Non-stationary departure process in a batch-arrival queue with finite buffer capacity and threshold-type control mechanism

Wojciech M. Kempa; Dariusz Kurzyk

Kybernetika (2022)

  • Volume: 58, Issue: 1, page 82-100
  • ISSN: 0023-5954

Abstract

top
Non-stationary behavior of departure process in a finite-buffer M X / G / 1 / K -type queueing model with batch arrivals, in which a threshold-type waking up N -policy is implemented, is studied. According to this policy, after each idle time a new busy period is being started with the N th message occurrence, where the threshold value N is fixed. Using the analytical approach based on the idea of an embedded Markov chain, integral equations, continuous total probability law, renewal theory and linear algebra, a compact-form representation for the mixed double transform (probability generating function of the Laplace transform) of the probability distribution of the number of messages completely served up to fixed time t is obtained. The considered queueing system has potential applications in modeling nodes of wireless sensor networks (WSNs) with battery saving mechanism based on threshold-type waking up of the radio. An illustrating simulational and numerical study is attached.

How to cite

top

Kempa, Wojciech M., and Kurzyk, Dariusz. "Non-stationary departure process in a batch-arrival queue with finite buffer capacity and threshold-type control mechanism." Kybernetika 58.1 (2022): 82-100. <http://eudml.org/doc/297536>.

@article{Kempa2022,
abstract = {Non-stationary behavior of departure process in a finite-buffer $M^\{X\}/G/1/K$-type queueing model with batch arrivals, in which a threshold-type waking up $N$-policy is implemented, is studied. According to this policy, after each idle time a new busy period is being started with the $N$th message occurrence, where the threshold value $N$ is fixed. Using the analytical approach based on the idea of an embedded Markov chain, integral equations, continuous total probability law, renewal theory and linear algebra, a compact-form representation for the mixed double transform (probability generating function of the Laplace transform) of the probability distribution of the number of messages completely served up to fixed time $t$ is obtained. The considered queueing system has potential applications in modeling nodes of wireless sensor networks (WSNs) with battery saving mechanism based on threshold-type waking up of the radio. An illustrating simulational and numerical study is attached.},
author = {Kempa, Wojciech M., Kurzyk, Dariusz},
journal = {Kybernetika},
keywords = {departure process; finite-buffer queue; $N$-policy; power saving; transient state; wireless sensor network (WSN)},
language = {eng},
number = {1},
pages = {82-100},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Non-stationary departure process in a batch-arrival queue with finite buffer capacity and threshold-type control mechanism},
url = {http://eudml.org/doc/297536},
volume = {58},
year = {2022},
}

TY - JOUR
AU - Kempa, Wojciech M.
AU - Kurzyk, Dariusz
TI - Non-stationary departure process in a batch-arrival queue with finite buffer capacity and threshold-type control mechanism
JO - Kybernetika
PY - 2022
PB - Institute of Information Theory and Automation AS CR
VL - 58
IS - 1
SP - 82
EP - 100
AB - Non-stationary behavior of departure process in a finite-buffer $M^{X}/G/1/K$-type queueing model with batch arrivals, in which a threshold-type waking up $N$-policy is implemented, is studied. According to this policy, after each idle time a new busy period is being started with the $N$th message occurrence, where the threshold value $N$ is fixed. Using the analytical approach based on the idea of an embedded Markov chain, integral equations, continuous total probability law, renewal theory and linear algebra, a compact-form representation for the mixed double transform (probability generating function of the Laplace transform) of the probability distribution of the number of messages completely served up to fixed time $t$ is obtained. The considered queueing system has potential applications in modeling nodes of wireless sensor networks (WSNs) with battery saving mechanism based on threshold-type waking up of the radio. An illustrating simulational and numerical study is attached.
LA - eng
KW - departure process; finite-buffer queue; $N$-policy; power saving; transient state; wireless sensor network (WSN)
UR - http://eudml.org/doc/297536
ER -

References

top
  1. Abate, J., L., G., Choudhury, Whitt, W., , In: Computational Probability (W. Grassmann, ed.), Kluwer, Boston 2000, pp. 257-323. DOI
  2. Arumuganathan, R., Jeyakumar, S., , Appl. Math. Model. 29 (2005), 972-986. MR2038103DOI
  3. Choudhury, G., Baruah, H. K., , Sankhya Ser. B 62 (2000), 303-316. MR1802636DOI
  4. Choudhury, G., Borthakur, A., Stochastic decomposition results of batch arrival Poisson queue with a grand vacation process., Sankhya Ser. B 62 (2000), 448-462. MR1834167
  5. Choudhury, G., Paul, M., , Appl. Math. Comput. 156 (2004), 115-130. MR2087256DOI
  6. Cohen, J. W., The Single Server Queue., North-Holland, Amsterdam 1982. MR0668697
  7. Doshi, B. T., , Queueing Syst. 1 (1986), 29-66. MR0896237DOI
  8. García, Y. H., Diaz-Infante, S., Minjárez-Sosa, J. A., , Kybernetika 57 (2021), 493-512. MR4299460DOI
  9. Gerhardt, I., Nelson, B. L., , Informs J. Comput. 21 (2009), 630-640. MR2588345DOI
  10. Jiang, F. C., Huang, D. C., Yang, C. T., Leu, F. Y., , J. Supercomput. 59 (2012), 1312-1335. DOI
  11. Ke, J.-C., , Math. Method. Oper. Res. 54 (2001), 471-490. MR1890915DOI
  12. Ke, J.-C., Wang, K.-H., , Eur. J. Oper. Res. 142 (2002), 577-594. MR1922375DOI
  13. Kempa, W. M., , Stoch. Anal. Appl. 22 (2004), 1235-1255. MR2089066DOI
  14. Kempa, W. M., , Math. Meth. Oper. Res. 69 (2009), 81-97. Zbl1170.60032MR2476049DOI
  15. Kempa, W. M., , Commun. Stat. Theory 40 (2011), 2856-2865. MR2860790DOI
  16. Kempa, W. M., , Math. Commun. 17 (2012), 285-302. MR2946149DOI
  17. Kempa, W. M., , Kybernetika 50 (2014), 126-141. MR3195008DOI
  18. Kempa, W. M., , Perform. Eval. 108 (2017), 1-15. DOI
  19. Kempa, W. M., Kurzyk, D., , In: Software, Telecommunications and Computer Networks (SoftCOM), 2015, 23rd International Conference on IEEE, pp. 32-36. DOI
  20. Korolyuk, V. S., 10.1137/1119001, Theor. Probab. Appl. 19 (1974), 1-13. MR0402939DOI10.1137/1119001
  21. Reddy, G. V. Krishna, Nadarajan, R., Arumuganathan, R., , Comput. Oper. Res. 25 (1998), 957-967. MR1638645DOI
  22. Lee, H. W., Lee, S. S., Chae, K. C., , Queueing Syst. 15 (1994), 387-399. MR1266802DOI
  23. Lee, H. W., Lee, S. S., Park, J. O., Chae, K. C., , J. Appl. Prob. 31 (1994), 467-496. MR1274803DOI
  24. Lee, S. S., Lee, H. W., Chae, K. C., , Comput. Oper. Res. 22 (1995), 173-189. DOI
  25. Lee, H. S., Srinivasan, M. M., , Manag. Sci. 35 (1989), 708-721. MR1001484DOI
  26. Levy, Y., Yechiali, U., , Manag. Sci. 22 (1975), 202-211. DOI
  27. Maheswar, R., Jayaparvathy, R., Power control algorithm for wireless sensor networks using N -policy M / M / 1 queueing model., Power 2 (2010), 2378-2382. 
  28. Nasr, W. W., Taaffe, M. R., , Informs J. Comput. 25 (2013), 758-773. MR3120933DOI
  29. Takagi, H., Queueing Analysis: A Foundation of Performance Evaluation, Vacation and Priority Systems, Part I, vol. I., North-Holland, Amsterdam 1991. MR1149382
  30. Takagi, H., , Queueing Syst. 14 (1993), 79-98. MR1238663DOI
  31. Tian, N., Zhang, Z. G., Vacation Queueing Models: Theory and Applications., Springer, 2006. MR2248264
  32. Yadin, M., Naor, P., , J. Oper. Res. Soc. 14 (1963), 393-405. DOI
  33. Yang, D.-Y., Cho, Y.-Ch., , Comput. J. 62 (2019), 130-143. MR3897421DOI

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.