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Volumn 42, Issue 1, 2002, Pages 33-62

The finite element method for computing the stationary distribution of an SRBM in a hypercube with applications to finite buffer queueing networks

Author keywords

Basic adjoint relationship; BNAfm; BNAsm; Brownian approximation; Finite buffer; Finite element method; Heavy traffic; Numerical algorithm; Performance analysis; Queueing networks; Semimartingale reflecting Brownian motion; Stationary distribution

Indexed keywords

APPROXIMATION ALGORITHMS; BROWNIAN MOVEMENT; COMPUTER PROGRAMMING; HYPERCUBE NETWORKS; NUMERICAL METHODS; QUEUEING NETWORKS; QUEUEING THEORY;

EID: 0036355797     PISSN: 02570130     EISSN: 15729443     Source Type: Journal    
DOI: 10.1023/A:1019942711261     Document Type: Article
Times cited : (29)

References (42)
  • 1
    • 84872983121 scopus 로고    scopus 로고
    • Ordering sparse matrices and transforming front trees
    • C. Ashcraft, Ordering sparse matrices and transforming front trees, Working paper (1999).
    • (1999) Working Paper
    • Ashcraft, C.1
  • 6
    • 21144476000 scopus 로고
    • Design of manufacturing systems using queueing models
    • J. Buzacott and J.G. Shanthikumar, Design of manufacturing systems using queueing models, Queueing Systems 12 (1992) 135-213.
    • (1992) Queueing Systems , vol.12 , pp. 135-213
    • Buzacott, J.1    Shanthikumar, J.G.2
  • 9
    • 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 Modeling and Analysis of Manufacturing Systems, ed. D.D. Yao (Springer, Berlin, 1994) pp. 107-131.
    • (1994) Stochastic Modeling and Analysis of Manufacturing Systems , pp. 107-131
    • Chen, H.1    Mandelbaum, A.2
  • 13
    • 0033245829 scopus 로고    scopus 로고
    • A heavy traffic limit theorem for a class of open queueing networks with finite buffers
    • J.G. Dai and W. Dai, A heavy traffic limit theorem for a class of open queueing networks with finite buffers, Queueing Systems 32 (1998) 5-40.
    • (1998) Queueing Systems , vol.32 , pp. 5-40
    • Dai, J.G.1    Dai, W.2
  • 14
    • 0003064374 scopus 로고
    • Steady-state analysis of RBM in a rectangle: Numerical methods and a queueing application
    • J.G. Dai and J.M. Harrison, Steady-state analysis of RBM in a rectangle: Numerical methods and a queueing application, Ann. Appl. Probab. 1 (1991) 16-35.
    • (1991) Ann. Appl. Probab. , vol.1 , pp. 16-35
    • Dai, J.G.1    Harrison, J.M.2
  • 15
    • 0002933073 scopus 로고
    • Reflected Brownian motion in an orthant: Numerical methods for steady-state analysis
    • J.G. Dai and J.M. Harrison, Reflected Brownian motion in an orthant: Numerical methods for steady-state analysis, Ann. Appl. Probab. 2 (1992) 65-86.
    • (1992) Ann. Appl. Probab. , vol.2 , pp. 65-86
    • Dai, J.G.1    Harrison, J.M.2
  • 17
    • 0027927313 scopus 로고
    • Sequential bottleneck decompositions: An approximation method for generalized Jackson networks
    • J.G. Dai, V. Nguyen and M.I. Reiman, Sequential bottleneck decompositions: An approximation method for generalized Jackson networks, Oper. Res. 42 (1994) 119-136.
    • (1994) Oper. Res. , vol.42 , pp. 119-136
    • Dai, J.G.1    Nguyen, V.2    Reiman, M.I.3
  • 18
    • 0002611604 scopus 로고
    • Existence and uniqueness of semimartingale reflecting Brownian motions in convex polyhedrons
    • J.G. Dai and R. Williams, Existence and uniqueness of semimartingale reflecting Brownian motions in convex polyhedrons, Theory Probab. Appl. 40 (1995) 1-40.
    • (1995) Theory Probab. Appl. , vol.40 , pp. 1-40
    • Dai, J.G.1    Williams, R.2
  • 21
    • 0025402476 scopus 로고
    • A set of level 3 basic linear algebra subprograms
    • J. Dongarra, A set of level 3 basic linear algebra subprograms, ACM Trans. Math. Software 16 (1990) 1-17.
    • (1990) ACM Trans. Math. Software , vol.16 , pp. 1-17
    • Dongarra, J.1
  • 24
    • 0001521395 scopus 로고
    • The stationary distribution of reflected Brownian motion in a planar region
    • J.M. Harrison, H. Landau and L.A. Shepp, The stationary distribution of reflected Brownian motion in a planar region, Ann. Probab. 13 (1985) 744-757.
    • (1985) Ann. Probab. , vol.13 , pp. 744-757
    • Harrison, J.M.1    Landau, H.2    Shepp, L.A.3
  • 26
    • 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
  • 27
    • 21144478130 scopus 로고
    • Brownian models of multiclass queueing networks: Current status and open problems
    • J.M. Harrison and V. Nguyen, Brownian models of multiclass queueing networks: Current status and open problems, Queueing Systems 13 (1993) 5-40.
    • (1993) Queueing Systems , vol.13 , pp. 5-40
    • Harrison, J.M.1    Nguyen, V.2
  • 28
    • 0001086728 scopus 로고
    • Multidimensional reflected Brownian motions having exponential stationary distributions
    • J.M. Harrison and R.J. Williams, Multidimensional reflected Brownian motions having exponential stationary distributions, Ann. Probab. 15 (1987) 115-137.
    • (1987) Ann. Probab. , vol.15 , pp. 115-137
    • Harrison, J.M.1    Williams, R.J.2
  • 29
    • 0001930641 scopus 로고
    • Job shop-like queueing systems
    • J.R. Jackson, Job shop-like queueing systems, Managm. Sci. 10 (1963) 131-142.
    • (1963) Managm. Sci. , vol.10 , pp. 131-142
    • Jackson, J.R.1
  • 32
    • 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
  • 37
    • 0022661928 scopus 로고
    • Conformal mapping solution of Laplace's equation on a polygon with oblique derivative boundary conditions
    • L. Trefethen and R.J. Williams, Conformal mapping solution of Laplace's equation on a polygon with oblique derivative boundary conditions, J. Comput. Appl. Math. 14 (1985) 227-249.
    • (1985) J. Comput. Appl. Math. , vol.14 , pp. 227-249
    • Trefethen, L.1    Williams, R.J.2
  • 39
    • 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
  • 40
    • 0020848139 scopus 로고
    • The queueing network analyzer
    • W. Whitt, The queueing network analyzer, Bell System Tech. J. 62(9) (1983) 2779-2815.
    • (1983) Bell System Tech. J. , vol.62 , Issue.9 , pp. 2779-2815
    • Whitt, W.1
  • 41
    • 0002248871 scopus 로고    scopus 로고
    • On the approximation of queueing networks in heavy traffic
    • eds. F.P. Kelly, S. Zachary and I. Ziedins (Oxford Univ. Press, Oxford)
    • R.J. Williams, On the approximation of queueing networks in heavy traffic, in: Stochastic Networks: Theory and Applications, eds. F.P. Kelly, S. Zachary and I. Ziedins (Oxford Univ. Press, Oxford, 1996) pp. 35-56.
    • (1996) Stochastic Networks: Theory and Applications , pp. 35-56
    • Williams, R.J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.