Technical Note: The MAPt/Pht/∞ Queueing System and Multiclass [MAPt/Pht/∞]K Queueing Network

Published Online:https://doi.org/10.1287/ijoc.2016.0736

References

  • Artalejo J, Gómez-Corral A, He QM (2010) Markovian arrivals in stochastic modeling: A survey and some new results. Statist. Oper. Res. Trans. 34(2):101–144.Google Scholar
  • Asmussen S (1987) Applied Probability and Queues (John Wiley & Sons, New York).Google Scholar
  • Asmussen S (2000) Matrix-analytic models and their analysis. Scandinavian J. Statist. 27(2):193–226.CrossrefGoogle Scholar
  • Asmussen S, Koole G (1993) Marked point processes as limits of Markovian arrival streams. J. Appl. Probab. 30(2):365–372.CrossrefGoogle Scholar
  • Bitran GR, Dasu S (1993) Approximating nonrenewal processes by Markov chains: Use of Super-Erlang (SE) chains. Oper. Res. 41(5):903–923.LinkGoogle Scholar
  • Casale G, Zhang EZ, Smirni E (2010a) Trace data characterization and fitting for Markov modeling. Performance Eval. 67(2):61–79.CrossrefGoogle Scholar
  • Casale G, Zhang EZ, Smirni E (2010b) KPC-toolbox: Best recipes for automatic trace fitting using Markovian arrival processes. Perform. Eval. 67(9):873–896.CrossrefGoogle Scholar
  • Diamond JE, Alfa AS (2000) On approximating higher order MAPs with MAPs of order two. Queueing Systems 34(1):269–288.CrossrefGoogle Scholar
  • Ferng HW, Chang JF (2001) Connection-wise end-to-end performance analysis of queuing networks with MMPP inputs. Performance Evaluation 43(1):39–62.CrossrefGoogle Scholar
  • Fischer W, Meier-Hellstern K (1993) The Markov-modulated Poisson process (MMPP) cookbook. Performance Evaluation 18(2):149–171.CrossrefGoogle Scholar
  • Heffes H (1980) A class of data traffic processes: Covariance function characterization and related queueing results. Bell System Tech. J. 59(6):897–929.CrossrefGoogle Scholar
  • Horváth A, Telek M (2006) Formal methods and stochastic models for performance evaluation. Third Euro. Performance Engrg. Workshop (EPEW 2006), Budapest, Hungary.CrossrefGoogle Scholar
  • Horváth G, Telek M, Buchholz P (2005) A MAP fitting approach with independent approximation of the inter-arrival time distribution and the lag correlation. QEST '05 Proc. Second Internat. Conf. Quantitative Eval. Systems (IEEE Computer Society, Los Alamitos, CA), 124–133.CrossrefGoogle Scholar
  • Johnson MA (1998) Markov MECO: A simple Markovian model for approximating nonrenewal arrival processes. Comm. Statist.–Stochastic Models 14(1&2):419–442.CrossrefGoogle Scholar
  • Liu DM, Neuts MF (1991) Counter-examples involving Markovian arrival processes. Commun. Statist.-Stochastic Models 7(3):499–509.CrossrefGoogle Scholar
  • Lucantoni DM (1991) New results on the single server queue with a batch Markovian arrival process. Comm. Statist.–Stochastic Models 7(1):1–46.CrossrefGoogle Scholar
  • Narayana S, Neuts MF (1992) The first two moments matrices of the counts for the Markovian arrival processes. Commun. Statist.-Stochastic Models 8(3):459–477.CrossrefGoogle Scholar
  • Nelson BL, Taaffe MR (2004a) The [Ph(t)/Ph(t)/∞]K queueing system: Part II—The multiclass network. INFORMS J. Comput. 16(3):275–283.LinkGoogle Scholar
  • Nelson BL, Taaffe MR (2004b) The Ph(t)/Ph(t)/∞ queueing system: Part I—The single node. INFORMS J. Comput. 16(3):266–274.LinkGoogle Scholar
  • Neuts MF (1979) A versatile Markovian point process. J. Appl. Probab. 16(4):764–779.CrossrefGoogle Scholar
  • Neuts MF, Liu D, Narayana S (1992) Local Poissonification of the Markovian arrival process. Stochastic Models 8(1):87–129.CrossrefGoogle Scholar
  • Takine T, Hasegawa TT (1994) The workload in the MAP/G/1 queue with state-dependent services: Its application to a queue with preemptive resume priority. Commun. Statist.-Stochastic Models 10(1):183–204.CrossrefGoogle Scholar
  • Whitt W, Massey WA (1993) Networks of infinite-server queues with nonstationary Poisson input. Queueing Systems 13(1):183–250.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.