Approximate analysis of a network of fluid queues

ABSTRACT

Fluid models have for some time been used to approximate stochastic networks with discrete state. These range from traditional 'heavy traffic' approximations to the recent advances in bio-chemical system models. Here we use an approximate compositional method to analyse a simple feedforward network of fluid queues which comprises both probabilistic branching and superposition. This extends our earlier work that showed the approximation to yield excellent results for a linear chain of fluid queues. The results are compared with those from a simulation model of the same system. The compositional approach is shown to yield good approximations, deteriorating for nodes with high load when there is correlation between their immediate inputs. This correlation arises when a common set of external sources feeds more than one queue, directly or indirectly.

REFERENCES

• 1: O. J. Boxma , V. Dumas, The busy period in the fluid queue, Proceedings of the 1998 ACM SIGMETRICS joint international conference on Measurement and modeling of computer systems, p.100-110, June 22-26, 1998, Madison, Wisconsin, United States
• 2: A. J. Field , P. G. Harrison, An approximate compositional approach to the analysis of fluid queue networks, Performance Evaluation, v.64 n.9-12, p.1137-1152, October, 2007 [doi>10.1016/j.peva.2007.06.025]
• 3: Offer Kella, Markov-modulated Feedforward Fluid Networks, Queueing Systems: Theory and Applications, v.37 n.1-3, p.141-161, March 2001 [doi>10.1023/A:1011096201765]
• 4: O. Kella and W. Whitt. Useful martingales for stochastic storage processes with Levy input. Journal of Applied Probability, 29(2):396--403, 1992.
• 5: Dirk P. Kroese , Werner R. W. Scheinhardt, Joint Distributions for Interacting Fluid Queues, Queueing Systems: Theory and Applications, v.37 n.1-3, p.99-139, March 2001 [doi>10.1023/A:1011044217695]
• 6: L. Rabehasaina. Moments of a Markov-modulated, irreducible network of fluid queues. Journal of Applied Probability, 43(2):510--522, 2006.
• 7: Werner R. W. Scheinhardt , Bert Zwart, A TANDEM FLUID QUEUE WITH GRADUAL INPUT, Probability in the Engineering and Informational Sciences, v.16 n.1, p.29-45, January 2002 [doi>10.1017/S0269964802161031]

INDEX TERMS

Primary Classification:
  C. Computer Systems Organization
  C.2 COMPUTER-COMMUNICATION NETWORKS
      C.2.1 Network Architecture and Design
          Subjects: Network communications

Additional Classification:
  G. Mathematics of Computing
  G.3 PROBABILITY AND STATISTICS
      Subjects: Queueing theory

  I. Computing Methodologies
  I.6 SIMULATION AND MODELING
      I.6.4 Model Validation and Analysis
      I.6.5 Model Development
          Subjects: Modeling methodologies
      I.6.6 Simulation Output Analysis

General Terms:
Algorithms, Design, Performance