Power series approximations for two-class generalized processor sharing systems
| Autor: | Onno Boxma, Joris Walraevens, Johan S. Leeuwaarden |
|---|---|
| Přispěvatelé: | Department of Telecommunications and Information Processing, Universiteit Gent = Ghent University [Belgium] (UGENT), European Institute for Statistics, Probability, Stochastic Operations Research and its Applications (EURANDOM), Eindhoven University of Technology [Eindhoven] (TU/e), Eurandom, Stochastic Operations Research |
| Jazyk: | angličtina |
| Rok vydání: | 2010 |
| Předmět: |
60G50
Technology and Engineering Discrete time MODELS 0211 other engineering and technologies M/M/1 queue LINES 02 engineering and technology Management Science and Operations Research Fork–join queue Generalized processor sharing 01 natural sciences [INFO.INFO-NI]Computer Science [cs]/Networking and Internet Architecture [cs.NI] 010104 statistics & probability 60K25 Two-dimensional random walk QUEUES CUSTOMERS Computer Science::Networking and Internet Architecture DISCIPLINE 0101 mathematics Mathematics Discrete mathematics 021103 operations research DISCRETE-TIME M/G/k queue 30B10 M/D/c queue G/G/1 queue Computer Science Applications Computer Science::Performance Computational Theory and Mathematics M/G/1 queue PARALLEL Priority queue Bulk queue Power series approximation |
| Zdroj: | QUEUEING SYSTEMS Queueing Systems Queueing Systems, Springer Verlag, 2010, 66 (2), pp.107-130. ⟨10.1007/s11134-010-9188-8⟩ Queueing Systems: Theory and Applications, 66(2), 107-130. Springer |
| ISSN: | 0257-0130 1572-9443 |
| DOI: | 10.1007/s11134-010-9188-8⟩ |
| Popis: | We develop power series approximations for a discrete-time queueing system with two parallel queues and one processor. If both queues are nonempty, a customer of queue 1 is served with probability ß, and a customer of queue 2 is served with probability 1-ß. If one of the queues is empty, a customer of the other queue is served with probability 1. We first describe the generating function U(z_1,z_2) of the stationary queue lengths in terms of a functional equation, and show how to solve this using the theory of boundary value problems. Then, we propose to use the same functional equation to obtain a power series for U(z_1,z_2) in ß. The first coefficient of this power series corresponds to the priority case ß=0, which allows for an explicit solution. All higher coefficients are expressed in terms of the priority case. Accurate approximations for the mean stationary queue lengths are obtained from combining truncated power series and Padé approximation. Keywords: Generalized processor sharing - Power series approximation - Discrete time - Two-dimensional random walk. |
| Databáze: | OpenAIRE |
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