Asymptotic analysis for closed multichain queueing networks with bottlenecks

Queueing Systems

Volumn 23, Issue 1-4, 1996, Pages 235-258

  Kogan, Yaakov ^a   Yakovlev, Andrei ^b  

^a AT AND T LABS RESEARCH   (United States)

^b UNIVERSITÉ D'ORLÉANS   (France)

Author keywords

BCMP networks; Generating function; Homology; Multidimensional residues; Partition function; Saddle point

Indexed keywords

ASYMPTOTIC ANALYSIS;

GENERATING FUNCTIONS; HOMOLOGY; MULTIDIMENSIONAL RESIDUES; PARTITION FUNCTIONS; SADDLE POINT;

QUEUEING NETWORKS;

EID: 0040156061     PISSN: 02570130     EISSN: 15729443     Source Type: Journal    
DOI: 10.1007/bf01206559     Document Type: Article

References (16)

1. L.V. Ahlfors and L. Sario, Riemann Surfaces (Princeton Univ. Press, Princeton, NJ, 1960).
2. L.A. Aizenberg and A.P. Yuzhakov, Integral Representations and Residues in Multidimensional Complex Analysis (American Mathematical Society, Providence, RI, 1983).
3. F. Baskett, K.M. Chandy, R.R. Muntz and F.G. Palacios, Open, closed, and mixed networks of queues with different classes of customers, J. ACM 22 (1975) 248-260.
4. A. Bertozzi and J. McKenna, Multidimensional residues, generating functions, and their application to queueing networks, SIAM Review 35 (1993) 239-268.
5. A. Birman and Y. Kogan, Asymptotic evaluation of closed queueing networks with many stations, Communications in Statistics. Stochastic Models 8 (1992) 543-564.
6. J.J. Gordon, The evaluation of normalizing constants in closed queueing networks, Operations Research 38 (1990) 863-869.
7. P. Griffiths and J. Harris, Principles of Algebraic Geometry (Wiley, New York, 1978).
8. Y. Kogan and A. Birman, Asymptotic analysis of closed queueing networks with bottlenecks, in: IFIP Transactions C-5, Performance of Distributed Systems and Integrated Communication Networks, eds. T. Hasegawa, H. Takagi and Y. Takahashi (North-Holland, Amsterdam, 1992).
9. Y. Kogan, Another approach to asymptotic expansions for large closed queueing networks, Operations Research Letters 11 (1992) 317-321.
10. V.A. Malyshev and A.V. Yakovlev, Condensation in large closed Jackson networks, Rapports de Recherche de l'INRIA-Rocquencourt, #1854 (1993).
11. J. McKenna and D. Mitra, Integral representations and asymptotic expansions for closed Markovian queueing networks: Normal usage, Bell System Technical Journal 61 (1982) 661-683.
12. J. McKenna, D. Mitra and K.G. Ramakrishnan, A class of closed Markovian queueing networks: Integral representations, asymptotic expansions, generalizations, The Bell System Technical Journal 60 (1981) 599-641.
13. J.J. Rotman, An Introduction to Algebraic Topology (Springer-Verlag, New York, 1988).
14. A.G. Vitushkin (ed.), Several Complex Variables I (Springer-Verlag, Berlin, 1990).
15. J. Wang and K.W. Ross, Asymptotic analysis for closed multiclass queueing networks in critical usage, Queueing Systems 16 (1994) 167-191.
16. R. Wong, Asymptotic Approximations of Integrals (Academic Press, Boston, 1986).