한국산업정보학회논문지 (Journal of Korea Society of Industrial Information Systems)

한국산업정보학회 (Korea Society of Industrial Information Systems)
권호 표지
DOI QR코드

DOI QR Code

D-정책과 집단도착을 갖는 이산시간 MAP/G/1 대기행렬시스템의 일량 분석

Workload Analysis of Discrete-Time BMAP/G/1 queue under D-policy

  • 투고 : 2016.12.06
  • 심사 : 2016.12.26
  • 발행 : 2016.12.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

본 논문에서는 D-정책을 갖는 이산시간 BMAP/G/1 대기행렬시스템의 일량을 분석한다. 유휴한 서버는 시스템에 도착한 고객집단의 서비스시간의 총합이 이미 정해진 일량 임계값 D를 초과하면 시스템에 서비스할 고객이 없을 때까지 서비스를 제공한다. 시스템의 안정상태 일량변환벡터를 유도하고 성능척도로서 평균일량을 구하였다. 시뮬레이션을 통해 이론값들의 타당성을 검증하고 간단한 수치예제를 보였다.

In this paper, we consider a general discrete-time queueing system with D-BMAP(discrete-time batch Markovian arrival process) and D-policy. An idle single server becomes busy when the total service times of waiting customer group exceeds the predetermined workload threshold D. Once the server starts busy period, the server provides service until there is no customer in the system. The steady-state workload distribution is derived in the form of generating function. Mean workload is derived as a performance measure. Simulation is also performed for the purpose of verification and a simple numerical example is shown.

키워드

참고문헌

  1. Balachandran, K.R., “Control Policies for a Single Server System,” Management Science, Vol. 19, No. 9, pp. 1013-1018, 1973. https://doi.org/10.1287/mnsc.19.9.1013
  2. Bachandran, K.R. and Tijms, H., “On the D-policy for the M/G/1 Queue,” Management Science, Vol. 21, No. 9, pp. 1073-1076, 1975.
  3. Li, J. and Niu, S.C., “The Waiting Time Distribution for the GI/G/1 Queue under the D-policy,” Probability in the Engineering and Informational Sciences, Vol. 6, No. 3, pp. 287-308, 1992. https://doi.org/10.1017/S0269964800002552
  4. Dshalalow, J.H., “Queueing Processes in Bulk Systems under the D-policy,” Journal of Applied Probability, Vol. 35, No. 4, pp. 976-989, 1998. https://doi.org/10.1239/jap/1032438392
  5. Dshalaow, J.H., “A Note on D-policy Bulk Queueing Systems,” Journal of Applied Probability, Vol. 38, No. 1, pp. 280-283, 2001. https://doi.org/10.1239/jap/996986664
  6. Lee, H. W., Baek, J. W. and Jeon, J., “Analysis of the $M^X$/G/1 Queue under D-policy,” Stochastic Analysis and Applications, Vol. 23, No. 4, pp. 785-808, 2005. https://doi.org/10.1081/SAP-200064479
  7. Lee, H. W., Cheon, S. H. and Seo, W. J., “Queue Length and Waiting Time of the M/G/1 Queue under the D-policy and Multiple Vacations,” Queueing Systems, Vol. 54, No. 4, pp. 261-280, 2006. https://doi.org/10.1007/s11134-006-0301-y
  8. Baek, J. W. and Lee, H. W., “Waiting Time Analysis of a Batch Arrival Queue under a Workload Control,” International Journal of Industrial Engineering, Vol. 14, No. 3, pp. 298-306, 2007.
  9. Lee, H. W. and Seo, W. J., “The Performance of the M/G/1 Queue under the Dyadic Min(N,D)-policy and Its Cost Optimization,” Performance Evaluation, Vol. 65, No. 10, pp. 742-758, 2008. https://doi.org/10.1016/j.peva.2008.04.006
  10. Lee, H. W., Seo, W. J., Lee, S. W. and Jeon, J., “Analysis of MAP/G/1 Queue under Min(N,D)-policy,” Stochastic Models, Vol. 26, No. 1, pp. 98-123, 2010. https://doi.org/10.1080/15326340903517121
  11. Lee, H. W., Seo, W. J. and Lee, S. W., “Analysis of the M/G/1 Queueing System under the Triadic (N,D,T)-policies,” Quality Technology and Quantitative Management, Vol. 8, No. 3, pp. 333-357, 2011. https://doi.org/10.1080/16843703.2011.11673262
  12. Lee, H. W., Cheon, S. H., Lee, S. W. and Baek, J. W., “MAP/G/1 Queue under Workload Control and Postprocessing,” Stochastic Analysis and Applications, Vol. 27, No. 2, pp. 331-352, 2009. https://doi.org/10.1080/07362990802678952
  13. Paxson, V. and Floyd, S., “Wide Area Traffic: The Failure of Poisson Modeling,” IEEE/ACM Transactions on Networking, Vol. 3, No. 3, pp. 226-244, 1995. https://doi.org/10.1109/90.392383
  14. Bruneel, H. and Kim, B. G., "Discrete-Time Models for Communication Systems Including ATM," Kluwer Academic Publishers, 1993.
  15. Takagi, H., "Queueing Analysis: Vol III, Discrete-Time Systems," North-Holland, 1993.
  16. Lee, S. W., Lee, H. W., and Baek, J. W., "Analysis of Discrete-Time Geo/G/1 Queue under the D-policy," 6th International Conference on Queueing Theory and Network Analysis, 2011, Seoul, Korea, QTNA2011.
  17. Lee, S. W., Lee, H. W., and Baek, J. W., “Analysis of Discrete-Time MAP/G/1 Queue under Workload Control,” Performance Evaluation, Vol. 69, No. 2, pp. 71-85, 2012. https://doi.org/10.1016/j.peva.2011.11.001
  18. Kim, S. J., Kim, N. K., Park, H. M., Chae, K. C., and Lim, D. E., "On the Discrete-Time $Geo^X$/G/1 Queues under N-policy with Single and Multiple Vacations," Journal of Applied Mathematics, Vol. 2013, Article ID 587163, 2013.
  19. Liu, R. and Deng, Z., "The Steady-State System Size Distribution for a Modified D-policy Geo/G/1 Queueing System," Mathematical Problems in Engineering, Vol. 2014, Article ID 345129, 2014.
  20. Lan, S. and Tang, Y., "Analysis of a Discrete-Time $Geo^{\lambda_1,\lambda_2}$ Queue with N-policy and D-policy," Journal of Applied Mathematics and Computing, pp. 1-25, 2016. (online first article)
  21. Lucantoni, D. M., “New Results for the Single Server Queue with a Batch Markovian Arrival Process,” Stochastic Models, Vol. 7, No. 1, pp. 1-46, 1991. https://doi.org/10.1080/15326349108807174
  22. Latouche, G. and Ramaswami, V., "A Unified Stochastic Model for the Packet Stream from Periodic Sources," Performance Evaluation, Vol 14, No. 12, pp. 103-121, 1992. https://doi.org/10.1016/0166-5316(92)90013-7
  23. Ramaswami, V. and Latouche, G., Modeling Packet Arrivals from Asynchronous Input Lines, in "Teletraffic Science for New Cost-Effective Systems, Networks and Services," ITC-12, M. Bonatti Ed., North-Holland, Amsterdam, pp. 721-727, 1989.
  24. Wang, S. S. and Silvester, J. A., "A Discrete-Time Performance Model for Integrated Service ATM Multiplexers," Proceeding of IEEE COLBECOM, pp. 757-761, 1993.
  25. Lee, H. W., "Queueing Theory," Sigma Press, 2006 (in Korean)
  26. Baek, J. W., Lee, H. W., Lee, S. W., and Ahn, S., “A Markov-Modulated Fluid Flow Queueing Model under D-policy,” Numerical Linear Algebra with Applications, Vol. 18, No. 6, pp. 993-1010, 2011. https://doi.org/10.1002/nla.811
  27. Mitra, D., "Stochastic Theory of Fluid Model of Producers and Consumers Coupled by a Buffer," Advances in Applied Probability, Vol. 20, No. 3, pp.646-676, 1988 https://doi.org/10.1017/S000186780001819X
  28. Lucantoni, D. M. and Neuts, M.F., “Simpler Proofs of Some Properties of the Fundamental Period of the MAP/G/1 Queue,” Journal of Applied Probability, Vol. 31, No. 1, pp. 235-243, 1994. https://doi.org/10.1017/S0021900200107478
  29. Lee, K. G., Choi, S. and Ryu, S. W., “Development of Simulation System for Evaluating Performance of the Flat Display Manufacturing Line with Repetitive Process,” The Journal of Information Systems, Vol. 17, No. 4, pp. 301-319, 2008. https://doi.org/10.5859/KAIS.2008.17.4.301

피인용 문헌

  1. 일량제어정책과 단수휴가를 갖는 이산시간 대기행렬의 고객수 분석 vol.25, pp.1, 2020, https://doi.org/10.9723/jksiis.2020.25.1.089