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On the stability of polling models with multiple servers

Part of: Special processes Operations research and management science

Published online by Cambridge University Press:  14 July 2016

D. Down
D. Down*
Affiliation:
CWI, Amsterdam
*
∗Postal address: School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA. Email address: [email protected].
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Abstract

The stability of polling models is examined using associated fluid limit models. Examples are presented which generalize existing results in the literature or provide new stability conditions while in both cases providing simple and intuitive proofs of stability. The analysis is performed for both general single server models and specific multiple server models.

Keywords

Polling modelmultiple serversstabilityfluid model

MSC classification

Primary: 60K25: Queueing theory 90B22: Queues and service
Type
Research Papers
Information
Journal of Applied Probability , Volume 35 , Issue 4 , December 1998 , pp. 925 - 935
Copyright
Copyright © Applied Probability Trust 1998 

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References

Altman, E., and Spieksma, F. (1992). Polling systems–-moment stability of station times and central limit theorems. Technical Report R 92/9, University of Leiden.Google Scholar
Altman, E., Konstantopoulos, P., and Liu, Z. (1992). Stability, monotonicity and invariant quantities in general polling systems. Queueing Systems 11, 35–57.Google Scholar
Borovkov, A. A., and Schassberger, R. (1994). Ergodicity of a polling network. Stoch. Proc. Appl. 50, 253–262.Google Scholar
Chen, H. (1995). Fluid approximations and stability of multiclass queueing networks I: Work conserving disciplines. Adv. Appl. Prob. 5, 637–665.Google Scholar
Dai, J. G. (1995). On the positive Harris recurrence for multiclass queueing networks: A unified approach via fluid limit models. Ann. Appl. Prob. 5, 49–77.Google Scholar
Dai, J. G., and Meyn, S. P. (1995). Stability and convergence of moments for multiclass queueing networks via fluid models. IEEE Trans. Automat. Control 40, 1889–1904.Google Scholar
Foss, S., and Last, G. (1996). Stability of polling systems with exhaustive service policies and state dependent routing. Ann. Appl. Prob. 6, 116–137.Google Scholar
Foss, S., and Last, G. (1998). On the stability of greedy polling systems with general service policies. Prob. Engrg. Inform. Sci. 12, 49–68.Google Scholar
Fricker, C. and Jaïbi, M. R. (1994). Monotonicity and stability of periodic polling models. Queueing Systems 15, 211–238.Google Scholar
Fricker, C. and Jaïbi, M. R. (1994). Stability of a polling model with a Markovian scheme. Technical Report RR2278, INRIA.Google Scholar
Gamse, B., and Newell, G. F. (1982). An analysis of elevator operation in moderate height buildings–-II. multiple elevators. Transp. Res. B 16, 321–335.Google Scholar
Georgiadis, L., and Szpankowski, W. (1992). Stability of token passing rings. Queueing Systems 11, 7–33.Google Scholar
Georgiadis, L., Szpankowski, W., and Tassiulas, L. (1994). Stability analysis of quota allocation access protocols in ring networks with spatial reuse. Technical report CSD-TR-94-047, Purdue University.Google Scholar
Levy, H., and Sidi, M. (1990). Polling systems: applications, modeling, and optimization. IEEE Trans. Comm. 38, 1750–1760.Google Scholar
Massoulié, L. (1995). Stability of non-Markovian polling systems. Queueing Systems 21, 67–95.Google Scholar
Meyn, S. P. (1994). Transience of multiclass queueing networks via fluid limit models. Ann. Appl. Prob. 5, 946–957.Google Scholar
Meyn, S. P., and Down, D. (1994). Stability of generalized Jackson networks. Ann. Appl. Prob. 4, 124–148.Google Scholar
Morris, R. J. T., and Wang, Y. T. (1984). Some results for multi-queue systems with multiple cyclic servers. In Performance of Computer-Communication Systems, ed. Bux, W. and Rudin, H. North-Holland, Amsterdam, pp. 245–248.Google Scholar
Sigman, K. (1990). The stability of open queueing networks. Stoch. Proc. Appl. 35, 11–25.Google Scholar
van der Mei, R. D., and Borst, S. C. (1994). Analysis of multiple-server polling systems by means of the power-series algorithm. Technical report BS-R9410, CWI.Google Scholar