Fluctuation smoothing policies are stable for stochastic re-entrant lines
- 43 Downloads
In this paper we establish that all the policies in the class of Fluctuation Smoothing Policies for Mean Cycle Time (FSMCT), proposed in (Lu et al. 1992) and (Lu and Kumar 1993), are stable, in the sense of positive Harris recurrence, for all stochastic re-entrant lines. These constitute the first analytical results on this promising class of scheduling policies which have been shown to substantially reduce the mean and variance of cycle times in stochastic re-entrant lines. Stability is established by showing that the fluid limits corresponding to the FSMCT policies empty in finite time from all suitable initial conditions. A special case of FSMCT policies is the Last Buffer First Serve policy, and its stability is also thus established.
Unable to display preview. Download preview PDF.
- Chen, H. 1993. Fluid approximations and stability of multiclass queueing networks I: Work conserving disciplines. University of British Columbia, tech. rep.Google Scholar
- Dai, J. G. 1995. On positive Harris recurrence of multiclass queueing networks: A unified approach via fluid limit models.Annals of Applied Probability 5: 49–77.Google Scholar
- Dai, J. and Weiss, G. 1994. Stability and instability of fluid models for certain re-entrant lines. Preprint, February. To appear inMathematics of Operations Research.Google Scholar
- Dai, J. G. and Williams, R. J. 1994. Existence and uniqueness of semimartingale reflecting Brownian motions in convex polyhedrons. Submitted toTheory of Probability and its Applications.Google Scholar
- Kumar, S. and Kumar, P. R. 1994. Fluctuation smoothing policies are stable for stochastic re-entrant lines.Proc. 33rd IEEE Conference on Decision and Control, pp. 1476–1480.Google Scholar
- Lu, S. H., and Kumar, P. R. 1991. Distributed scheduling based on due dates and buffer priorities.IEEE Transactions on Automatic Control AC-36: 1406–1416.Google Scholar
- Lu, S. H., and Kumar, P. R. 1993. Fluctuation smoothing scheduling policies for queueing systems. To appear inProc. of the Silver Jubilee Workshop on Computing and Intelligent Systems, Indian Institute of Science, Bangalore, December.Google Scholar
- Lu, S. C. H., Ramaswamy, D., and Kumar, P. R. 1992. Efficient scheduling policies to reduce mean and variance of cycle-time in semiconductor manufacturing plants. University of Illinois, Urbana, IL, technical report. To appear inIEEE Transactions on Semiconductor Manufacturing, 1994.Google Scholar