
  • [34] Norros I, Reittu H (2006) On a conditionally Poissonian graph process. Adv. Appl. Probab. 38(1):59–75.CrossrefGoogle Scholar
  • [35] Pender J (2015) The truncated normal distribution: Applications to queues with impatient customers. Oper. Res. Lett. 43(1):40–45.CrossrefGoogle Scholar
  • [36] Skorokhod AV (1956) Limit theorems for stochastic processes. Theory Probab. Appl. 1(3):261–290.CrossrefGoogle Scholar
  • [37] van der Hofstad R (2013) Critical behavior in inhomogeneous random graphs. Random Structures Algorithms 42(4):480–508.CrossrefGoogle Scholar
  • [38] van der Hofstad R (2017) Random Graphs and Complex Networks, vol. 1 (Cambridge University Press, Cambridge, UK).CrossrefGoogle Scholar
  • [39] van der Hofstad R, Janssen AJEM, van Leeuwaarden JSH (2010) Critical epidemics, random graphs, and Brownian motion with a parabolic drift. Adv. Appl. Probab. 42(4):1187–1206.CrossrefGoogle Scholar
  • [40] Whitt W (1980) Some useful functions for functional limit theorems. Math. Oper. Res. 5(1):67–85.LinkGoogle Scholar
  • [41] Whitt W (2002) Stochastic-Process Limits: An Introduction to Stochastic-Process Limits and their Application to Queues (Springer, New York).CrossrefGoogle Scholar
  • [42] Whitt W (2007) Proofs of the martingale FCLT. Probab. Surv. 4:268–302.CrossrefGoogle Scholar
  • [43] Whitt W (2016) Queues with time-varying arrival rates: A bibliography. Accessed September 30, 2018, http://www.columbia.edu/ww2040/TV_bibliography_091016.pdf.Google Scholar
  • [44] Yang YP, Knessl C (1997) Asymptotic analysis of the M/G/1 queue with a time-dependent arrival rate. Queueing Syst. 26(1–2):23–68.CrossrefGoogle 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.