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# Analysis of BMAP vacation queue and its application to IEEE 802.16e sleep mode

• The paper deals with the continuous-time BM AP/G/1 queue with multiple vacations and with its application to IEEE 802.16e sleep mode. The lengths of the vacation periods have general distribution and they depend on the number of preceding vacations (dependent multiple vacation). We give the expressions for the vector generating function of the stationary number of customers and its mean. Moreover we obtain new formulas for the vector Laplace-Stieljes transform of the stationary virtual waiting time and for its first two moments in case of First-Come First-Serve scheduling.
We apply this vacation model to the IEEE 802.16e sleep mode mechanism, and we evaluate its performance as a function of the traffic intensity and the traffic correlation parameter. We give an example for determining the best sleep mode parameters for a simple optimization criteria and we also develop a cost model for the more general case. For traffic modeling we use a two-phase Markovian Arrival Process, which is appropriate to model a fairly general correlated traffic.
Mathematics Subject Classification: Primary: 60K25, 68M20; Secondary: 90B22.

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