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doi:10.1016/j.peva.2005.09.001 
Copyright © 2005 Elsevier B.V. All rights reserved.
Approximating multi-skill blocking systems by HyperExponential Decomposition
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Received 25 October 2004;
Abstract
We consider multi-class blocking systems in which jobs require a single processing step. There are groups of servers that can each serve a different subset of all job classes. The assignment of jobs occurs according to some fixed overflow policy. We are interested in the blocking probabilities of each class. This model can be used for call centers, tele-communication and computer networks. An approximation method is presented that takes the burstiness of the overflow processes into account. This is achieved by assuming hyperexponential distributions of the inter-overflow times. The approximations are validated with simulation and we make a comparison to existing approximation methods. The overall blocking probability turns out to be approximated with high accuracy by several methods. However, the individual blocking probabilities per class are significantly more accurate for the method that is introduced in this paper.
Keywords: Multi-class blocking system; Blocking probability; Equivalent Random Method; Hayward-Fredericks method; Interrupted Poisson Process method; Call center; Hyperexponential distribution; Decomposition; Overflow routing
Article Outline
- 1. Introduction
- 1.1. Equivalent Random Method
- 1.2. Hayward-Fredericks method
- 1.3. Interrupted Poisson Process method
- 1.4. HyperExponential Decomposition
- 2. Model description
- 2.1. Model limitation
- 3. Fitting the overflow process of the M/M/s/s model
- 4. HyperExponential Decomposition algorithm
- 4.1. Determining the level of each group (line 1)
- 4.2. Weighted average service rate (line 4)
- 4.3. Calculating the overflow rate (line 5)
- 4.4. Determining the second and third moment of the overflow process (line 7)
- 4.5. Determining overflow processes to the next groups, dispatching (line 9)
- 5. Comparison to simulation (computation times)
- 6. Numerical results
- 7. Conclusions and further research
- Acknowledgements
- Appendix A. Exact analysis
- A.1. Transitions
- A.2. Assignment
- A.3. Blocking
- A.4. Completion
- A.5. Equilibrium probabilities
- Appendix B. Numerical comparison
- Instance 1
- Instance 2
- Instance 3
- Instance 4
- Instance 5
- Instance 6
- Instance 7
- Instance 8
- Instance 9
- Instance 10
- Instance 11
- Instance 12
- Instance 13
- Instance 14
- Instance 15
- Instance 16
- Instance 17
- Instance 18
- References
- Vitae
