Models of the departure process of a BMAP/MAP/1 queue

ABSTRACT

We propose a family of finite approximations for the departure process of a BMAP/MAP/1 queue. The departure process approximations are derived via an exact aggregate solution technique (called ETAQA) applied to M/G/1-type Markov processes. The proposed approximations are indexed by a parameter n (n < 1), which determines the size of the output model as n + 1 block levels of the M/G/1-type process. This output approximation preserves exactly the marginal distribution of the true departure process and the lag correlations of the inter-departure times up to lag n-2. Experimental results support the applicability of the proposed approximation in traffic-based decomposition of queueing networks.

REFERENCES

• 1: D. Green. Departure Processes from MAP/PH/1 Queues. PhD thesis, Department of Applied Mathematics, University of Adelaide, 1999.
• 2: D. M. Lucantoni. New results on the single server queue with a batch Markovian arrival process. Commun. Statist.-Stochastic Models, 7(1):1--46, 1991.
• 3: Alma Riska , Evgenia Smirni, Exact aggregate solutions for M/G/1-type Markov processes, Proceedings of the 2002 ACM SIGMETRICS international conference on Measurement and modeling of computer systems, June 15-19, 2002, Marina Del Rey, California
• 4: Q. Zhang, A. Heindl, and E. Smirni. Characterizing the BMAP/MAP/1 departure process via the ETAQA truncation. Commun. Statist.-Stochastic Models, 2005.

INDEX TERMS

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

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

  D. Software
  D.4 OPERATING SYSTEMS
      D.4.8 Performance
          Subjects: Queueing theory

  I. Computing Methodologies
  I.6 SIMULATION AND MODELING
      I.6.5 Model Development

General Terms:
Performance, Theory