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On truncations for weakly ergodic inhomogeneous birth and death processes

Open Access
|Sep 2014

References

  1. Daleckij, J.L. and Krein, M.G. (1974). Stability of Solutions of Differential Equations in Banach Space, American Mathematical Society, Providence, RI.
  2. Di Crescenzo, A., Giorno, V., Kumar, B.K. and Nobile, A.G. (2012). A double-ended queue with catastrophes and repairs, and a jump-diffusion approximation, Methodology and Computing in Applied Probability 14(4): 937-954, DOI:10.1007/s11009-011-9214-2.10.1007/s11009-011-9214-2
  3. Di Crescenzo, A., Giorno, V., Nobile, A.G. and Ricciardi, L.M. (2003). On the M/M/1 queue with catastrophes and its continuous approximation, Queueing Systems 43(4): 329-347, DOI:10.1023/A:1023261830362.10.1023/A:1023261830362
  4. Di Crescenzo, A. and Nobile, A.G. (1995). Diffusion approximation to a queueing system with time dependent arrival and service rates, Queueing systems 19(1): 41-62, DOI:10.1007/BF01148939.10.1007/BF01148939
  5. Granovsky, B. and Zeifman, A. (2004). Nonstationary queues: Estimation of the rate of convergence, Queueing Systems 46(3): 369-388, DOI:10.1023/B:QUES.0000027991.19758.b4.10.1023/B:QUES.0000027991.19758.b4
  6. Knessl, C. (2000). Exact and asymptotic solutions to a PDE that arises in time-dependent queues, Advances in Applied Probability 32(1): 256-283.10.1239/aap/1013540033
  7. Knessl, C. and Yang, Y.P. (2002). An exact solution for an M(t)/M(t)/1 queue with time-dependent arrivals and service, Advances in Applied Probability 40(3): 233-248, DOI:10.1023/A:1014786928831.10.1023/A:1014786928831
  8. Mandelbaum, A. and Massey,W. (1995). Strong approximations for time-dependent queues, Mathematics of Operations Research 20(1): 33-64, DOI:10.1287/moor.20.1.33.10.1287/moor.20.1.33
  9. Margolius, B. (2007a). Periodic solution to the time-inhomogeneous multi-server Poisson queue, Operations Research Letters 35(1): 125-138, DOI:10.1016/j.orl.2005.12.008.10.1016/j.orl.2005.12.008
  10. Margolius, B. (2007b). Transient and periodic solution to the time-inhomogeneous quasi-birth death process, Queueing Systems 56(3): 183-194, DOI:10.1007/s11134-007-9027-8.10.1007/s11134-007-9027-8
  11. Massey, W. (2002). The analysis of queues with time-varying rates for telecommunication models, Telecommunication Systems 21(2): 173-204, DOI:10.1023/A:1020990313587.10.1023/A:1020990313587
  12. Massey, W. and Pender, J. (2013). Gaussian skewness approximation for dynamic rate multi-server queues with abandonment, Queueing Systems 75(2): 243-277.10.1007/s11134-012-9340-8
  13. Massey, W. and Whitt, W. (1994). On analysis of the modified offered-load approximation for the nonstationary Erlang loss model, Annals of Applied Probability 4(4): 1145-1160, DOI:10.1214/aoap/1177004908.10.1214/aoap/1177004908
  14. Olwal, T.O., Djouani, K., Kogeda, O.P. and van Wyk, B.J.V (2012). Joint queue-perturbed and weakly coupled power control for wireless backbone networks, International Journal of Applied Mathematics and Computer Science 22(3): 749-764, DOI: 10.2478/v10006-012-0056-z.10.2478/v10006-012-0056-z
  15. Tan, X., Knessl, C. and Yang, Y.P. (2013). On finite capacity queues with time dependent arrival rates, Stochastic Processes and their Applications 123(6): 2175-2227, DOI:10.1016/j.spa.2013.02.002.10.1016/j.spa.2013.02.002
  16. Van Doorn, E.A., Zeifman, A.I. and Panfilova, T.L. (2010). Bounds and asymptotics for the rate of convergence of birth-death processes, Theory of Probability and Its Applications 54(1): 97-113, DOI:10.1137/S0040585X97984097.10.1137/S0040585X97984097
  17. Zeifman, A. (1995a). Upper and lower bounds on the rate of convergence for nonhomogeneous birth and death processes, Stochastic Processes and Their Applications 59(1): 157-173, DOI:10.1016/0304-4149(95)00028-6.10.1016/0304-4149(95)00028-6
  18. Zeifman, A.I. (1985). Stability for continuous-time nonhomogeneous Markov chains, in V.V. Kalashnikov and V.M. Zolotarev (Eds.), Stability Problems for Stochastic Models, Lecture Notes in Mathematics, Vol. 1155, Springer, Berlin/Heidelberg, pp. 401-414, DOI:10.1007/BFb0074830.10.1007/BFb0074830
  19. Zeifman, A.I. (1988). Truncation error in a birth and death system, USSR Computational Mathematics and Mathematical Physics 28(6): 210-211, DOI:10.1016/0041-5553(88)90068-7.10.1016/0041-5553(88)90068-7
  20. Zeifman, A.I. (1995b). On the estimation of probabilities for birth and death processes, Journal of Applied Probability 32(3): 623-634.10.2307/3215117
  21. Zeifman, A., Korolev, V., Satin, Y., Korotysheva, A. and Bening, V. (2014). Perturbation bounds and truncations for a class of Markovian queues, Queueing Systems 76(2): 205-221, DOI:10.1007/s11134-013-9388-0.10.1007/s11134-013-9388-0
  22. Zeifman, A. and Korotysheva, A. (2012). Perturbation bounds forMt/Mt/N queue with catastrophes, Stochastic Models 281(1): 49-62, DOI:10.1080/15326349.2011.614900.10.1080/15326349.2011.614900
  23. Zeifman, A., Leorato, S., Orsingher, E., Satin, Y. and Shilova, G. (2006). Some universal limits for nonhomogeneous birth and death processes, Queueing Systems 52(2): 139-151, DOI:10.1007/s11134-006-4353-9.10.1007/s11134-006-4353-9
  24. Zeifman, A., Satin, Y. and Panfilova, T. (2013a). Limiting characteristics for finite birth-death-catastrophe processes, Mathematical Biosciences 245(1): 96-102, DOI:10.1016/j.mbs.2013.02.009.10.1016/j.mbs.2013.02.00923458510
  25. Zeifman, A., Satin, Y., Shilova, G., Korolev, V., Bening, V. and Shorgin, S. (2013b). On Mt/Mt/S type queue with group services, Proceedings of the 27th European Conference on Modeling and Simulation, Aalesund, Norway, pp. 604-609.10.7148/2013-0604
  26. Zhang, J. and Coyle, E.J.J. (1991). The transient solution of time-dependent M/M/L queues, IEEE Transactions on Information Theory 37(6): 1690-1696, DOI:10.1109/18.104335 10.1109/18.104335
DOI: https://doi.org/10.2478/amcs-2014-0037 | Journal eISSN: 2083-8492 | Journal ISSN: 1641-876X
Language: English
Page range: 503 - 518
Submitted on: Jul 30, 2013
Published on: Sep 25, 2014
Published by: University of Zielona Góra
In partnership with: Paradigm Publishing Services
Publication frequency: 4 times per year

© 2014 Alexander Zeifman, Yacov Satin, Victor Korolev, Sergey Shorgin, published by University of Zielona Góra
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.