Abstract
In the following, we present an iterative algorithm that is based on decomposition. It approximates the throughput of a closed queueing system with linear flow, general processing times, and finite buffer spaces. The service times at each station are assumed to be i. i. d. random variables with a general distribution that is described by the mean and the coefficient of variation. The stations consist of single servers with a first-come first-served queueing discipline.
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- 1.
The assignment of λ is carried out according to a mechanism that is explained in Sect. 4.1.1.
- 2.
The evaluation is explained in Sect. 4.1.2.
- 3.
This is explained in Sect. 4.1.2.
- 4.
For more information, see Sect. 4.1.2.
- 5.
For further details on the coherence of the production-rate function and the blocking and starving probabilities, see Sect. 2.2.
- 6.
Numerical tests with different \({\zeta }_{u}(1, 2)\) proved that the mean deviation of the production-rate estimate over all test instances is higher, the higher the coefficient of variation of the inter-arrival time at the input station, \({\zeta }_{u}(1, 2)\), is.
- 7.
The station capacity equals the buffer capacity, C i, j , plus one unit for the server.
- 8.
For the calculation of \({P}_{i}({n}_{i})\), see Manitz (2005, p. 138).
- 9.
This has been observed by Whitt (1984) for queueing models as well.
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Lagershausen, S. (2013). Decomposition Approach. In: Performance Analysis of Closed Queueing Networks. Lecture Notes in Economics and Mathematical Systems, vol 663. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32214-3_4
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DOI: https://doi.org/10.1007/978-3-642-32214-3_4
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