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2014 | 24 | 3 | 503-518
Tytuł artykułu

On truncations for weakly ergodic inhomogeneous birth and death processes

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We investigate a class of exponentially weakly ergodic inhomogeneous birth and death processes. We consider special transformations of the reduced intensity matrix of the process and obtain uniform (in time) error bounds of truncations. Our approach also guarantees that we can find limiting characteristics approximately with an arbitrarily fixed error. As an example, we obtain the respective bounds of the truncation error for an Mt /Mt /S queue for any number of servers S. Arbitrary intensity functions instead of periodic ones can be considered in the same manner.
Rocznik
Tom
24
Numer
3
Strony
503-518
Opis fizyczny
Daty
wydano
2014
otrzymano
2013-07-30
poprawiono
2014-02-03
Twórcy
  • Institute of Socio-Economic Development of Territories, Russian Academy of Sciences, Gorkogo Str., 56A, Vologda, Russia
  • Department of Applied Mathematics, Vologda State University, Vologda, S. Orlova, 6, Russia
autor
  • Department of Applied Mathematics, Vologda State University, Vologda, S. Orlova, 6, Russia
  • Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Leninskie Gory, Moscow, Russia
  • Institute of Problems of Informatics, Russian Academy of Sciences, Vavilova str., 44-2, Moscow, Russia
  • Institute of Problems of Informatics, Russian Academy of Sciences, Vavilova str., 44-2, Moscow, Russia
Bibliografia
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  • 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.
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  • Knessl, C. (2000). Exact and asymptotic solutions to a PDE that arises in time-dependent queues, Advances in Applied Probability 32(1): 256-283.
  • 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.
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  • 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.
  • 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.
  • Massey, W. and Pender, J. (2013). Gaussian skewness approximation for dynamic rate multi-server queues with abandonment, Queueing Systems 75(2): 243-277.
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  • 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.
  • 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.
  • 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.
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  • 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.
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  • 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.
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  • 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.
  • 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.
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Typ dokumentu
Bibliografia
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Identyfikator YADDA
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