Analysis of the BMAP/G/1 queue with gated service and adaptive vacations duration

We consider a BMAP/G/1 type queueing model with gated service and duration of vacations depending on how many times in turn the system was empty at the previous vacation completion moments. We compute stationary distributions of the queue length at the embedded moments (vacation completions) and at arbitrary time as well as of a customer waiting time. The results of our analysis can be useful for determining strategy of adaptive choosing duration of sleep periods, e.g., in mobile networks where power consumption is an important issue.

[1]  D. van Dantzig.  Chaînes de Markof dans les ensembles abstraits et applications aux processus avec régions absorbantes et au problème des boucles , 1955 .

[2]  L. Javier García-Villalba,et al.  A proposal of a wireless sensor network routing protocol , 2008, PWC.

[3]  Srinivas R. Chakravarthy.  The Batch Markovian Arrival Process: A Review and Future Work , 2001 .

[4]  David M. Lucantoni,et al.  New results for the single server queue with a batch Markovian arrival process , 1991 .

[5]  Barry E. Mullins,et al.  A trajectory-based selective broadcast query protocol for large-scale, high-density wireless sensor networks , 2007, Telecommun. Syst..

[6]  Bong Dae Choi,et al.  Performance analysis of bandwidth requests under unicast, multicast and broadcast pollings in IEEE 802.16d/e , 2012, Telecommun. Syst..

[7]  Daniel P. Heyman,et al.  Modeling multiple IP traffic streams with rate limits , 2003, TNET.

[8]  Christoph Lindemann,et al.  Modeling IP traffic using the batch Markovian arrival process , 2003, Perform. Evaluation.

[9]  Dieter Fiems,et al.  Performance analysis of the IEEE 802.16e sleep mode for correlated downlink traffic , 2008, Telecommun. Syst..

[10]  H. Kesten,et al.  Priority in Waiting Line Problems 1). II , 1957 .

[11]  Antoine-S Bailly,et al.  Science régionale - Walter Isard, Introduction to régional science. Englewood Cliffs (NJ), Prentice-Hall, 1975 , 1975 .

[12]  Falah H. Ali,et al.  Collision Free Mobility Adaptive (CFMA) MAC for wireless sensor networks , 2013, Telecommun. Syst..

[13]  Markus Anwander,et al.  Evaluation of WiseMAC and extensions on wireless sensor nodes , 2010, Telecommun. Syst..

[14]  Valentina Klimenok,et al.  Approximate Method to Study M/G/1-Type Polling System with Adaptive Polling Mechanism , 2012 .

[15]  Adhir K Basu,et al.  Introduction to Stochastic Process , 2002 .

[16]  Miklós Telek,et al.  Analysis of BMAP vacation queue and its application to IEEE 802.16e sleep mode , 2010 .

[17]  Marcel F. Neuts,et al.  Some steady-state distributions for the MAP /SM /1 queue , 1994 .

[18]  A. N. Dudin,et al.  Queueing Model with Gated Service and Adaptive Vacations , 2009, 2009 IEEE International Conference on Communications Workshops.

[19]  V. M. Vishnevskii,et al.  A model of the polling system for studying the broadband wireless networks , 2006 .

[20]  Bong Dae Choi,et al.  Performance analysis of Push-To-Talk over IEEE 802.16e with  sleep mode and idle mode , 2011, Telecommun. Syst..

[21]  Marcel F. Neuts,et al.  Structured Stochastic Matrices of M/G/1 Type and Their Applications , 1989 .

[22]  Hideaki Takagi,et al.  Queueing analysis: a foundation of performance evaluation , 1993 .

[23]  Alexander N. Dudin,et al.  Performance analysis of the BMAP/G/1 queue with gated servicing and adaptive vacations , 2011, Perform. Evaluation.