We study the message queueing delays in a node of a communication system, where a message consists of a block of consecutive packets. The message delay is defined as the time elapsing between the arrival epoch of the first packet of the message to the system until after the transmission of the last packet of that message is completed. We distinguish between two types of message generation processes. The message can be generated as abatch or it can bedispersed over time. In this paper we focus on the dispersed generation model. The main difficulty in the analysis is due to the correlation between the system states observed by different packets of the same message. This paper introduces a new technique to analyze the message delay in such systems for different arrival models and different number of sessions. For anM/M/1 system with variable size messages and for the bursty traffic model, we obtain an explicit expression for the Laplace-Stieltjes transform (LST) of the message delay. Derivations are also provided for anM/G/1 system, for multiple session systems and for fixed message sizes. We show that the correlation has a strong effect on the performance of the system, and that the commonly usedindependence assumption, i.e., the assumption that the delays of packets are independent from packet to packet, can lead to wrong conclusions.
KeywordsMessage delay dispersed messages M/M/1 M/G/1 bursty traffic
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- L.V. Ahlfors,Complex Analysis, 3rd ed. (McGraw-Hill International Editions, 1979).Google Scholar
- D. Bertsekas and R. Gallager,Data Networks (Prentice-Hall International Editions, 1987).Google Scholar
- CCITT SG XVIII, Draft Recommendation 1.121: Broadband Aspects of ISDN, Geneva, (January 1990).Google Scholar
- D. Comer,Internetworking with TCP/IP, Principles, Protocols, and Architectures (Prentice-Hall, Englewood Cliffs, NJ, 1988).Google Scholar
- I. Cidon, A. Khamisy and M. Sidi, On packet loss processes in high-speed networks, IEEE Trans. Information Theory 39 (1) (1993) 98–108.Google Scholar
- S. Halfin, Batch delays versus customer delays, Bell Syst. Tech. J. 62 (September 1983).Google Scholar
- L. Kleinrock,Queueing Systems, Vol. 1 (Wiley, New York, 1975).Google Scholar
- R. Rom and M. Sidi,Multiple Access Protocols; Performance and Analysis (Springer, Berlin, 1990).Google Scholar
- K. Sohraby, Delay analysis of a single server queue with poisson cluster arrival process arising in ATM networks, in:GLOBECOM'89 (1989) pp. 611–616.Google Scholar
- G.M. Woodruff, R.G.H. Rogers and P.S. Richards, A congestion control framework for high-speed integrated packetized transport, in:GLOBECOM'88 (1988) pp. 203–207.Google Scholar