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Volumn 63, Issue 1, 2009, Pages 3-12

The first Erlang century-and the next

(1)  Kingman, J F C a  

a NONE

Author keywords

History of queueing theory; Martingales; Multi server queues; Poisson arrivals; Teletraffic

Indexed keywords

APPLIED PROBABILITY; MARTINGALES; MULTI-SERVER QUEUE; OPERATIONAL RESEARCH; POISSON ARRIVALS; TELETRAFFIC; UNSOLVED PROBLEMS;

EID: 72249085365     PISSN: 02570130     EISSN: 15729443     Source Type: Journal    
DOI: 10.1007/s11134-009-9147-4     Document Type: Article
Times cited : (47)

References (31)
  • 4
    • 0000168129 scopus 로고
    • Some statistical models related to series of events
    • Cox, D. R.: Some statistical models related to series of events. J. R. Stat. Soc. B 17, 129-164 (1955).
    • (1955) J. R. Stat. Soc. B , vol.17 , pp. 129-164
    • Cox, D.R.1
  • 8
    • 0003525228 scopus 로고    scopus 로고
    • F. P. Kelly, S. Zachary, and I. Ziedins (Eds.), Oxford: Oxford University Press
    • Kelly, F. P., Zachary, S., Ziedins, I. (eds.): Stochastic Networks: Theory and Applications. Oxford University Press, Oxford (1996).
    • (1996) Stochastic Networks: Theory and Applications
  • 9
    • 0000257712 scopus 로고
    • Some problems in the theory of queues
    • discussion 173-185
    • Kendall, D. G.: Some problems in the theory of queues. J. R. Stat. Soc. B 13, 151-173 (1951); discussion 173-185.
    • (1951) J. R. Stat. Soc. B , vol.13 , pp. 151-173
    • Kendall, D.G.1
  • 10
    • 0000107197 scopus 로고
    • Stochastic processes occurring in the theory of queues and their analysis by the method of the imbedded Markov chain
    • Kendall, D. G.: Stochastic processes occurring in the theory of queues and their analysis by the method of the imbedded Markov chain. Ann. Math. Stat. 24, 338-354 (1953).
    • (1953) Ann. Math. Stat. , vol.24 , pp. 338-354
    • Kendall, D.G.1
  • 12
    • 84934112704 scopus 로고
    • On queues in which customers are served in random order
    • Kingman, J. F. C.: On queues in which customers are served in random order. Proc. Camb. Philos. Soc. 58, 79-91 (1962).
    • (1962) Proc. Camb. Philos. Soc. , vol.58 , pp. 79-91
    • Kingman, J.F.C.1
  • 13
    • 35349028196 scopus 로고
    • The use of Spitzer's identity in the investigation of the busy period and other quantities in the queue GI/G/1
    • Kingman, J. F. C.: The use of Spitzer's identity in the investigation of the busy period and other quantities in the queue GI/G/1. J. Aust. Math. Soc. 2, 345-356 (1962).
    • (1962) J. Aust. Math. Soc. , vol.2 , pp. 345-356
    • Kingman, J.F.C.1
  • 14
    • 0010081441 scopus 로고
    • On doubly stochastic Poisson processes
    • Kingman, J. F. C.: On doubly stochastic Poisson processes. Proc. Camb. Philos. Soc. 60, 923-930 (1964).
    • (1964) Proc. Camb. Philos. Soc. , vol.60 , pp. 923-930
    • Kingman, J.F.C.1
  • 15
    • 0038562372 scopus 로고
    • On the algebra of queues
    • Kingman, J. F. C.: On the algebra of queues. J. Appl. Probab. 3, 285-326 (1966).
    • (1966) J. Appl. Probab. , vol.3 , pp. 285-326
    • Kingman, J.F.C.1
  • 18
    • 84959640781 scopus 로고
    • The theory of queues with a single server
    • Lindley, D. V.: The theory of queues with a single server. Proc. Camb. Philos. Soc. 48, 277-289 (1952).
    • (1952) Proc. Camb. Philos. Soc. , vol.48 , pp. 277-289
    • Lindley, D.V.1
  • 19
    • 84959708559 scopus 로고
    • The stability of a queue with non-independent interarrival and service times
    • Loynes, R. M.: The stability of a queue with non-independent interarrival and service times. Proc. Camb. Philos. Soc. 58, 497-520 (1962).
    • (1962) Proc. Camb. Philos. Soc. , vol.58 , pp. 497-520
    • Loynes, R.M.1
  • 20
    • 0343361240 scopus 로고
    • Ueber eine Aufgabe derWahrscheinlichkeitstheorie
    • 729-750
    • Pollaczek, F.: Ueber eine Aufgabe derWahrscheinlichkeitstheorie. Math. Z. 32, 64-100 (1930) 729-750.
    • (1930) Math. Z. , vol.32 , pp. 64-100
    • Pollaczek, F.1
  • 21
    • 52549096923 scopus 로고
    • Problèmes stochastiques posés par lephénomène deformation d'une queue d'attente à un guichet et par des phénomènes apparentés
    • Pollaczek, F.: Problèmes stochastiques posés par lephénomène deformation d'une queue d'attente à un guichet et par des phénomènes apparentés. Mém. Sci. Math. 136, 1-122 (1957).
    • (1957) Mém. Sci. Math. , vol.136 , pp. 1-122
    • Pollaczek, F.1
  • 22
    • 84871161545 scopus 로고
    • Théorie analytique des problèmes stochastiques relatifs à un groupe delignes téléphoniques avec dispositif d'attente
    • Pollaczek, F.: Théorie analytique des problèmes stochastiques relatifs à un groupe delignes téléphoniques avec dispositif d'attente. Mém. Sci. Math. 150, 1-114 (1961).
    • (1961) Mém. Sci. Math. , vol.150 , pp. 1-114
    • Pollaczek, F.1
  • 23
    • 4344651731 scopus 로고
    • Concerning an analytic method for the treatment of queueing problems
    • W. L. Smith and W. E. Wilkinson (Eds.), Chapel Hill: University of North Carolina
    • Pollaczek, F.: Concerning an analytic method for the treatment of queueing problems. In: Smith, W. L., Wilkinson, W. E. (eds.) Congestion Theory, pp. 1-42. University of North Carolina, Chapel Hill (1964).
    • (1964) Congestion Theory , pp. 1-42
    • Pollaczek, F.1
  • 24
    • 72249102697 scopus 로고
    • Order statistics of partial sums of mutually independent random variables
    • Pollaczek, F.: Order statistics of partial sums of mutually independent random variables. J. Appl. Probab. 12, 390-395 (1975).
    • (1975) J. Appl. Probab. , vol.12 , pp. 390-395
    • Pollaczek, F.1
  • 25
    • 72249093261 scopus 로고
    • Stochastic network flows: Advances in networks of queues
    • W. L. Smith and W. E. Wilkinson (Eds.), Chapel Hill: University of North Carolina
    • Saaty, T. L.: Stochastic network flows: advances in networks of queues. In: Smith, W. L., Wilkinson, W. E. (eds.) Congestion Theory, pp. 86-107. University of North Carolina, Chapel Hill (1964).
    • (1964) Congestion Theory , pp. 86-107
    • Saaty, T.L.1
  • 27
    • 72249097006 scopus 로고    scopus 로고
    • Networks: Modelling and control
    • Smith, M., Briggs, K., Kelly, F. P. (eds.)
    • Smith, M., Briggs, K., Kelly, F. P. (eds.): Networks: modelling and control. Philos. Trans. R. Soc. A 366, 1875-2092 (2008).
    • (2008) Philos. Trans. R. Soc. A , vol.366 , pp. 1875-2092
  • 28
    • 84959655852 scopus 로고
    • On the distribution of queueing times
    • Smith, W. L.: On the distribution of queueing times. Proc. Camb. Philos. Soc. 49, 449-461 (1953).
    • (1953) Proc. Camb. Philos. Soc. , vol.49 , pp. 449-461
    • Smith, W.L.1
  • 29
    • 72249083426 scopus 로고
    • W. L. Smith and W. E. Wilkinson (Eds.), Chapel Hill: University of North Carolina
    • Smith, W. L., Wilkinson, W. E. (eds.): Congestion Theory. University of North Carolina, Chapel Hill (1964).
    • (1964) Congestion Theory
  • 30
    • 0034339409 scopus 로고    scopus 로고
    • The impact of a heavy-tailed service-time distribution upon the M/GI/s waiting-time distribution
    • Whitt, W.: The impact of a heavy-tailed service-time distribution upon the M/GI/s waiting-time distribution. Queueing Syst. Theory Appl. 36, 71-87 (2000).
    • (2000) Queueing Syst. Theory Appl. , vol.36 , pp. 71-87
    • Whitt, W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.