Journal of the Korean Statistical Society

  • 제35권3호
  • /
  • Pages.281-303
  • /
  • 2006
  • /
  • 1226-3192(pISSN)
  • /
  • 2005-2863(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지

MARKOVIAN EARLY ARRIVAL DISCRETE TIME JACKSON NETWORKS

  • Aboul-Hassan A. (Department of Engineering Mathematics and Physics, Alexandria University) ;
  • Rabia S.I. (Department of Engineering Mathematics and Physics, Alexandria University)
  • 발행 : 2006.09.01
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In an earlier work, we investigated the problem of using linear programming to bound performance measures in a discrete time Jackson network. There it was assumed that the system evolution is controlled by the early arrival scheme. This assumption implies that the system can't be modelled by a Markov chain. This problem was resolved and performance bounds were calculated. In the present work, we use a modification of the early arrival scheme (without corrupting it) in order to make the system evolves as a Markov chain. This modification enables us to obtain explicit expressions for certain moments that could not be calculated explicitly in the pure early arrival scheme setting. Moreover, this feature implies a reduction in the linear program size as well as the computation time. In addition, we obtained tighter bounds than those appeared before due to the new setting.

키워드

참고문헌

  1. ABOUL-HASSAN, A. AND RABIA, S. I. (2002). 'Approximate analysis of discrete time queueing systems with early arrival scheme', Presented in the Madrid Conference on Queueing Theory, Madrid, June 2002
  2. ABOUL-HASSAN, A. AND RABIA, S. I. (2003). 'Performance bounds for early arrival discrete time queueing systems', Alexandria Engineering Journal, 42, 755-766
  3. ATENCIA, I. AND MORENO, P. (2004). 'A discrete-time Geo/G/1 retrial queue with general retrial times', Queueing Systems, 48, 5-21 https://doi.org/10.1023/B:QUES.0000039885.12490.02
  4. BHARATH-KUMAR, K. (1980). 'Discrete time queueing systems and their networks', IEEE Transactions on communications, COM-28, 260-263
  5. BURKE, P. J. (1956). 'The output of a queuing system', Operations Research, 4, 699-704 https://doi.org/10.1287/opre.4.6.699
  6. GELENBE, E. AND PUJOLLE, G. (1997). Introduction to Queueing Networks, 2nd ed., John Wiley & Sons, New York
  7. HENDERSON, W. AND TAYLOR, P. G. (1990). 'Product form in networks of queues with batch arrivals and batch services', Queueing Systems-Theory and Applications, 6, 71-87 https://doi.org/10.1007/BF02411466
  8. Hsu, J. AND BURKE, P. J. (1976). 'Behavior of tandem buffers with geometric input and Markovian output', IEEE Transactions on communications, COM-24, 358-361
  9. JACKSON, J. R. (1957). 'Networks of waiting lines', Operations Research, 5, 518-521 https://doi.org/10.1287/opre.5.4.518
  10. KUMAR, S. AND KUMAR, P. R. (1994). 'Performance bounds for queueing networks and scheduling policies', IEEE Transactions on Automatic Control, 39, 1600-1611 https://doi.org/10.1109/9.310033
  11. LI, H. AND YANG, T. (1998). 'Geo/G/1 discrete time retrial queue with Bernoulli schedule', European Journal of Operational Research, 111, 629-649 https://doi.org/10.1016/S0377-2217(97)90357-X
  12. NELSON, B. L. (1995). Stochastic Modeling; Analysis and Simulation, McGraw-Hill, New York
  13. WOLFRAM, S. (1996). The Mathematica Book, 3rd ed., Wolfram Media, Champaign
  14. WOODWARD, M. E. (1998). 'Towards the accurate modelling of high speed communication networks with product form discrete-time networks of queues', Computer Communications. 21. 1530-1543 https://doi.org/10.1016/S0140-3664(98)00220-5