Journal of Korean Society of Industrial and Systems Engineering (산업경영시스템학회지)

Society of Korea Industrial and System Engineering (한국산업경영시스템학회)
권호 표지

Analysis of BMAP/M/N/0 Queueing System for Telecommunication Network Traffic Control

통신망 트래픽 제어를 위한 BMAP/M/N/0 대기행렬모형 분석

  • Lee, Seok-Jun (School of Business Administration, Sangji University) ;
  • Kim, Che-Soong (Department of Industrial Engineering, Sangji University)
  • Published : 2007.12.31
Download PDF
⟨ Previous Next ⟩

Abstract

The BMAP/M/N/0 queueing system operating in Markovian random environment is investigated. The stationary distribution of the system is derived. Loss probability and other performance measures of the system also are calculated. Numerical experiments which show the necessity of taking into account the influence of random environment and correlation in input flow are presented.

Keywords

References

  1. Bocharov, P. P., D'Apice, C., Pechinkin, A. V., and Salerno, S.; 'The stationary characteristics of the G/MS P/1/r queueing system,' Automation and Remote Control, 64 : 288-301, 2003 https://doi.org/10.1023/A:1022219232282
  2. Fisher, W. and Meier-Hellstern, K. S.; 'The Markovmodulated Poisson Process (MMPP) cookbook,' Performance Evaluation, 18 : 149-171, 1993 https://doi.org/10.1016/0166-5316(93)90035-S
  3. He, Q. M.; 'Queues with marked customers,' Advances in Applied Probability, 28 : 567-587, 1996 https://doi.org/10.2307/1428072
  4. Kim, C. S., Klimenok, V. I., Orlovsky, D. S., Dudin, and A. N.; 'Lack of invariant property of the Erlang loss model in case of MAP input,' Queueing Systems, 49 : 187-213, 2005 https://doi.org/10.1007/s11134-005-6481-z
  5. Klimenok, V. I.; 'Characteristics calculation for multi-server queue with losses and bursty traffic,' Automatic Control and Computer Sciences, 12 : 393-415, 1999
  6. Klimenok, V. I. and Dudin, A. N.; 'Multi-dimensional asymptotically quasi-Toeplitz Markov chains and their application in queueing theory,' Queueing Systems, 54 : 245-259, 2006 https://doi.org/10.1007/s11134-006-0300-z
  7. Lucantoni, D.; 'New results on the single server queue with a batch Markovian arrival process,' Comm. Stat. -Stochastic Models, 7 : 1-46, 1991 https://doi.org/10.1080/15326349108807174
  8. Neuts, M. F.; Matrix-geometric solutions in stochastic models, The Johns Hopkins University Press, Baltimore, 1981
  9. Neuts, M. F.; Structured stochastic matrices of M/G/1 type and their applications. Marcel Dekker, NY, 1983
  10. Panchenko, A. and Buchholz, P.; 'A hybrid algorithm for parameter fitting of Markovian arrival,' 14th Int. Conf. Analytical and stochastic modelling technique and applications, Prague, 2007
  11. Sevastjanov, B. A.; 'Erlang formula in telephone systems under the arbitrary distribution of conversations duration,' Proceedings of 3rd All-Union Mathematical Congress, Academy of Science, Moscow, 4 : 68-70, 1959
  12. Yechiali, U. and Naor, P.; 'Queueing problems with heterogeneous arrivals and service,' Operations Research, 19 : 722-734, 1971 https://doi.org/10.1287/opre.19.3.722