메뉴 건너뛰기




Volumn 79, Issue 2, 1999, Pages 265-286

Sampling at subexponential times, with queueing applications

Author keywords

Busy period; Independent sampling; Laplace's method; Large deviations; Little's law; Markov additive process; Poisson process; Random walk; Regular variation; Subexponential distribution; Vacation model; Weibull distribution

Indexed keywords


EID: 0033074450     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4149(98)00064-7     Document Type: Article
Times cited : (92)

References (38)
  • 1
    • 84958313722 scopus 로고
    • Asymptotics for steady-state tail probabilities in structured Markov queueing models
    • Abate J., Choudhury G.L., Whitt W. Asymptotics for steady-state tail probabilities in structured Markov queueing models. Stochastic Models. 10:1994;99-144.
    • (1994) Stochastic Models , vol.10 , pp. 99-144
    • Abate, J.1    Choudhury, G.L.2    Whitt, W.3
  • 2
    • 0000290477 scopus 로고
    • Exponential approximations for tail probabilities of queues, I: Waiting times
    • Abate J., Choudhury G.L., Whitt W. Exponential approximations for tail probabilities of queues, I: waiting times. Oper. Res. 43:1995;885-901.
    • (1995) Oper. Res. , vol.43 , pp. 885-901
    • Abate, J.1    Choudhury, G.L.2    Whitt, W.3
  • 3
    • 0030234409 scopus 로고    scopus 로고
    • Exponential approximations for tail probabilities of queues, II: Sojourn time and workload
    • Abate J., Choudhury G.L., Whitt W. Exponential approximations for tail probabilities of queues, II: sojourn time and workload. Oper. Res. 44:1996;758-763.
    • (1996) Oper. Res. , vol.44 , pp. 758-763
    • Abate, J.1    Choudhury, G.L.2    Whitt, W.3
  • 4
    • 0031515337 scopus 로고    scopus 로고
    • Asymptotics for M / G / 1 low priority waiting-time tail probabilities
    • Abate J., Whitt W. Asymptotics for M. / G / 1 low priority waiting-time tail probabilities Queueing Systems. 25:1997;173-233.
    • (1997) Queueing Systems , vol.25 , pp. 173-233
    • Abate, J.1    Whitt, W.2
  • 5
    • 0002488519 scopus 로고
    • Equilibrium properties of the M / G / l queue
    • Asmussen S. Equilibrium properties of the M. / G / l queue Z. Wahrscheinlichkeitsth. Verw. Geb. 58:1981;267-281.
    • (1981) Z. Wahrscheinlichkeitsth. Verw. Geb. , vol.58 , pp. 267-281
    • Asmussen, S.1
  • 7
    • 0001979508 scopus 로고
    • Large claims approximations for risk processes in a Markovian environment
    • Asmussen, S., Fl ø e Henriksen, L., Klüppelberg, C., 1994. Large claims approximations for risk processes in a Markovian environment. Stochastic Process. Appl. 54, 29-43.
    • (1994) Stochastic Process. Appl. , vol.54 , pp. 29-43
    • Asmussen, S.1    Fløehenriksen, L.2    Klüppelberg, C.3
  • 8
    • 0002300756 scopus 로고    scopus 로고
    • Ruin probability approximations for Markov-modulated risk processes with heavy tails
    • Asmussen, S., H ø jgaard, B., 1996. Ruin probability approximations for Markov-modulated risk processes with heavy tails. Theory Random Proc. 2, 96-107.
    • (1996) Theory Random Proc. , vol.2 , pp. 96-107
    • Asmussen, S.1    Højgaard, B.2
  • 9
    • 0033140818 scopus 로고    scopus 로고
    • Tail probabilities for non-standard risk and queueing processes with subexponential jumps
    • to appear.
    • Asmussen, S., Schmidli, H., Schmidt, V., 1999. Tail probabilities for non-standard risk and queueing processes with subexponential jumps. Adv. Appl. Probab., 31, to appear.
    • (1999) Adv. Appl. Probab. , vol.31
    • Asmussen, S.1    Schmidli, H.2    Schmidt, V.3
  • 10
    • 0030355399 scopus 로고    scopus 로고
    • Convergence rates for M / G / 1 queues and ruin problems with heavy tails
    • Asmussen S., Teugels J.L. Convergence rates for M. / G / 1 queues and ruin problems with heavy tails J. Appl. Probab. 33:1996;1181-1190.
    • (1996) J. Appl. Probab. , vol.33 , pp. 1181-1190
    • Asmussen, S.1    Teugels, J.L.2
  • 11
    • 84963197855 scopus 로고
    • Large deviation results for time-dependent queue length probabilities
    • Asmussen S., Thorisson H. Large deviation results for time-dependent queue length probabilities. Stochastic Models. 4:1988;99-116.
    • (1988) Stochastic Models , vol.4 , pp. 99-116
    • Asmussen, S.1    Thorisson, H.2
  • 12
    • 0008980968 scopus 로고
    • Asymptotic ruin probabilities when exponential moments do not exist
    • von Bahr, B., 1975. Asymptotic ruin probabilities when exponential moments do not exist. Scand. Actuar. J. 1975, 6-10.
    • (1975) Scand. Actuar. J. , pp. 6-10
    • Von Bahr, B.1
  • 15
    • 0031483143 scopus 로고    scopus 로고
    • Transient laws of non-stationary systems
    • Bertsimas D., Mourtzinou G. Transient laws of non-stationary systems. Queueing Systems. 25:1997;115-155.
    • (1997) Queueing Systems , vol.25 , pp. 115-155
    • Bertsimas, D.1    Mourtzinou, G.2
  • 19
    • 0002944036 scopus 로고
    • Estimates for the probability of ruin with special emphasis on the possibility of large claims
    • Embrechts P., Veraverbeke N. Estimates for the probability of ruin with special emphasis on the possibility of large claims. Insurance Math. Econom. 1:1982;55-72.
    • (1982) Insurance Math. Econom. , vol.1 , pp. 55-72
    • Embrechts, P.1    Veraverbeke, N.2
  • 20
    • 0000172253 scopus 로고
    • Stochastic decomposition in the M / G / 1 queue with general vacations
    • Fuhrmann S.W., Cooper R.B. Stochastic decomposition in the M. / G / 1 queue with general vacations Oper. Res. 32:1985;1368-1373.
    • (1985) Oper. Res. , vol.32 , pp. 1368-1373
    • Fuhrmann, S.W.1    Cooper, R.B.2
  • 21
    • 0001294576 scopus 로고
    • Imbedded Markov chain analysis of a waiting line process in continuous time
    • Gaver, D.P., Jr., 1959. Imbedded Markov chain analysis of a waiting line process in continuous time. Ann. Math. Statist. 30, 698-720.
    • (1959) Ann. Math. Statist. , vol.30 , pp. 698-720
    • Gaver D.P., Jr.1
  • 22
    • 0141770796 scopus 로고
    • Logarithmic asymptotics for steady-state tail probabilities in a single-server queue
    • Glynn, P.W., Whitt, W., 1994. Logarithmic asymptotics for steady-state tail probabilities in a single-server queue. Adv. Appl. Probab. Takacs issue, 131-156.
    • (1994) Adv. Appl. Probab. Takacs Issue , pp. 131-156
    • Glynn, P.W.1    Whitt, W.2
  • 25
    • 0001354247 scopus 로고
    • A relation between stationary queue and waiting time distribution
    • Haji R., Newell G.F. A relation between stationary queue and waiting time distribution. J. Appl. Probab. 8:1971;617-620.
    • (1971) J. Appl. Probab. , vol.8 , pp. 617-620
    • Haji, R.1    Newell, G.F.2
  • 26
    • 0032378453 scopus 로고    scopus 로고
    • Subexponential asymptotics of a Markov-modulated random walk with queueing applications
    • Jelenkovic, P.R., Lazar, A.A., 1998. Subexponential asymptotics of a Markov-modulated random walk with queueing applications. J. Appl. Probab. 35(2), 325-347.
    • (1998) J. Appl. Probab. , vol.35 , Issue.2 , pp. 325-347
    • Jelenkovic, P.R.1    Lazar, A.A.2
  • 28
    • 0025459879 scopus 로고
    • The distributional form of Little's law and the Fuhrmann-Cooper decomposition
    • Keilson J., Servi L. The distributional form of Little's law and the Fuhrmann-Cooper decomposition. Oper. Res. Lett. 9:1990;239-247.
    • (1990) Oper. Res. Lett. , vol.9 , pp. 239-247
    • Keilson, J.1    Servi, L.2
  • 29
    • 0001001934 scopus 로고
    • Subexponential distributions and integrated tails
    • Klüppelberg C. Subexponential distributions and integrated tails. J. Appl. Probab. 25:1988;132-141.
    • (1988) J. Appl. Probab. , vol.25 , pp. 132-141
    • Klüppelberg, C.1
  • 31
    • 0001499828 scopus 로고
    • On the asymptotic behaviour of the distributions of the busy period and service time in M/G/1
    • de Meyer, A., Teugels, J.L.T., 1980. On the asymptotic behaviour of the distributions of the busy period and service time in M/G/1. J. Appl. Probab. 17, 802-813.
    • (1980) J. Appl. Probab. , vol.17 , pp. 802-813
    • De Meyer, A.1    Teugels, J.L.T.2
  • 32
    • 0000710972 scopus 로고
    • The caudal characteristic curve of queues
    • Neuts M.F. The caudal characteristic curve of queues. Adv. Appl. Probab. 18:1986;221-254.
    • (1986) Adv. Appl. Probab. , vol.18 , pp. 221-254
    • Neuts, M.F.1
  • 33
    • 0016556936 scopus 로고
    • On the tails of waiting time distributions
    • Pakes A. On the tails of waiting time distributions. J. Appl. Probab. 12:1975;555-564.
    • (1975) J. Appl. Probab. , vol.12 , pp. 555-564
    • Pakes, A.1
  • 34
    • 11244255363 scopus 로고
    • Large deviations analysis of the single server queue
    • Puhalskii A. Large deviations analysis of the single server queue. Queueing Systems. 21:1995;5-66.
    • (1995) Queueing Systems , vol.21 , pp. 5-66
    • Puhalskii, A.1
  • 35
    • 0031287497 scopus 로고    scopus 로고
    • Functional large deviations principles for first-passage-time processes
    • Puhalskii A., Whitt W. Functional large deviations principles for first-passage-time processes. Ann. Appl. Probab. 7:1997;362-381.
    • (1997) Ann. Appl. Probab. , vol.7 , pp. 362-381
    • Puhalskii, A.1    Whitt, W.2
  • 36
    • 0032593260 scopus 로고    scopus 로고
    • Asymptotics of Palm-stationary buffer content distributions in fluid flow queues
    • to appear
    • Rolski, T., Schlegel, S., Schmidt, V., 1999. Asymptotics of Palm-stationary buffer content distributions in fluid flow queues. Adv. Appl. Probab., 31, to appear.
    • (1999) Adv. Appl. Probab. , vol.31
    • Rolski, T.1    Schlegel, S.2    Schmidt, V.3
  • 37
    • 85034161577 scopus 로고    scopus 로고
    • Compound sums and subexponentiality
    • to appear
    • Schmidli, H., 1997. Compound sums and subexponentiality. Bernoulli, to appear.
    • (1997) Bernoulli
    • Schmidli, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.