메뉴 건너뛰기




Volumn 17, Issue 3, 2001, Pages 341-368

A linear programming approach to the steady-state analysis of reflected Brownian motion

(1)  Schwerer, Elizabeth a  

a NONE   (United States)

Author keywords

Linear programming; Queueing networks; Reflected Brownian motion; Steady state analysis

Indexed keywords


EID: 0013530452     PISSN: 08820287     EISSN: None     Source Type: Journal    
DOI: 10.1081/stm-100002277     Document Type: Article
Times cited : (10)

References (47)
  • 1
    • 0002154450 scopus 로고
    • Optimization of multiclass queueing networks: Polyhedral and nonlinear characterizations of achievable performance
    • Bertsimas, D.; Paschalidis, I. C.; Tsitsiklis, J. N. Optimization of multiclass queueing networks: Polyhedral and nonlinear characterizations of achievable performance. Annals of Applied Probability. 1994, 4, 43-75.
    • (1994) Annals of Applied Probability , vol.4 , pp. 43-75
    • Bertsimas, D.1    Paschalidis, I.C.2    Tsitsiklis, J.N.3
  • 2
    • 0028494016 scopus 로고
    • Performance bounds for queueing networks and scheduling policies
    • Kumar, S.; Kumar, P. R. Performance bounds for queueing networks and scheduling policies. IEEE Transactions on Automatic Control. 1994, 39, 1600-1611.
    • (1994) IEEE Transactions on Automatic Control , vol.39 , pp. 1600-1611
    • Kumar, S.1    Kumar, P.R.2
  • 6
    • 0000005045 scopus 로고
    • On the distribution of multidimensional reflected Brownian motion
    • Harrison, J. M.; Reiman, M. I. On the distribution of multidimensional reflected Brownian motion. SIAM Journal of Applied Mathematics. 1981, 41, 345-361.
    • (1981) SIAM Journal of Applied Mathematics , vol.41 , pp. 345-361
    • Harrison, J.M.1    Reiman, M.I.2
  • 7
    • 0002500631 scopus 로고
    • Brownian models of open queueing networks with homogeneous customer populations
    • Harrison, J. M.; Williams, R. J. Brownian models of open queueing networks with homogeneous customer populations. Stochastics. 1987, 22, 77-115.
    • (1987) Stochastics , vol.22 , pp. 77-115
    • Harrison, J.M.1    Williams, R.J.2
  • 8
    • 0038874317 scopus 로고
    • Brownian models of closed queueing networks with homogeneous customer populations
    • Harrison, J. M.; Williams, R. J.; Chen, H. Brownian models of closed queueing networks with homogeneous customer populations. Stochastics. 1990, 29, 37-74.
    • (1990) Stochastics , vol.29 , pp. 37-74
    • Harrison, J.M.1    Williams, R.J.2    Chen, H.3
  • 10
    • 33747385691 scopus 로고
    • Characterizing networks whose 'natural' Brownian approximations are product-form: Some illustrative examples
    • Stanford University
    • Afèche, P.; Harrison, J. M.; Tsay, A. Characterizing networks whose 'natural' Brownian approximations are product-form: Some illustrative examples. Presented at the Brownian Mini-conference, Stanford University. 1992.
    • (1992) Brownian Mini-conference
    • Afèche, P.1    Harrison, J.M.2    Tsay, A.3
  • 11
    • 0011813264 scopus 로고
    • The QNET method for two-moment analysis of closed queueing networks
    • Dai, J. G.; Harrison, J. M. The QNET method for two-moment analysis of closed queueing networks. Annals of Applied Probability. 1993, 3, 968-1012.
    • (1993) Annals of Applied Probability , vol.3 , pp. 968-1012
    • Dai, J.G.1    Harrison, J.M.2
  • 12
    • 0000585232 scopus 로고
    • The diffusion approximation for tandem queues in heavy traffic
    • Harrison, J. M. The diffusion approximation for tandem queues in heavy traffic. Advances in Applied Probability. 1978, 9, 302-308.
    • (1978) Advances in Applied Probability , vol.9 , pp. 302-308
    • Harrison, J.M.1
  • 13
    • 0001521395 scopus 로고
    • The stationary distribution of reflected Brownian motion in a planar region
    • Harrison, J. M.; Landau, H. J.; Shepp, L. A. The stationary distribution of reflected Brownian motion in a planar region. The Annals of Probability. 1985, 13, 744-757.
    • (1985) The Annals of Probability , vol.13 , pp. 744-757
    • Harrison, J.M.1    Landau, H.J.2    Shepp, L.A.3
  • 15
    • 21144478130 scopus 로고
    • Brownian models of multiclass queueing networks: Current status and open problems
    • queueing networks
    • Harrison, J. M.; Nguyen, V. Brownian models of multiclass queueing networks: Current status and open problems. Queueing Systems: Theory and Applications, special issue on queueing networks. 1993, 13, 5-40.
    • (1993) Queueing Systems: Theory and Applications , vol.13 , Issue.SPEC. ISSUE , pp. 5-40
    • Harrison, J.M.1    Nguyen, V.2
  • 17
    • 0001086728 scopus 로고
    • Multidimensional reflected Brownian motions having exponential stationary distributions
    • Harrison, J. M.; Williams, R. J. Multidimensional reflected Brownian motions having exponential stationary distributions. The Annals of Probability. 1987, 15, 115-137.
    • (1987) The Annals of Probability , vol.15 , pp. 115-137
    • Harrison, J.M.1    Williams, R.J.2
  • 18
    • 0039111513 scopus 로고
    • Brownian models of closed queueing networks: Explicit solutions for balanced three-stations systems
    • Schwerer, E.; Van Mieghem, J. A. Brownian models of closed queueing networks: Explicit solutions for balanced three-stations systems. Annals of applied Probability. 1994, 4, 448-477.
    • (1994) Annals of Applied Probability , vol.4 , pp. 448-477
    • Schwerer, E.1    Van Mieghem, J.A.2
  • 19
    • 0022661928 scopus 로고
    • Conformal mapping solutiion of Laplace's equation on a polygon with oblique derivative boundary conditions
    • Trefethen, L. N.; Williams, R. J. Conformal mapping solutiion of Laplace's equation on a polygon with oblique derivative boundary conditions. Journal of Computational Applied Mathematics. 1986, 14, 227-249.
    • (1986) Journal of Computational Applied Mathematics , vol.14 , pp. 227-249
    • Trefethen, L.N.1    Williams, R.J.2
  • 21
    • 0003064374 scopus 로고
    • Steady-state analysis of RBM in a rectangle: Numerical methods and a queueing application
    • Dai, J. G.; Harrison, J. M. Steady-state analysis of RBM in a rectangle: Numerical methods and a queueing application. Annals of Applied Probability. 1991, 1, 16-35.
    • (1991) Annals of Applied Probability , vol.1 , pp. 16-35
    • Dai, J.G.1    Harrison, J.M.2
  • 22
    • 0002933073 scopus 로고
    • Reflected Brownian motion in an orthant: Numerical methods for steady-state analysis
    • Dai, J. G.; Harrison, J. M. Reflected Brownian motion in an orthant: Numerical methods for steady-state analysis. Annals of Applied Probability. 1992, 2, 65-86.
    • (1992) Annals of Applied Probability , vol.2 , pp. 65-86
    • Dai, J.G.1    Harrison, J.M.2
  • 23
    • 0027927313 scopus 로고
    • Sequential bottleneck decomposition: An approximation method for generalized Jackson networks
    • Dai, J. G.; Nguyen, V.; Reiman, M. I. Sequential bottleneck decomposition: An approximation method for generalized Jackson networks. Operations Research. 1994, 42, 119-136.
    • (1994) Operations Research , vol.42 , pp. 119-136
    • Dai, J.G.1    Nguyen, V.2    Reiman, M.I.3
  • 25
    • 0001340189 scopus 로고
    • Stability of Markovian processes I: Criteria for discrete-time chains
    • Meyn, S. P.; Tweedie, R. L. Stability of Markovian processes I: Criteria for discrete-time chains. Advances in Applied Probability. 1992, 24, 542-574.
    • (1992) Advances in Applied Probability , vol.24 , pp. 542-574
    • Meyn, S.P.1    Tweedie, R.L.2
  • 26
    • 0000684659 scopus 로고
    • Stability of Markovian processes II: Continuous time processes and sampled chains
    • Meyn, S. P.; Tweedie, R. L. Stability of Markovian processes II: Continuous time processes and sampled chains. Advances in Applied Probability. 1993, 25, 487-517.
    • (1993) Advances in Applied Probability , vol.25 , pp. 487-517
    • Meyn, S.P.1    Tweedie, R.L.2
  • 27
    • 0001340188 scopus 로고
    • Stability of Markovian processes III: Foster-Lyapunov criteria for continuous-time processes
    • Meyn, S. P.; Tweedie, R. L. Stability of Markovian processes III: Foster-Lyapunov criteria for continuous-time processes. Advances in Applied Probability. 1993, 25, 518-548.
    • (1993) Advances in Applied Probability , vol.25 , pp. 518-548
    • Meyn, S.P.1    Tweedie, R.L.2
  • 28
    • 0001521124 scopus 로고
    • Lyapunov functions for semimartingale reflecting Brownian motions
    • Dupuis, P.; Williams, R. J. Lyapunov functions for semimartingale reflecting Brownian motions. The Annals of Probability. 1994, 22, 680-702.
    • (1994) The Annals of Probability , vol.22 , pp. 680-702
    • Dupuis, P.1    Williams, R.J.2
  • 30
    • 0003301123 scopus 로고
    • The Problem of Moments
    • The American Mathematical Society: Baltimore, MD
    • Shohat, J. A.; Tamarkin, J. D. The Problem of Moments, Mathematical Surveys, No. 1, The American Mathematical Society: Baltimore, MD, 1943.
    • (1943) Mathematical Surveys , Issue.1
    • Shohat, J.A.1    Tamarkin, J.D.2
  • 31
    • 0024073120 scopus 로고
    • Characterization and optimization of achievable performance in general queueing systems
    • Federgruen, A.; Groenevelt, H. Characterization and optimization of achievable performance in general queueing systems. Operations Research. 1988, 36, 733-741.
    • (1988) Operations Research , vol.36 , pp. 733-741
    • Federgruen, A.1    Groenevelt, H.2
  • 32
    • 0026861383 scopus 로고
    • Multiclass queueing systems: Polymatroidal structure and optimal scheduling control
    • Shanthikumar, J. G.; Yao, D. D. Multiclass queueing systems: Polymatroidal structure and optimal scheduling control. Operations Research, Supplement. 1992, 40, S293-S299.
    • (1992) Operations Research, Supplement , vol.40
    • Shanthikumar, J.G.1    Yao, D.D.2
  • 35
    • 0002611604 scopus 로고
    • Existence and uniqueness of semimartingale reflecting Brownian motions in convex polyhedrons
    • SIAM translation journal of the same name
    • Dai, J. G.; Williams, R. J. Existence and uniqueness of semimartingale reflecting Brownian motions in convex polyhedrons (in Russian). Theory of Probability and its Applications. 1995, 40, 3-53, to appear in the SIAM translation journal of the same name.
    • (1995) Theory of Probability and Its Applications , vol.40 , pp. 3-53
    • Dai, J.G.1    Williams, R.J.2
  • 36
    • 0002800360 scopus 로고
    • A boundary property of semimartingale reflecting Brownian motions
    • Reiman, M. I.; Williams, R. J. A boundary property of semimartingale reflecting Brownian motions. Probability Theory and Related Fields. 1988, 77, 87-97
    • (1988) Probability Theory and Related Fields , vol.77 , pp. 87-97
    • Reiman, M.I.1    Williams, R.J.2
  • 38
    • 21144473462 scopus 로고
    • Existence and uniqueness of semimartingale reflecting Brownian motions in an orthant
    • Taylor, L. M.; Williams, R. J. Existence and uniqueness of semimartingale reflecting Brownian motions in an orthant. Probability Theory and Related Fields. 1993, 96, 283-317.
    • (1993) Probability Theory and Related Fields , vol.96 , pp. 283-317
    • Taylor, L.M.1    Williams, R.J.2
  • 39
    • 0000585232 scopus 로고
    • Reflected Brownian motion on an orthant
    • Harrison, J. M.; Reiman, M. I. Reflected Brownian motion on an orthant. Annals of Probability. 1981, 9, 302-308.
    • (1981) Annals of Probability , vol.9 , pp. 302-308
    • Harrison, J.M.1    Reiman, M.I.2
  • 43
    • 0005423140 scopus 로고
    • Suites complètement définies positives, majoration de Schur et le problème des moments de Stieltjes en dimension k
    • Berg, C.; Christensen, J. P. R. Suites complètement définies positives, majoration de Schur et le problème des moments de Stieltjes en dimension k. Comptes Rendues de l'Académie Scientifique de Paris. 1983, 297, 45-48.
    • (1983) Comptes Rendues de l'Académie Scientifique de Paris , vol.297 , pp. 45-48
    • Berg, C.1    Christensen, J.P.R.2
  • 44
    • 0000893882 scopus 로고
    • n et décomposition de polynômes a plusieurs variables
    • n et décomposition de polynômes a plusieurs variables. Journal of Functional Analysis. 1984, 55, 254-266.
    • (1984) Journal of Functional Analysis , vol.55 , pp. 254-266
    • Cassier, G.1
  • 45
    • 0001923625 scopus 로고
    • The multidimensional moment problem
    • Fuglede, B. The multidimensional moment problem. Expositiones Mathematicae. 1983, 1, 47-65.
    • (1983) Expositiones Mathematicae , vol.1 , pp. 47-65
    • Fuglede, B.1
  • 46
    • 0003769203 scopus 로고
    • John Wiley & Sons: New York
    • Folland, G. B. Real Analysis; John Wiley & Sons: New York, 1984.
    • (1984) Real Analysis
    • Folland, G.B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.