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Product Form Solutions for Multiserver Centers with Hierarchical Concurrency Constraints

Published online by Cambridge University Press:  27 July 2009

A. E. Krzesinski  and
R. Schassberger
A. E. Krzesinski
Affiliation:
Institute for Applied Computer Science University of Stellenbosch 7600 Stellenbosch, South Africa
R. Schassberger
Affiliation:
Institut für Mathematische Stochastik TU Braunschweig 3300 Braunschweig, Germany
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Abstract

We establish the quasireversibility of a certain exponential multiserver queue. The queuing discipline imposes restrictions on the numbers of customers of different classes and subclasses that can be served simultaneously. Customer loss is also allowed. Due to its quasireversibility the queue can be used as a node in a product form network. Our work generalizes work of Le Boudec, Krzesinski, and Crosby.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 6 , Issue 2 , April 1992 , pp. 147 - 156
Copyright
Copyright © Cambridge University Press 1992

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References

Ajmone, Marsan M., Donatelli, S., & Neri, F. (1991). Multiserver multiqueue systems with limited service time and zero walk time. Proceedings of the IEEE INFOCOM '91 3: 10C.2.1–10C.2.11.Google Scholar
Baskett, F., Chandy, K.M., Muntz, R.R., & Palacios, J. (1975). Open, closed and mixed networks of queues with different classes of customers. Journal of the ACM 22(2): 249–260.CrossRefGoogle Scholar
Crosby, S. & Krzesinski, A.E. (1990). Product from solutions for multiserver centres with concurrent class of customers. Performance Evaluation 11(4): 265–281.CrossRefGoogle Scholar
Crosby, S., Krzesinski, A.E., & Le, Boudec J.-Y. (1990). Generalized product form solutions for multiserver centres with concurrent classes of customers. IBM Research Report RZ 2019 (#71388) 9/4/90.Google Scholar
Crosby, S., Krzesinski, A.E., & Le, Boudec J.-Y. (1991). A MSHCC model of multilayer window flow control. In Balbo, G. & Serazzi, G. (eds.), Proceedings of the Fifth International Conference on Modelling Techniques and Tools for Computer Performance Evaluation. Turin, Italy: Elsevier Science Publishers, pp. 71–85.Google Scholar
Kelly, F.P. (1979). Reversibility and stochastic networks. New York: J. Wiley and Sons.Google Scholar
Le, Boudec J.-Y. (1986). A BCMP extension to multiserver stations with concurrent classes of customers. Performance Evaluation Review 14(1): 78–91.Google Scholar
Le, Boudec J.-Y. (1988). The MULTIBUS algorithm. Performance Evaluation 8(1): 1–18.Google Scholar