메뉴 건너뛰기




Volumn 8, Issue 4, 1998, Pages 1130-1155

Uniform acceleration expansions for Markov chains with time-varying rates

Author keywords

Asymptotic expansions; Erlang loss model; Nonstationary queueing models; Pointwise stationary approximation; Poisson's equation; Time inhomogeneous Markov chains

Indexed keywords


EID: 0032261416     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/aoap/1028903375     Document Type: Article
Times cited : (73)

References (28)
  • 6
    • 0002273684 scopus 로고
    • The pointwise stationary approximation for queues with nonstationary arrivals
    • GREEN, L. and KOLESAR, P. (1991). The pointwise stationary approximation for queues with nonstationary arrivals. Management Sci. 37 84-97.
    • (1991) Management Sci. , vol.37 , pp. 84-97
    • Green, L.1    Kolesar, P.2
  • 8
    • 0021390136 scopus 로고
    • The asymptotic behavior of queues with time-varying arrival rates
    • HEYMAN, D. P. and WHITT, W. (1984). The asymptotic behavior of queues with time-varying arrival rates. J. Appl. Probab. 21 143-156.
    • (1984) J. Appl. Probab. , vol.21 , pp. 143-156
    • Heyman, D.P.1    Whitt, W.2
  • 10
    • 0030084736 scopus 로고    scopus 로고
    • Asymptotic expansions of singularly perturbed systems involving rapidly fluctuating markov chains
    • KHASMINSKII, R. Z., YIN, G. and ZHANG, Q. (1996). Asymptotic expansions of singularly perturbed systems involving rapidly fluctuating Markov chains. SIAM J. Appl. Math. 56 277-293.
    • (1996) SIAM J. Appl. Math. , vol.56 , pp. 277-293
    • Khasminskii, R.Z.1    Yin, G.2    Zhang, Q.3
  • 11
    • 0009212812 scopus 로고
    • Time-dependent queues
    • KELLER, J. B. (1982). Time-dependent queues. SIAM Rev. 24 401-412.
    • (1982) SIAM Rev. , vol.24 , pp. 401-412
    • Keller, J.B.1
  • 12
    • 0001835972 scopus 로고
    • Strong approximations for time-dependent queues
    • MANDELBAUM, A. and MASSEY, W. A. (1995). Strong approximations for time-dependent queues. Math. Oper. Res. 20 33-64.
    • (1995) Math. Oper. Res. , vol.20 , pp. 33-64
    • Mandelbaum, A.1    Massey, W.A.2
  • 13
  • 14
    • 0022064665 scopus 로고
    • Asymptotic analysis for the time-dependent M/M/1 queue
    • MASSEY, W. A. (1985). Asymptotic analysis for the time-dependent M/M/1 queue. Math. Oper. Res. 10 305-327.
    • (1985) Math. Oper. Res. , vol.10 , pp. 305-327
    • Massey, W.A.1
  • 15
    • 21344451115 scopus 로고    scopus 로고
    • Estimating the parameters of a non-homogeneous Poisson process with linear rate
    • MASSEY, W. A., PARKER, G. A. and WHITT, W. (1996). Estimating the parameters of a non-homogeneous Poisson process with linear rate. Telecommunication Systems 5 361-388.
    • (1996) Telecommunication Systems , vol.5 , pp. 361-388
    • Massey, W.A.1    Parker, G.A.2    Whitt, W.3
  • 16
    • 38249004693 scopus 로고
    • A probabilistic generalization of Taylor's theorem
    • MASSEY, W. A. and WHITT, W. (1993a). A probabilistic generalization of Taylor's theorem. Statist. Probab. Lett. 16 51-54.
    • (1993) Statist. Probab. Lett. , vol.16 , pp. 51-54
    • Massey, W.A.1    Whitt, W.2
  • 17
    • 21144482469 scopus 로고
    • Networks of infinite server queues with nonstationary Poisson input
    • MASSEY, W. A. and WHITT, W. (1993b). Networks of infinite server queues with nonstationary Poisson input. Queueing Systems 13 183-250.
    • (1993) Queueing Systems , vol.13 , pp. 183-250
    • Massey, W.A.1    Whitt, W.2
  • 18
    • 0000375933 scopus 로고
    • Unstable asymptotics for nonstationary queues
    • MASSEY, W. A. and WHITT, W. (1994a). Unstable asymptotics for nonstationary queues. Math. Oper. Res. 19 267-291.
    • (1994) Math. Oper. Res. , vol.19 , pp. 267-291
    • Massey, W.A.1    Whitt, W.2
  • 19
    • 0009160012 scopus 로고
    • An analysis of the modified-offered-load approximation for the nonstationary Erlang loss model
    • MASSEY, W. A. and WHITT, W. (1994b). An analysis of the modified-offered-load approximation for the nonstationary Erlang loss model. Ann. Appl. Probab. 4 1145-1160.
    • (1994) Ann. Appl. Probab. , vol.4 , pp. 1145-1160
    • Massey, W.A.1    Whitt, W.2
  • 20
    • 0031486854 scopus 로고    scopus 로고
    • Peak congestion in multi-server service systems with slowly varying arrival rates
    • MASSEY, W. A. and WHITT, W. (1997). Peak congestion in multi-server service systems with slowly varying arrival rates. Queueing Systems 25 157-172.
    • (1997) Queueing Systems , vol.25 , pp. 157-172
    • Massey, W.A.1    Whitt, W.2
  • 21
    • 0009280838 scopus 로고
    • Queues with time-dependent arrival rates I, II and III
    • NEWELL, G. F. (1968). Queues with time-dependent arrival rates I, II and III. J. Appl. Probab. 5 436-451 and 579-606.
    • (1968) J. Appl. Probab. , vol.5 , pp. 436-451
    • Newell, G.F.1
  • 23
    • 0001296683 scopus 로고
    • Perturbation theory and finite markov chains
    • SCHWEITZER, P. J. (1968). Perturbation theory and finite Markov chains. J. Appl. Probab. 5 401-413.
    • (1968) J. Appl. Probab. , vol.5 , pp. 401-413
    • Schweitzer, P.J.1
  • 26
    • 0002273686 scopus 로고
    • t/s queues is asymptotically correct as the rates increase
    • t/s queues is asymptotically correct as the rates increase. Management Sci. 37 307-314.
    • (1991) Management Sci. , vol.37 , pp. 307-314
    • Whitt, W.1
  • 27
    • 0000552628 scopus 로고
    • Asymptotic formulas for Markov processes with applications to simulation
    • WHITT, W. (1992). Asymptotic formulas for Markov processes with applications to simulation. Oper. Res. 40 279-291.
    • (1992) Oper. Res. , vol.40 , pp. 279-291
    • Whitt, W.1
  • 28
    • 84904777793 scopus 로고
    • Properties of a system with losses in the case of variable rates
    • ZEIFMAN, A. I. (1989). Properties of a system with losses in the case of variable rates. Automat. Remote Control 1 82-87.
    • (1989) Automat. Remote Control , vol.1 , pp. 82-87
    • Zeifman, A.I.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.