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Volumn 25, Issue 1-4, 1997, Pages 173-233

Asymptotics for M/G/1 low-priority waiting-time tail probabilities

Author keywords

Algebraic singularities; Asymptotic expansions; Asymptotics; Laplace transforms; Low priority waiting time; M G 1 queue; Non exponential asymptotics; Priority queues; Tail probabilities

Indexed keywords

EXPANSION; LAPLACE TRANSFORMS; QUEUEING THEORY;

EID: 0031515337     PISSN: 02570130     EISSN: 15729443     Source Type: Journal    
DOI: 10.1023/a:1019104402024     Document Type: Article
Times cited : (122)

References (54)
  • 1
    • 0001191115 scopus 로고
    • Transient behavior of the M/M/1 queue via Laplace transforms
    • J. Abate and W. Whitt, Transient behavior of the M/M/1 queue via Laplace transforms, Adv. Appl. Probab. 20 (1988) 145-178.
    • (1988) Adv. Appl. Probab. , vol.20 , pp. 145-178
    • Abate, J.1    Whitt, W.2
  • 2
    • 0012748041 scopus 로고
    • Simple spectral representations for the M/M/1 queue
    • J. Abate and W. Whitt, Simple spectral representations for the M/M/1 queue, Queueing Systems 3 (1988) 321-346.
    • (1988) Queueing Systems , vol.3 , pp. 321-346
    • Abate, J.1    Whitt, W.2
  • 3
    • 0043259291 scopus 로고
    • Approximations for the M/M/1 busy-period distribution
    • eds. O.J. Boxma and R. Syski North-Holland, Amsterdam
    • J. Abate and W. Whitt, Approximations for the M/M/1 busy-period distribution, in: Queueing Theory and Its Applications - Liber Amicorium for J.W. Cohen, eds. O.J. Boxma and R. Syski (North-Holland, Amsterdam, 1988) pp. 149-191.
    • (1988) Queueing Theory and Its Applications - Liber Amicorium for J.W. Cohen , pp. 149-191
    • Abate, J.1    Whitt, W.2
  • 4
    • 27544447048 scopus 로고
    • The Fourier-series method for inverting transforms of probability distributions
    • J. Abate and W. Whitt, The Fourier-series method for inverting transforms of probability distributions, Queueing Systems 10 (1992) 5-88.
    • (1992) Queueing Systems , vol.10 , pp. 5-88
    • Abate, J.1    Whitt, W.2
  • 5
    • 38249008389 scopus 로고
    • Solving probability transform functional equations for numerical inversion
    • J. Abate and W. Whitt, Solving probability transform functional equations for numerical inversion, Oper. Res. Lett. 12 (1992) 275-281.
    • (1992) Oper. Res. Lett. , vol.12 , pp. 275-281
    • Abate, J.1    Whitt, W.2
  • 6
    • 0028460939 scopus 로고
    • Transient behavior of the M/G/1 workload process
    • J. Abate and W. Whitt, Transient behavior of the M/G/1 workload process, Oper. Res. 42 (1994) 750-764.
    • (1994) Oper. Res. , vol.42 , pp. 750-764
    • Abate, J.1    Whitt, W.2
  • 7
    • 0028442469 scopus 로고
    • A heavy-traffic expansion for the asymptotic decay rates of tail probabilities in multi-channel queues
    • J. Abate and W. Whitt, A heavy-traffic expansion for the asymptotic decay rates of tail probabilities in multi-channel queues, Oper. Res. Lett. 15 (1994) 223-230.
    • (1994) Oper. Res. Lett. , vol.15 , pp. 223-230
    • Abate, J.1    Whitt, W.2
  • 8
    • 84973962386 scopus 로고
    • Limits and approximations for the busy-period distribution in single-server queues
    • J. Abate and W. Whitt, Limits and approximations for the busy-period distribution in single-server queues, Probab. Engrg. Inform. Sci. 9 (1995) 581-602.
    • (1995) Probab. Engrg. Inform. Sci. , vol.9 , pp. 581-602
    • Abate, J.1    Whitt, W.2
  • 9
    • 0002047384 scopus 로고    scopus 로고
    • An operational calculus for probability distributions via Laplace transforms
    • J. Abate and W. Whitt, An operational calculus for probability distributions via Laplace transforms, Adv. Appl. Probab. 28 (1996) 75-113.
    • (1996) Adv. Appl. Probab. , vol.28 , pp. 75-113
    • Abate, J.1    Whitt, W.2
  • 10
    • 84873008680 scopus 로고    scopus 로고
    • Limits and approximations for the M/G/1 LIFO waiting-time distribution
    • to appear
    • J. Abate and W. Whitt, Limits and approximations for the M/G/1 LIFO waiting-time distribution, Oper. Res. Lett., to appear.
    • Oper. Res. Lett.
    • Abate, J.1    Whitt, W.2
  • 11
    • 21344494520 scopus 로고
    • Waiting time tail probabilities in queues with long-tail service-time distributions
    • J. Abate, G.L. Choudhury and W. Whitt, Waiting time tail probabilities in queues with long-tail service-time distributions, Queueing Systems 16 (1994) 311-338.
    • (1994) Queueing Systems , vol.16 , pp. 311-338
    • Abate, J.1    Choudhury, G.L.2    Whitt, W.3
  • 12
    • 0000290477 scopus 로고
    • Exponential approximations for tail probabilities in queues, I: Waiting times
    • J. Abate, G.L. Choudhury and W. Whitt, Exponential approximations for tail probabilities in 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
  • 13
    • 0009454517 scopus 로고
    • Calculating the M/G/1 busy-period density and LIFO waiting-time distribution by direct numerical transform inversion
    • J. Abate, G.L. Choudhury and W. Whitt, Calculating the M/G/1 busy-period density and LIFO waiting-time distribution by direct numerical transform inversion, Oper. Res. Lett. 18 (1995) 113-119.
    • (1995) Oper. Res. Lett. , vol.18 , pp. 113-119
    • Abate, J.1    Choudhury, G.L.2    Whitt, W.3
  • 14
    • 0030234409 scopus 로고    scopus 로고
    • Exponential approximations for tail probabilities in queues, II: Sojourn time and workload
    • J. Abate, G.L. Choudhury and W. Whitt, Exponential approximations for tail probabilities in 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
  • 15
    • 0002652166 scopus 로고    scopus 로고
    • On the Laguerre method for numerically inverting Laplace transforms
    • J. Abate, G.L. Choudhury and W. Whitt, On the Laguerre method for numerically inverting Laplace transforms, INFORMS J. Comput. 8 (1996) 413-427.
    • (1996) INFORMS J. Comput. , vol.8 , pp. 413-427
    • Abate, J.1    Choudhury, G.L.2    Whitt, W.3
  • 16
    • 84872987290 scopus 로고    scopus 로고
    • Numerical inversion of multidimensional Laplace transforms by the Laguerre method
    • to appear
    • J. Abate, G.L. Choudhury and W. Whitt, Numerical inversion of multidimensional Laplace transforms by the Laguerre method, Perf. Eval., to appear.
    • Perf. Eval.
    • Abate, J.1    Choudhury, G.L.2    Whitt, W.3
  • 17
    • 0040953853 scopus 로고
    • Decompositions of the M/M/1 transition function
    • J. Abate, M. Kijima and W. Whitt, Decompositions of the M/M/1 transition function, Queueing Systems 9 (1993) 323-336.
    • (1993) Queueing Systems , vol.9 , pp. 323-336
    • Abate, J.1    Kijima, M.2    Whitt, W.3
  • 19
    • 84872983225 scopus 로고    scopus 로고
    • Convergence rates for M/G/1 queues and ruin problems with heavy tails
    • to appear
    • S. Asmussen and J.L. Teugels, Convergence rates for M/G/1 queues and ruin problems with heavy tails, Adv. Appl. Probab., to appear.
    • Adv. Appl. Probab.
    • Asmussen, S.1    Teugels, J.L.2
  • 24
    • 0029357705 scopus 로고
    • Effective bandwidths in high-speed digital networks
    • C.S. Chang and J.A. Thomas, Effective bandwidths in high-speed digital networks, IEEE J. Sel. Areas Commun. 13 (1995) 1091-1100.
    • (1995) IEEE J. Sel. Areas Commun. , vol.13 , pp. 1091-1100
    • Chang, C.S.1    Thomas, J.A.2
  • 25
    • 0000708942 scopus 로고
    • A theorem on sums of independent positive random variables and its applications to branching processes
    • V.P. Chistyakov, A theorem on sums of independent positive random variables and its applications to branching processes, Theory Probab. Appl. 9 (1964) 640-648.
    • (1964) Theory Probab. Appl. , vol.9 , pp. 640-648
    • Chistyakov, V.P.1
  • 26
    • 0030171710 scopus 로고    scopus 로고
    • Computing distributions and moments in polling models by numerical transform inversion
    • G.L. Choudhury and W. Whitt, Computing distributions and moments in polling models by numerical transform inversion, Perf. Eval. 25 (1996) 267-292.
    • (1996) Perf. Eval. , vol.25 , pp. 267-292
    • Choudhury, G.L.1    Whitt, W.2
  • 27
    • 0001622198 scopus 로고
    • Multidimensional transform inversion with applications to the transient M/G/1 queue
    • G.L. Choudhury, D.M. Lucantoni and W. Whitt, Multidimensional transform inversion with applications to the transient M/G/1 queue, Ann. Appl. Probab. 4 (1994) 719-740.
    • (1994) Ann. Appl. Probab. , vol.4 , pp. 719-740
    • Choudhury, G.L.1    Lucantoni, D.M.2    Whitt, W.3
  • 28
    • 51249187686 scopus 로고
    • Functions of probability measures
    • J. Chover, P. Ney and S. Wainger, Functions of probability measures, J. Analyse Math. 26 (1973) 255-302.
    • (1973) J. Analyse Math. , vol.26 , pp. 255-302
    • Chover, J.1    Ney, P.2    Wainger, S.3
  • 29
    • 0001432293 scopus 로고
    • Degeneracy properties of subcritical branching process
    • J. Chover, P. Ney and S. Wainger, Degeneracy properties of subcritical branching process, Ann. Probab. 1 (1973) 663-673.
    • (1973) Ann. Probab. , vol.1 , pp. 663-673
    • Chover, J.1    Ney, P.2    Wainger, S.3
  • 32
    • 0001499828 scopus 로고
    • On the asymptotic behavior of the distribution of the busy period and the service time in M/G/1
    • A. De Meyer and J.L. Teugels, On the asymptotic behavior of the distribution of the busy period and the service time in M/G/1, Adv. Appl. Probab. 17 (1980) 802-813.
    • (1980) Adv. Appl. Probab. , vol.17 , pp. 802-813
    • De Meyer, A.1    Teugels, J.L.2
  • 33
    • 0029357488 scopus 로고
    • Resource management in wide-area ATM networks using effective bandwidths
    • G. de Veciana, G. Kesidis and J. Walrand, Resource management in wide-area ATM networks using effective bandwidths, IEEE J. Sel. Areas Commun. 13 (1995) 1081-1090.
    • (1995) IEEE J. Sel. Areas Commun. , vol.13 , pp. 1081-1090
    • De Veciana, G.1    Kesidis, G.2    Walrand, J.3
  • 35
    • 84872996330 scopus 로고    scopus 로고
    • Exponents for the tails of distributions in some polling models
    • to appear
    • N. Duffield, Exponents for the tails of distributions in some polling models, Queueing Systems, to appear.
    • Queueing Systems
    • Duffield, N.1
  • 39
    • 84873015390 scopus 로고    scopus 로고
    • The waiting time distribution for random order of service
    • to appear
    • L. Flatto, The waiting time distribution for random order of service, Ann. Appl. Probab., to appear.
    • Ann. Appl. Probab.
    • Flatto, L.1
  • 40
    • 0002542536 scopus 로고
    • A waiting line with interrupted service, including priorities
    • D.P. Gaver, Jr., A waiting line with interrupted service, including priorities, J. Roy. Statist. Soc. Ser. B 25 (1962) 73-90.
    • (1962) J. Roy. Statist. Soc. Ser. B , vol.25 , pp. 73-90
    • Gaver Jr., D.P.1
  • 42
    • 0007197349 scopus 로고
    • A limit theorem for priority queues in heavy traffic
    • J.M. Harrison, A limit theorem for priority queues in heavy traffic, J. Appl. Probab. 10 (1973) 907-912.
    • (1973) J. Appl. Probab. , vol.10 , pp. 907-912
    • Harrison, J.M.1
  • 44
    • 0000497195 scopus 로고
    • Parallel and tandem fluid networks with dependent Lévy inputs
    • O. Kella, Parallel and tandem fluid networks with dependent Lévy inputs, Ann. Appl. Probab. 3 (1993) 682-695.
    • (1993) Ann. Appl. Probab. , vol.3 , pp. 682-695
    • Kella, O.1
  • 45
    • 0019611975 scopus 로고
    • Computation of steady-state probabilities for M/M/1 priority queues
    • D.R. Miller, Computation of steady-state probabilities for M/M/1 priority queues, Oper. Res. 29 (1981) 945-958.
    • (1981) Oper. Res. , vol.29 , pp. 945-958
    • Miller, D.R.1
  • 47
    • 0016556936 scopus 로고
    • On the tails of waiting-time distributions
    • A.G. Pakes, 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.G.1
  • 50
    • 84963060324 scopus 로고
    • The asymptotic expansion of a function whose operational equivalent is known
    • W.G.L. Sutton, The asymptotic expansion of a function whose operational equivalent is known, J. London Math. Soc. 9 (1934) 131-137.
    • (1934) J. London Math. Soc. , vol.9 , pp. 131-137
    • Sutton, W.G.L.1
  • 52
    • 84873018012 scopus 로고
    • A particular two-priority queue
    • A. Washburn, A particular two-priority queue, Oper. Res. 18 (1970) 1760-1764.
    • (1970) Oper. Res. , vol.18 , pp. 1760-1764
    • Washburn, A.1
  • 53
    • 0002612004 scopus 로고
    • Weak convergence theorems for priority queues: Preemptive-resume discipline
    • W. Whitt, Weak convergence theorems for priority queues: preemptive-resume discipline, J. Appl. Probab. 8 (1971) 74-94.
    • (1971) J. Appl. Probab. , vol.8 , pp. 74-94
    • Whitt, W.1


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