An Analysis of the E<sub>l</sub>/E<sub>k</sub>/1 Queueing System by Restricted Minimal Lattice Paths

The usual procedure for obtaining the equilibrium probability distribution of the queue length in a queueing system is by constructing and solving the difference-differential equations. In this paper, a new approach for deriving the equilibrium probability distributions of the queue length in the M/...

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Veröffentlicht in:The Journal of the Operational Research Society. - Taylor & Francis, Ltd.. - 46(1995), 2, Seite 245-253
1. Verfasser: Arizono, Ikuo (VerfasserIn)
Weitere Verfasser: Ohta, Hiroshi, Deutsch, Stuart J., Wang, Ching-Cheng
Format: Online-Aufsatz
Sprache:English
Veröffentlicht: 1995
Zugriff auf das übergeordnete Werk:The Journal of the Operational Research Society
Schlagworte:Combinatorial Theory Equilibrium Probability Distribution Minimal Lattice Paths Queueing Systems Mathematics Philosophy Behavioral sciences Social sciences
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520 |a The usual procedure for obtaining the equilibrium probability distribution of the queue length in a queueing system is by constructing and solving the difference-differential equations. In this paper, a new approach for deriving the equilibrium probability distributions of the queue length in the M/M/1, M/E<sub>k</sub>/1 and E<sub>l</sub>/E<sub>k</sub>/1 queueing systems is presented, based on the generating function of the number of the minimal lattice paths. The proposed procedure obtains the equilibrium probability distribution more easily than the usual procedure, which solves difference-differential equations. 
540 |a Copyright 1995 Operational Research Society Ltd 
650 4 |a Combinatorial Theory 
650 4 |a Equilibrium Probability Distribution 
650 4 |a Minimal Lattice Paths 
650 4 |a Queueing Systems 
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650 4 |a Mathematics  |x Applied mathematics  |x Statistics  |x Applied statistics  |x Descriptive statistics  |x Statistical distributions  |x Distribution functions  |x Probability distributions 
650 4 |a Philosophy  |x Logic  |x Logical topics  |x Formal logic  |x Mathematical logic  |x Mathematical set theory  |x Lattice theory  |x Mathematical lattices 
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650 4 |a Mathematics  |x Pure mathematics  |x Geometry  |x Coordinate systems  |x Cartesian coordinates 
650 4 |a Behavioral sciences  |x Psychology  |x Cognitive psychology  |x Decision theory  |x Operations research 
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655 4 |a research-article 
700 1 |a Ohta, Hiroshi  |e verfasserin  |4 aut 
700 1 |a Deutsch, Stuart J.  |e verfasserin  |4 aut 
700 1 |a Wang, Ching-Cheng  |e verfasserin  |4 aut 
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