메뉴 건너뛰기




Volumn 34, Issue 1-4, 2000, Pages 237-268

A sufficient condition and a necessary condition for the diffusion approximations of multiclass queueing networks under priority service disciplines

Author keywords

Diffusion approximation; Fluid approximation; Heavy traffic; Multiclass queueing network; Priority service discipline; Semimartingale reflecting Brownian motion

Indexed keywords

DIFFUSION IN LIQUIDS; QUEUEING THEORY;

EID: 0034343609     PISSN: 02570130     EISSN: 15729443     Source Type: Journal    
DOI: 10.1023/a:1019113204634     Document Type: Article
Times cited : (21)

References (32)
  • 3
    • 0032262849 scopus 로고    scopus 로고
    • State space collapse with application to heavy traffic limits for multiclass queueing networks
    • M. Bramson, State space collapse with application to heavy traffic limits for multiclass queueing networks, Queueing Systems 30 (1998) 89-148.
    • (1998) Queueing Systems , vol.30 , pp. 89-148
    • Bramson, M.1
  • 4
    • 21844491189 scopus 로고
    • Fluid approximations and stability of multiclass queueing networks: Work-conserving disciplines
    • H. Chen, Fluid approximations and stability of multiclass queueing networks: Work-conserving disciplines, Ann. Appl. Probab. 5(3) (1995) 637-665.
    • (1995) Ann. Appl. Probab. , vol.5 , Issue.3 , pp. 637-665
    • Chen, H.1
  • 5
    • 85041120433 scopus 로고    scopus 로고
    • A sufficient condition for the positive recurrence of a semimartingale reflecting Brownian motion in an orthant
    • H. Chen, A sufficient condition for the positive recurrence of a semimartingale reflecting Brownian motion in an orthant, Ann. Appl. Probab. 6(3) (1996) 758-765.
    • (1996) Ann. Appl. Probab. , vol.6 , Issue.3 , pp. 758-765
    • Chen, H.1
  • 6
    • 0001736003 scopus 로고
    • Hierarchical modelling of stochastic networks, part II: Strong approximations
    • ed. D.D. Yao Springer, Berlin
    • H. Chen and A Mandelbaum, Hierarchical modelling of stochastic networks, Part II: Strong approximations, in: Stochastic Modelling and Analysis of Manufacturing Systems, ed. D.D. Yao (Springer, Berlin, 1994) pp. 107-131.
    • (1994) Stochastic Modelling and Analysis of Manufacturing Systems , pp. 107-131
    • Chen, H.1    Mandelbaum, A.2
  • 8
    • 0040750211 scopus 로고    scopus 로고
    • Diffusion approximations for reentrant lines with a first-buffer-first-served priority discipline
    • H. Chen and H. Zhang, Diffusion approximations for reentrant lines with a first-buffer-first-served priority discipline, Queueing Systems 23 (1996) 177-195.
    • (1996) Queueing Systems , vol.23 , pp. 177-195
    • Chen, H.1    Zhang, H.2
  • 9
    • 0032178317 scopus 로고    scopus 로고
    • Diffusion approximations for Kumar-Seidman network under a priority service discipline
    • H. Chen and H. Zhang, Diffusion approximations for Kumar-Seidman network under a priority service discipline, Oper. Res. Lett. 23 (1998) 171-181.
    • (1998) Oper. Res. Lett. , vol.23 , pp. 171-181
    • Chen, H.1    Zhang, H.2
  • 10
    • 84872984083 scopus 로고    scopus 로고
    • Stability of multiclass queueing networks under priority service disciplines
    • to appear
    • H. Chen and H. Zhang, Stability of multiclass queueing networks under priority service disciplines, Oper. Res. (1998) (to appear).
    • (1998) Oper. Res.
    • Chen, H.1    Zhang, H.2
  • 11
    • 0000683318 scopus 로고
    • A multiclass station with Markovian feedback in heavy traffic
    • J. Dai and T.G. Kurtz, A multiclass station with Markovian feedback in heavy traffic, Math. Oper. Res. 20 (1995) 721-742.
    • (1995) Math. Oper. Res. , vol.20 , pp. 721-742
    • Dai, J.1    Kurtz, T.G.2
  • 12
    • 0002973242 scopus 로고
    • On the convergence of multiclass queueing networks in heavy traffic
    • J. Dai and V. Nguyen, On the convergence of multiclass queueing networks in heavy traffic, Ann. Appl. Probab. 4 (1994) 26-42.
    • (1994) Ann. Appl. Probab. , vol.4 , pp. 26-42
    • Dai, J.1    Nguyen, V.2
  • 13
    • 0003124563 scopus 로고
    • Nonexistence of Brownian models of certain multiclass queueing networks
    • J. Dai and Y. Wang, Nonexistence of Brownian models of certain multiclass queueing networks, Queueing Systems 13 (1993) 41-46.
    • (1993) Queueing Systems , vol.13 , pp. 41-46
    • Dai, J.1    Wang, Y.2
  • 14
    • 0031514230 scopus 로고    scopus 로고
    • A multiclass network with non-linear, non-convex, non-monotonic stability conditions
    • V. Dumas, A multiclass network with non-linear, non-convex, non-monotonic stability conditions, Queueing Systems 25 (1997) 1-43.
    • (1997) Queueing Systems , vol.25 , pp. 1-43
    • Dumas, V.1
  • 17
    • 0000044386 scopus 로고
    • Brownian models of queueing networks with heterogeneous customer populations
    • IMA, eds. W. Fleming and P.L. Lions Springer, Berlin
    • J.M. Harrison, Brownian models of queueing networks with heterogeneous customer populations, in: Stochastic Differential Systems, Stochastic Control Theory and Applications, IMA, Vol. 10, eds. W. Fleming and P.L. Lions (Springer, Berlin, 1988) pp. 147-186.
    • (1988) Stochastic Differential Systems, Stochastic Control Theory and Applications , vol.10 , pp. 147-186
    • Harrison, J.M.1
  • 18
    • 0001828819 scopus 로고
    • The QNET method for two-moment analysis of open queueing networks
    • J.M. Harrison and V. Nguyen, The QNET method for two-moment analysis of open queueing networks, Queueing Systems 6 (1990) 1-32.
    • (1990) Queueing Systems , vol.6 , pp. 1-32
    • Harrison, J.M.1    Nguyen, V.2
  • 19
    • 21144478130 scopus 로고
    • Brownian models of multiclass queueing networks: Current status and open problem
    • J.M. Harrison and V. Nguyen, Brownian models of multiclass queueing networks: Current status and open problem, Queueing Systems 13 (1993) 5-40.
    • (1993) Queueing Systems , vol.13 , pp. 5-40
    • Harrison, J.M.1    Nguyen, V.2
  • 20
    • 0000585232 scopus 로고
    • Reflected Brownian motion on an orthant
    • J.M. Harrison and M.I. Reiman, Reflected Brownian motion on an orthant, Ann. Probab. 9 (1981) 302-308.
    • (1981) Ann. Probab. , vol.9 , pp. 302-308
    • Harrison, J.M.1    Reiman, M.I.2
  • 21
    • 0000505189 scopus 로고
    • Network of queues - A survey of weak convergence results
    • A.J. Lemoine, Network of queues - A survey of weak convergence results, Managm. Sci. 24 (1978) 1175-1193.
    • (1978) Managm. Sci. , vol.24 , pp. 1175-1193
    • Lemoine, A.J.1
  • 22
    • 0002816593 scopus 로고
    • A heavy traffic limit theorem for networks of queues with multiple customer types
    • W.P. Peterson, A heavy traffic limit theorem for networks of queues with multiple customer types, Math. Oper. Res. 16 (1991) 90-118.
    • (1991) Math. Oper. Res. , vol.16 , pp. 90-118
    • Peterson, W.P.1
  • 24
    • 0000279589 scopus 로고
    • A multiclass feedback queue in heavy traffic
    • M.I. Reiman, A multiclass feedback queue in heavy traffic, Adv. in Appl. Probab. 20 (1988) 179-207.
    • (1988) Adv. in Appl. Probab. , vol.20 , pp. 179-207
    • Reiman, M.I.1
  • 25
    • 0002800360 scopus 로고
    • A boundary property of semimartingale reflecting Brownian motions
    • M.I. Reiman and R.J. Williams, A boundary property of semimartingale reflecting Brownian motions, Probab. Theory Related Fields 77 (1988) 87-97, and 80 (1989) 633.
    • (1988) Probab. Theory Related Fields , vol.77 , pp. 87-97
    • Reiman, M.I.1    Williams, R.J.2
  • 26
    • 0002800360 scopus 로고
    • M.I. Reiman and R.J. Williams, A boundary property of semimartingale reflecting Brownian motions, Probab. Theory Related Fields 77 (1988) 87-97, and 80 (1989) 633.
    • (1989) Probab. Theory Related Fields , vol.80 , pp. 633
  • 27
    • 0001380311 scopus 로고
    • Limit theorems for stochastic processes
    • A.V. Skorohod, Limit theorems for stochastic processes, Theory Probab. Appl. 1 (1956) 261-290.
    • (1956) Theory Probab. Appl. , vol.1 , pp. 261-290
    • Skorohod, A.V.1
  • 28
    • 21144473462 scopus 로고
    • Existence and uniqueness of semimartingale reflecting Brownian motions in an orthant
    • L.M. Taylor and R.J. Williams, Existence and uniqueness of semimartingale reflecting Brownian motions in an orthant, Probab. Theory Related Fields 96 (1993) 283-317.
    • (1993) Probab. Theory Related Fields , vol.96 , pp. 283-317
    • Taylor, L.M.1    Williams, R.J.2
  • 29
    • 0000729824 scopus 로고
    • Heavy traffic theorems for queues: A survey
    • ed. A.B. Clarke Springer, Berlin
    • W. Whitt, Heavy traffic theorems for queues: A survey, in: Mathematical Methods in Queueing Theory, ed. A.B. Clarke (Springer, Berlin, 1974) pp. 307-350.
    • (1974) Mathematical Methods in Queueing Theory , pp. 307-350
    • Whitt, W.1
  • 30
    • 0018977055 scopus 로고
    • Some useful functions for functional limit theorems
    • W. Whitt, Some useful functions for functional limit theorems, Math. Oper. Res. 5 (1980) 67-85.
    • (1980) Math. Oper. Res. , vol.5 , pp. 67-85
    • Whitt, W.1
  • 31
    • 0032260551 scopus 로고    scopus 로고
    • An invariance principle for semimartingale reflecting Brownian motions in an orthant
    • R.J. Williams, An invariance principle for semimartingale reflecting Brownian motions in an orthant, Queueing Systems 30 (1998) 5-26.
    • (1998) Queueing Systems , vol.30 , pp. 5-26
    • Williams, R.J.1
  • 32
    • 0032262848 scopus 로고    scopus 로고
    • Diffusion approximations for open multiclass queueing networks: Sufficient conditions involving state space collapse
    • R.J. Williams, Diffusion approximations for open multiclass queueing networks: Sufficient conditions involving state space collapse, Queueing Systems 30 (1998) 27-88.
    • (1998) Queueing Systems , vol.30 , pp. 27-88
    • Williams, R.J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.