Abstract
In this paper, we consider a discrete-time queueing model with infinite waiting room and one single output channel. Users from an infinite user population can start and end sessions during which they are active and send packets to a buffer system. Each active user generates a random but strictly positive number of packets per time slot. The queueing model is applied to study the traffic of a web server, where each session corresponds to one file download. This approach has the advantage of leading to analytical expressions for the main performance measures (buffer occupancy, delay, ...) of the output buffer of the web server. Specifically, in this paper, a closed-form expression for the mean session delay is obtained. We then apply the model to a web server, based on a trace of actual web traffic. Using the model, we can rapidly study the influence of the different system parameters and compare various alternatives.
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References
Allman, M., Paxson, V., Stevens, W.: TCP Congestion Control. RFC 2581, Proposed Standard (1999)
Arlitt, M., Williamson, C.: Internet Web Servers: Workload Characterization and Performance Implications. IEEE/ACM Transactions on Networking 5, 631–645 (1997)
Bruneel, H.: Packet Delay and Queue Length for Statistical Multiplexers with Low-Speed Access Lines. Computer Networks and ISDN Systems 25, 1267–1277 (1993)
Bruneel, H.: Calculation of Message Delays and Message Waiting Times in Switching Elements with Slow Access Lines. IEEE Transactions on Communications 42, 255–259 (1994)
Bruneel, H., Kim, B.G.: Discrete-Time Models for Communication Systems Including ATM. Kluwer Academic Publishers, Boston (1993)
Choi, B.D., Choi, D.I., Lee, Y., Sung, D.K.: Priority Queueing System with Fixed-Length Packet-Train Arrivals. IEE Proceedings-Communications 145, 331–336 (1998)
Crovella, M.E., Bestavros, A.: Self-similarity in World Wide Web Traffic: Evidence and Possible Causes. IEEE/ACM Transactions on Networking 5, 835–846 (1997)
Daigle, J.: Message Delays at Packet-Switching Nodes Serving Multiple Classes. IEEE Transactions on Communications 38, 447–455 (1990)
De Vuyst, S., Wittevrongel, S., Bruneel, H.: Statistical Multiplexing of Correlated Variable-Length Packet Trains: an Analytic Performance Study. Journal of the Operational Research Society 52, 318–327 (2001)
De Vuyst, S., Wittevrongel, S., Bruneel, H.: Mean Value and Tail Distribution of the Message Delay in Statistical Multiplexers with Correlated Train Arrivals. Performance Evaluation 48, 103–129 (2002)
Hoflack, L., De Vuyst, S., Wittevrongel, S., Bruneel, H.: System Content and Packet Delay in Discrete-Time Queues with Session-Based Arrivals. In: 5th International Conference on Information Technology, ITNG 2008. Las Vegas (2008)
Kamoun, F.: Performance Analysis of a Discrete-Time Queuing System with a Correlated Train Arrival Process. Performance Evaluation 63, 315–340 (2006)
Takagi, H.: Queueing Analysis – A Foundation of Performance Evaluation. In: Discrete-Time Systems, vol. 3. North-Holland, Amsterdam (1993)
Walraevens, J., Wittevrongel, S., Bruneel, H.: A Discrete-Time Priority Queue with Train Arrivals. Stochastic Models 23, 489–512 (2007)
Wittevrongel, S.: Discrete-Time Buffers with Variable-Length Train Arrivals. Electronics Letters 34, 1719–1721 (1998)
Wittevrongel, S., Bruneel, H.: Correlation Effects in ATM Queues due to Data Format Conversions. Performance Evaluation 32, 35–56 (1998)
Xiong, Y., Bruneel, H.: Buffer Behaviour of Statistical Multiplexers with Correlated Train Arrivals. International Journal of Electronics and Communications 51, 178–186 (1997)
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Hoflack, L., De Vuyst, S., Wittevrongel, S., Bruneel, H. (2008). Modeling Web Server Traffic with Session-Based Arrival Streams. In: Al-Begain, K., Heindl, A., Telek, M. (eds) Analytical and Stochastic Modeling Techniques and Applications. ASMTA 2008. Lecture Notes in Computer Science, vol 5055. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68982-9_4
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DOI: https://doi.org/10.1007/978-3-540-68982-9_4
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