Logo PTI
Polish Information Processing Society
Logo FedCSIS

Annals of Computer Science and Information Systems, Volume 8

Proceedings of the 2016 Federated Conference on Computer Science and Information Systems

Time-Dependent Queue-Size Distribution in a Finite-Buffer Model with Server Setup Times


DOI: http://dx.doi.org/10.15439/2016F194

Citation: Proceedings of the 2016 Federated Conference on Computer Science and Information Systems, M. Ganzha, L. Maciaszek, M. Paprzycki (eds). ACSIS, Vol. 8, pages 10151019 ()

Full text

Abstract. Transient queue-size distribution in a finite-buffer system with Poisson arrivals and generally distributed processing times is investigated. In the evolution of the system the server needs randomly distributed setup times preceding the service initialization in each new busy period. Applying the paradigm of embedded Markov chain and the formula of total probability, a Volterra-type system of integral equations for the transient queue-size distribution, conditioned by the number of packets being accumulated in the buffer before the opening of the system, is built. The solution of the corresponding system written for Laplace transforms is obtained algebraically in the compact explicit form. Numerical examples are attached as well.


  1. E. P. Edward, “A Novel Seamless Handover Scheme for WiMAX/LTE Heterogeneous Networks,” Arab. J. Sci. Eng., vol. 41, iss. 3, 2016, pp. 1129–1143.
  2. J. N. Hu and P. D. Tuan, “Power Consumption Analysis for data Centers with Independent Setup Times and Threshold Controls,” AIP Conference Proceedings, vol. 1648, 2015.
  3. W. M. Kempa, “On Transient Queue-Size Distribution in the Batch Arrival System with the N -policy and Setup Times,” Math. Commun., vol. 17, iss. 1, 2012, 285–302.
  4. W. M. Kempa and D. Kurzyk, “Transient Departure Process in M/G/1/K-type Queue with Threshold Server’s Waking Up,” Proc. of the 23rd International Conference on Software, Telecommunications and Computer Networks (SoftCOM 2015),Split - Bol (Island of Brac), Croatia, 2015, pp. 32–36, http://dx.doi.org/10.1109/SOFTCOM.2015.7314127.
  5. V. S. Korolyuk, Boundary-value problems for compound Poisson processes, Naukova Dumka, Kiev, 1975.
  6. Q. Ma, “Analysis of a Clearing Queueing System with Setup Times,” RAIRO-Oper. Res., vol. 49, iss. 1, 2015, pp. 67–76, http://dx.doi.org/10.1051/ro/2014035.
  7. J. Miček and J. Kapitulík, “WSN Sensor Node for Protected Area Monitoring,” Proc. of FedCSIS 2012, 803–807.
  8. Z. S. Niu and X. Y. Guo and S. Zhou and P. R. Kumar, “Characterizing Energy-Delay Tradeoff in Hyper-Cellular Networks With Base Station Sleeping Control,” IEEE J. Sel. Area Comm., vol. 33, iss. 4, 2015, 641–650, http://dx.doi.org/10.1109/JSAC.2015.2393494.
  9. M. Salayma and A. Al-Dubai and I. Romdhani and M. B. Yassein, “Battery Aware Beacon Enabled IEEE802.15.4: An Adaptive and Cross-Layer Approach,” Proc. of FedCSIS 2015, 1267–1272, http://dx.doi.org/10.15439/2015F118.
  10. W. Sun and P. F. Guo and N. S. Tian, “Equilibrium Threshold Strategies in Observable Queueing Systems with Setup/Closedown Times,” Cent. Europ. J. Oper. Re., vol. 18, iss. 3, 2010, pp. 241–268, http://dx.doi.org/10.1007/s10100-009-0104-4.
  11. Q. T. Sun and S. F. Jin and C. Chen, “Energy Analysis of Sensor Nodes in WSN Based on Discrete-Time Queueing Model with a Setup,” Proc. of 22nd Chinese Control and Decision Conference, Xuzhou, China, vols. 1–5, 2010, pp. 4114-4118, http://dx.doi.org/10.1109/CCDC.2010.5498425.
  12. W. Y. Yue and Q. T. Sun and S. F. Jin, “Performance Analysis of Sensor Nodes in a WSN With Sleep/Wakeup Protocol,” Lect. Notes Oper. Res., vol. 12, 2010, pp. 370–377.
  13. M. Zieliński and F. Mieyeville and D. Navarro and O. Bareille, “A Low Power Wireless Sensor Node with Vibration Sensing and Energy Harvesting Capability,” Proc. of FedCSIS 2014, 1065–1071.