Threshold Workload Control in the BMAP/G/1 Queue

Authors:
Ho Woo Lee;Jung Woo Baek
Affiliations:
Sungkyunkwan University, Korea;Sungkyunkwan University, Korea
Venue:
QEST '06 Proceedings of the 3rd international conference on the Quantitative Evaluation of Systems
Year:
2006

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Abstract

We analyze the distribution of the workload in the queueing system with Batch Markovian Arrival process (BMAP) controlled according to the D-policy. The server begins to serve the customers only when the total workload exceeds some predetermined threshold value D. We first explore the stochastic nature of the idle period. Then we derive the Laplace-Stieltjes transform of the workload and the mean values at an arbitrary time. Finally we provide computational experiences and discuss the effects of the BMAP arrivals. Our study shows that the naive Poisson assumption heavily underestimates the workload in a queueing system. We also discuss the effect of the workload threshold control.