Geodesic
On main characteristics of the $M/M/1/N$ queue with single and batch arrivals and the queue size controlled by AQM algorithms
Kybernetika, Tome 47 (2011) no. 6, pp. 930-943.

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In the article finite-buffer queueing systems of the $M/M/1/N$ type with queue size controlled by AQM algorithms are considered, separately for single and batch arrivals. In the latter case two different acceptance strategies: WBAS (Whole Batch Acceptance Strategy) and PBAS (Partial Batch Acceptance Strategy) are distinguished. Three essential characteristics of the system are investigated: the stationary queue-size distribution, the number of consecutively dropped packets (batches of packets) and the time between two successive accepted packets (batches of packets). For these characteristics the formulae which can be easily numerically treated are derived. Numerical results obtained for three sample dropping functions are attached as well.
Classification : 60K25, 90B22
Keywords: active queue management (AQM); drop function; finite buffer; queue size 
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     author = {Kempa, Wojciech M.},
     title = {On main characteristics of the $M/M/1/N$ queue with single and batch arrivals and the queue size controlled by {AQM} algorithms},
     journal = {Kybernetika},
     pages = {930--943},
     publisher = {mathdoc},
     volume = {47},
     number = {6},
     year = {2011},
     mrnumber = {2907852},
     zbl = {1241.90035},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2011__47_6_a9/}
}
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Kempa, Wojciech M. On main characteristics of the $M/M/1/N$ queue with single and batch arrivals and the queue size controlled by AQM algorithms. Kybernetika, Tome 47 (2011) no. 6, pp. 930-943. http://geodesic.mathdoc.fr/item/KYB_2011__47_6_a9/