Browse > Article

Bounds for Stationary Waiting Times in a Class of Queueing Networks using Stochastic Ordering  

Seo Dong-Won (경희대학교 국제경영학부)
Publication Information
Journal of the Korean Operations Research and Management Science Society / v.29, no.4, 2004 , pp. 1-10 More about this Journal
Abstract
In this paper we study bounds for characteristics of stationary waiting times in (max, +)-linear systems with a Poisson arrival process. which are prevalent in manufacturing systems, kanban systems, cyclic and acyclic fork-and-join type systems, finite or infinite capacity tandem queues with various kinds of blocking, transportation systems, and telecommunication networks, and so on. Recently, some results on series expansion for characteristics, such as higher moments, Laplace transform, and tail probability, of transient and stationary waiting times in a class of (max, +)-linear systems via Taylor series expansions have been studied. In order to overcome the computational complexity in those results, we consider bounds for characteristics of stationary waiting times using valuable stochastic ordering results. Some numerical examples are also provided.
Keywords
queueing network; (max, +)-linear systems; waiting times; stochastic ordering;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Baccelli, F., G. Cohen, G.J. Olsder, and J-P. Quadrat, Synchronization and Linearity : An Algebra for Discrete Event Systems, John Wiley & Sons, 1992
2 Baccelli, F., S. Hasenfuss, and V. Schmidt, 'Transient and Stationary Waiting Times in (Max, -) Linear Systems with Poisson Input,' Queueing Systems, Vol.26(1997), pp. 301-342
3 Shaked, M. and J.G. Shanthikumar, Stochastic Orders and Their Applications, Academic Press, 1994
4 Ayhan, H. and D.W. Seo, 'Characteristics of Transient and Stationary Waiting Times in Poisson Driven (Max, +) Linear Systems,' Proceedings of the IFAC Symposium on System Structure and Control, (2001), pp. 227-234
5 Baccelli, F. and V. Schmidt, 'Taylor Series Expansions for Poisson Driven (Max, +) Linear Systems,' Annals of Applied Probability, Vol.6, No.1(1996), pp.138-185   DOI   ScienceOn
6 Henk, C., Tijms, Stochastic Models : An algorithmic Approach, Wiley, 1994
7 Ayhan, H. and DW. Seo, 'Laplace Transform and Moments of Waiting Times in Poisson Driven (Max,+)-Linear Systems,' Queueing Systems, Vol.37, No.4(2001), pp. 405-438   DOI   ScienceOn
8 Baccelli, F., S. Hasenfuss, and V. Schmidt, 'Expansions for Steady State Characteristics in (Max,+) Linear Systems,' Stochastic Models, Vol.14(1998), pp.1-24
9 Nelson, R. and AN. Tantawi, 'Approximate Analysis of Fork/Join Synchronization in Parallel Queues,' IEEE Transactions on Computers, Vol.37, No.6(1988), pp.739-743   DOI   ScienceOn
10 Hasenfuss, S., Performance Analysis of (Max, +)-Linear Systems via Taylor Series Expansions, PhD thesis, University of UIm, 1998
11 Seidel, W, KV. Kocemba, and K Mitreiter, 'On a Taylor Series Expansion for Waiting Times in Tandem Queues : an Algorithm for Calculating the Coefficients and an Investigation of the Approximation error,' Performance Evaluation, Vol.38(1999), pp.153-173
12 Ayhan, H. and D.W. Seo, 'Tail Probability of Transient and Stationary Waiting Times in (Max,+)-Linear Systems,' IEEE Transactions on Automatic Control, Vol.47, No.1 (2002), pp.151-157   DOI   ScienceOn