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Exact Analysis of Special Networks

  • Simonetta Balsamo
  • Vittoria de Nitto Personé
  • Raif Onvural
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 31)

Abstract

In this chapter we deal with some special classes of queueing networks with blocking for which efficient solution algorithms can be defined. The exact analysis of Markovian networks based on the Markov process underlying the network defined in Chapter 4 can be dramatically simplified for these particular networks.

Keywords

Queue Length Queueing Network Finite Capacity Convolution Algorithm Symmetrical Network 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Akyildiz, I.F. “Exact product form solution for queueing networks with blocking” IEEE Trans. on Computer, Vol. 36 (1987) 122–125.CrossRefGoogle Scholar
  2. Akyildiz, I.F., and N. Van Dijk “Exact Solution for Networks of Parallel Queues with Finite Buffers” in Performance ’90 (P.J.B. King, I. Mitrani and R.J. Pooley Eds.) North-Holland, 1990, 35–49.Google Scholar
  3. Akyildiz, I.F., and H. Von Brand “Central Server Models with Multiple Job Classes, State Dependent Routing, and Rejection Blocking” IEEE Trans. on Softw. Eng., Vol. 15 (1989) 1305–1312.CrossRefGoogle Scholar
  4. Akyildiz, I.F., and H. Von Brand “Computational Algorithms for Networks of Queues with Rejection Blocking” Acta Informatica, Vol. 26 (1989) 559–576.CrossRefGoogle Scholar
  5. Akyildiz, I.F., and H. Von Brand “Exact solutions for open, closed and mixed queueing networks with rejection blocking” J. Theor. Computer Science, Vol. 64 (1989) 203–219.CrossRefGoogle Scholar
  6. Balsamo, S., and C. Clò “State distribution at arrival times for closed queueing networks with blocking” Technical Report TR-35/92, Dept. of Comp. Sci., University of Pisa, 1992.Google Scholar
  7. Balsamo, S., C. Clò “A Convolution Algorithm for Product Form Queueing Networks with Blocking” Annals of Operations Research, Vol. 79 (1998) 97–117.CrossRefGoogle Scholar
  8. Balsamo, S., and V. De Nitto Personè “Closed queueing networks with finite capacities: blocking types, product form solution and performance indices” Performance Evaluation, Vol. 12, 4 (1991) 85–102.CrossRefGoogle Scholar
  9. Balsamo, S., and V. De Nitto Personè “A survey of Product form Queueing Networks with Blocking and their Equivalences” Annals of Operations Research, Vol. 48 (1994) 31–61.CrossRefGoogle Scholar
  10. Balsamo, S., and L. Donatiello “On the Cycle Time Distribution in a Two-stage Queueing Network with Blocking” IEEE Transactions on Software Engineering, Vol. 13 (1989) 1206–1216f.CrossRefGoogle Scholar
  11. Balsamo, S., and L. Donatiello “Two-stage Queueing Networks with Blocking: Cycle Time Distribution and Equivalence Properties”, in Modelling Techniques and Tools for Computer Performance Evaluation (R. Puigjaner, D. Potier Eds.) Plenum Press, 1989.Google Scholar
  12. Baskett, F., K.M. Chandy, R.R. Muntz, and G. Palacios “Open, closed, and mixed networks of queues with different classes of customers” J. of ACM, Vol. 22 (1975) 248–260.CrossRefGoogle Scholar
  13. Boucherie, R., and N. Van Dijk “On the arrival theorem for product form queueing networks with blocking” Performance Evaluation, Vol. 29 (1997) 155–176.CrossRefGoogle Scholar
  14. Buzen, J.P. “Computational Algorithms for Closed Queueing Networks with exponential servers” Comm. ACM, Vol. 16 (1973) 527–531.CrossRefGoogle Scholar
  15. Chandy, K.M., J.H. Howard, and D. Towsley “Product form and local balance in queueing networks”J. ACM, Vol.24 (1977) 250–263.CrossRefGoogle Scholar
  16. Chandy, K.M., and A.J. Martin “A characterization of product-form queueing networks” J. ACM, Vol.30 (1983) 286–299.CrossRefGoogle Scholar
  17. Choukri, T. “Exact Analysis of Multiple Job Classes and Different Types of Blocking” in Queueing Networks with Finite Capacities (R.O. Onvural and I.F. Akyidiz Eds.), Elsevier, 1993.Google Scholar
  18. Cohen, J.W. “The multiple phase service network with generalized processor sharing” Acta Informatica, Vol.12 (1979) 245–284.CrossRefGoogle Scholar
  19. Clò, C. “MVA for Product-Form Cyclic Queueing Networks with RS Blocking” Annals of Operations Research, Vol. 79 (1998).Google Scholar
  20. Daduna, H. “Busy Periods for Subnetworks in Stochastic Networks: Mean Value Analysis” xx, Vol. 35 (1988) 668–674.Google Scholar
  21. Dallery, Y., and D.D. Yao “Modelling a system of flexible manufacturing cells” in: Modeling and Design of Flexible Manufacturing Systems (Kusiak Ed.) North-Holland, 1986, 289–300.Google Scholar
  22. Dallery, Y., and D.F. Towsley “Symmetry property of the throughput in closed tandem queueing networks with finite buffers” Op. Res. Letters, Vol. 10 (1991) 541–547.CrossRefGoogle Scholar
  23. De Nitto Personè, V., and D. Grillo “Managing Blocking in Finite Capacity Symmetrical Ring Networks” Third Int. Conf. on Data Comm. Systems and their Performance, Rio de Janeiro, Brazil, June 22–25 (1987) 225–240.Google Scholar
  24. Gordon, W.J., and G.F. Newell “Cyclic queueing systems with restricted queues” Oper. Res., Vol. 15 (1967) 286–302.CrossRefGoogle Scholar
  25. Hordijk, A., and N. Van Dijk “Networks of queues with blocking”, in: Performance ’81 (K.J. Kylstra Ed.) North Holland (1981) 51–65.Google Scholar
  26. Hordijk, A., and N. Van Dijk “Networks of queues; Part I: job-local-balance and the adjoint process; Part II: General routing and service characteristics”, in: Lect. Notes in Control and Information Sciences (F. Baccelli and G. Fajolle Eds.) Springer-Verlag (1983) 158–205.Google Scholar
  27. Kant., K. Introduction to Computer System Performance Evaluation. McGraw-Hill, 1992.Google Scholar
  28. Kelly, F. P. Reversibility and Stochastic Networks. Wiley (1979).Google Scholar
  29. Kingman, J.F.C. “Markovian population process” J. Appl. Prob., Vol. 6 (1969) 1–18.CrossRefGoogle Scholar
  30. Krzesinski, A.E. “Multiclass queueing networks with state-dependent routing” Performance Evaluation, Vol.7 (1987) 125–145.CrossRefGoogle Scholar
  31. Lam, S.S. “Queueing networks with capacity constraints” IBM J. Res. Develop., Vol. 21 (1977) 370–378.CrossRefGoogle Scholar
  32. Lavenberg, S.S. Computer Performance Modeling Handbook. Prentice Hall, 1983.Google Scholar
  33. Lavenberg, S.S., and M. Reiser “Stationary State Probabilities at Arrival Instants for Closed Queueing Networks with multiple Types of Customers” J. Appl. Prob., Vol. 17 (1980) 1048–1061.CrossRefGoogle Scholar
  34. Onvural, R.O. “A Note on the Product Form Solutions of Multiclass Closed Queueing Networks with Blocking” Performance Evaluation, Vol.10 (1989) 247–253.CrossRefGoogle Scholar
  35. Pittel, B. “Closed exponential networks of queues with saturation: the Jackson-type stationary distribution and its asymptotic analysis” Math. Oper. Res. , Vol. 4 (1979) 367–378.CrossRefGoogle Scholar
  36. Raghavendra, C.S., and J.A. Silvester “A Survey of multi-connected loop topologies for local computer networks” Computer Networks and ISDN Systems, Vol. 11 (1986) 29–42.CrossRefGoogle Scholar
  37. Ree, D.A., and H.D. Shwetman “Cost-performance bounds for multicomputer networks” IEEE Trans. on Computer, Vol. 32 (1983) 83–95.CrossRefGoogle Scholar
  38. Reiser, M., and S.S. Lavenberg, “Mean Value Analysis of Closed Multichain Queueing Networks”, J. ACM, Vol. 27 (1980) 313–322.CrossRefGoogle Scholar
  39. Sereno, M. “Mean Value Analysis of product form solution queueing networks with repetitive service blocking” Performance Evaluation, Vol. 36–37 (1999) 19–33.CrossRefGoogle Scholar
  40. Sevcik, K.S., and I. Mitrani “The Distribution of Queueing Network States at Input and Output Instants” J. of ACM, Vol. 28 (1981) 358–371.CrossRefGoogle Scholar
  41. Towsley, D.F. “Queueing network models with state-dependent routing” J. ACM, Vol. 27 (1980) 323–337.CrossRefGoogle Scholar
  42. Van Dijk, N. “On the Arrival Theorem for communication networks” Computer Networks and ISDN Systems, Vol. 25 (1993) 1135–1142.CrossRefGoogle Scholar
  43. Van Dijk, N., and H.G. Tijms “Insensitivity in two node blocking models with applications” in: Proc. Teletraffic Analysis and Computer Performance Evaluation, (Boxma, Cohen and Tijms Eds.) North Holland, 1986, 329–340.Google Scholar
  44. Yao, D.D., and J.A. Buzacott “Modeling a class of state-dependent routing in flexible manufacturing systems” Annals of Oper. Res., Vol. 3 (1985) 153–167.CrossRefGoogle Scholar
  45. Yao, D.D., and J.A. Buzacott “Modeling a class of flexible manufacturing systems with reversible routing” Oper. Res., Vol. 35 (1987) 87–93.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Simonetta Balsamo
    • 1
  • Vittoria de Nitto Personé
    • 2
  • Raif Onvural
    • 3
  1. 1.Universita’ di VeneziaItaly
  2. 2.Universita’ di Roma “Tor Vergata”Italy
  3. 3.IBMUSA

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