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DELAY ANALYSIS OF A MULTIMEDIA ATM MULTIPLEXER WITH HOMOGENEOUS ARRIVALS

HAMED NASSAR

Faculty of Computers and Informatics, Suez Canal University, Ismailia, Egypt

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and

HASAN AL MAHDI

Faculty of Petroleum and Mining, Suez Canal University, Suez, Egypt

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https://doi.org/10.1142/S0218126604001842Cited by:2 (Source: Crossref)

Abstract

In this paper we present a delay analysis of an ATM multiplexer handling multimedia traffic of two classes: real time class, e.g., live audio and video and nonreal time class, e.g., file transfers. Packets arrive into the multiplexer in batches of general size and are output one at a time. The arrivals are homogeneous in the sense that either the arriving batch is all class-1 packets or all class-2 packets. The multiplexer is modeled as a priority discrete time queueing system with batch arrivals and geometric service. The homogeneity of the arrivals is reflected by the addition of an indicator random variable into the model. The analysis is comprehensive in that it covers the three main delay measures: the unfinished work, the busy period and the waiting time. For these measures, probability generating functions are derived, from which moments of arbitrary orders can be obtained. However, only the first moments are obtained in the article to produce expected values. Presented at the end is a special case when the arriving batches are of Poissonian size. Some numerical values are obtained and plotted for this case.

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References

M. De Prycker, Asynchronous transfer mode: Solution for broadband ISDN, Int. Conf. Telecommunication Systems (MASCOTS '94), Chichester, January 1994 . Google Scholar
K. Eddie and L. Gracia, IEEE Proc. INFOCOM 2, 663 (1996). Google Scholar
C. Kruskal and M. Snir, IEEE Trans. Comput. 37, 1347 (1988). Google Scholar
H. Nassar and H. Al Mahdi, Math. Comput. Modelling of Dynamical Syst. 8, 199 (2002). Crossref, Web of Science, Google Scholar
H. Nassar and M. Ali, Int. J. Electron. Commun. (AEU) 57, 190 (2003). Crossref, Web of Science, Google Scholar
H. Bruneel, Comput. Oper. Res. 20, 303 (1993). Crossref, Web of Science, Google Scholar
B. Steyaert and Y. Xiong, Perfor. Eval. 27, 277 (1996). Google Scholar
I. Cidon, A. Khamisy and M. Sidi, Perfor. Eval. 29, 85 (1997). Crossref, Web of Science, Google Scholar
M. Chaudhry and U. Gupta, INFORMS J. Comput. 13, 172 (2001). Crossref, Web of Science, Google Scholar
T. Takine and B. Sengupta, IEEE Trans. Commun. 42, 837 (1994). Google Scholar
F. Ishizaki and T. Takine, Perfor. Eval. 23, 121 (1995). Crossref, Web of Science, Google Scholar
J. Lee and C. Un, IEE Proc. Commun. 177, 229 (1997). Google Scholar
Y. Lee and B. Choi, Inform. Sci. 138, 7 (2001). Crossref, Web of Science, Google Scholar
Y. Lee and D. Sung, IEEE. Proc. Commun. 145, 331 (1998). Google Scholar
M. Takahashi, H. Osawa and T. Fujisawa, Asia Pacific J. Oper. Res. 16, 215 (1999). Web of Science, Google Scholar
H. Nassar and H. Al Mahdi, IEE Proc. Commun. 150, 189 (2003). Crossref, Google Scholar
J. Walraevens, B. Steyaert and H. Bruneel, Belgian J. Oper. Res., Stat. Comput. Sci. (JORBEL) 40, 140 (2000). Web of Science, Google Scholar
Y. Lee, Math. Comput. Modelling 34, 243 (2001). Crossref, Web of Science, Google Scholar
M. Woodward , Communication and Computer Networks ( IEEE Comput. Society Press , New York , 1994 ) . Google Scholar
H. Takagi , Queueing Analysis 1 ( Elsevier Science Publishers , B. V., Amsterdam , 1991 ) . Google Scholar