Abstract
Discrete-time queues are commonly used in the performance analysis of many computer and communications systems. As the independent and identically distributed (i.i.d.) arrival traffic model frequently adopted (due to its analytical tractability) in the literature does not capture some important properties of real-world traffics, such as self-similarity, long-range dependence, and burstiness, it is more realistic to model the arrival traffic as a time-correlated process.
A widely used time-correlated arrival traffic model is the ON-OFF traffic model as it is capable of capturing the burstiness of real-world traffics. In particular, it is commonly adopted for modeling voice traffics, where the talker is speaking (resp., silent) in the ON (resp., OFF) periods. In this paper, we present the performance analysis of a finite-buffer queue with ON-OFF Markovian arrival traffic and geometric service times, called ON-OFF/Geom/1/B queue in this paper. We derive closed-form expressions for the packet loss probability and the average packet delay. The closed-form expressions are given in term of the buffer size of the queue, the characterizing parameters of the ON-OFF Markovian traffic, and the service rate.
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References
Hunter, J.J.: Mathematical Techniques of Applied Probability, vol. 2. Academic Press, New York (1983)
Bruneel, H., Kim, B.G.: Discrete-Time Models for Communication Systems Including ATM. Kluwer Academic Publishers, Boston (1993)
Takagi, H.: Queueing Analysis, A Foundation of Performance Evaluation, vol. 3. North-Holland, Amsterdam (1993)
Rubin, I., Zhang, Z.: Message delay and queue-size analysis for circuit-switched TDMA systems. IEEE Trans. Commun. 39, 905–914 (1991)
Rubin, I., Zhang, Z.: Message delay analysis for TDMA schemes using contiguous-slot assignments. IEEE Trans. Commun. 40, 730–737 (1992)
Neuts, M., Guo, J., Zukerman, M., Vu, H.L.: The waiting time distribution for a TDMA model with a finite buffer and state-dependent service. IEEE Trans. Commun. 53, 1522–1533 (2005)
Andersen, A.T., Nielsen, B.F.: A Markovian approach for modeling packet traffic with long-range dependence. IEEE J. Sel. Areas Commun. 16, 719–732 (1998)
Heffes, H., Lucantoni, D.M.: A Markov modulated characterization of packetized voice and data traffic and related statistical multiplexer performance. IEEE J. Sel. Areas Commun. 4, 856–868 (1986)
Daigle, J.N., Langford, J.D.: Models for analysis of packet voice communications systems. IEEE J. Sel. Areas Commun. 4, 847–855 (1986)
Sriram, K., Whitt, W.: Characterizing superposition arrival processes in packet multiplexers for voice and data. IEEE J. Sel. Areas Commun. 4, 833–846 (1986)
Ren, Q., Ramamurthy, G.: A real-time dynamic connection admission controller based on traffic modeling, measurement, and fuzzy logic control. IEEE J. Sel. Areas Commun. 18, 184–196 (2000)
Chaskar, H.M., Madhow, U.: Statistical multiplexing and QoS provisioning for real-time traffic on wireless downlinks. IEEE J. Sel. Areas Commun. 19, 347–354 (2001)
Sheu, S.-T., Sheu, T.-F.: A bandwidth allocation/sharing/extension protocol for multimedia over IEEE 802.11 ad hoc wireless LANs. IEEE J. Sel. Areas Commun. 19, 2065–2080 (2001)
Sze, H.P., Liew, S.C., Lee, J.Y.B., Yip, D.C.S.: A multiplexing scheme for H.323 voice-over-IP applications. IEEE J. Sel. Areas Commun. 20, 1360–1368 (2002)
Wang, Y., Chan, S., Zukerman, M., Harris, R.J.: Priority-based fair scheduling for multimedia WiMAX uplink traffic. In: Proceedings IEEE International Conference on Communications (ICC 2008), Beijing, China, pp. 301–305 (2008)
Bruneel, H.: Queueing behavior of statistical multiplexers with correlated inputs. IEEE Trans. Commun. 36, 1339–1341 (1988)
Sohraby, K.: On the theory of general ON-OFF sources with applications in high-speed networks. In: Proceedings IEEE International Conference on Computer Communications (INFOCOM 1993), San Francisco, CA, USA, pp. 401–410 (1993)
Guo, Z., Zhang, Z., Yang, Y.: Performance modeling of hybrid optical packet switches with shared buffer. In: Proceedings IEEE International Conference on Computer Communications (INFOCOM 2011), Shanghai, China, pp. 1692–1700 (2011)
Resnick, S.I.: Adventures in Stochastic Processes. Birkhaüser, Boston (1992)
Gross, D., Shortle, J.F., Thompson, J.M., Harris, C.M.: Fundamentals of Queueing Theory, 4th edn. John Wiley & Sons, New York (2008)
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Yang, SH., Cheng, J., Chou, HH., Cheng, CH. (2013). Loss Probability and Delay of Finite-Buffer Queues with Discrete ON-OFF Markovian Arrivals and Geometric Service Times. In: Guyot, V. (eds) Advanced Infocomm Technology. ICAIT 2012. Lecture Notes in Computer Science, vol 7593. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38227-7_12
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DOI: https://doi.org/10.1007/978-3-642-38227-7_12
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