Decomposition of network of queues with self-similar traffic

Jackson's (1957) network of queues model greatly simplifies the performance analysis of telecommunication networks with Poisson traffic arrivals and exponential service times. It reduces the analysis of a network into the analysis of individual communication links, each of which may be modeled as an M/M/m queue. Motivation by the growing significance of self-similar traffic in modeling broadband network traffic, we propose a new network of queued model for telecommunication networks. Our model resembles Jackson's model except that the arrival is self-similar and the service time is deterministic. it captures the characteristics of modern high speed cell-based networks. We hypothesize a result analogous to Jackson's theorem, that each node of this network model behaves as a G/D/1 queue with self-similar arrival. Based on this hypothesis, many network-wide performance measures , such as the end-to-end delay, can be evaluated in a simple fashion. Our hypothesis is strongly supported by three facts, namely the sum of independent self-similar processes, the random splitting of self-similar processes, and the output process of a deterministic service time queue with self-similar input are all self-similar.

[1]  Ilkka Norros,et al.  A storage model with self-similar input , 1994, Queueing Syst. Theory Appl..

[2]  C. Granger,et al.  AN INTRODUCTION TO LONG‐MEMORY TIME SERIES MODELS AND FRACTIONAL DIFFERENCING , 1980 .

[3]  Michael Devetsikiotis,et al.  Modeling and simulation of self-similar variable bit rate compressed video: a unified approach , 1995, SIGCOMM '95.

[4]  Walter Willinger,et al.  Self-Similarity in High-Speed Packet Traffic: Analysis and Modeling of Ethernet Traffic Measurements , 1995 .

[5]  Nicolas D. Georganas,et al.  On self-similar traffic in ATM queues: definitions, overflow probability bound, and cell delay distribution , 1997, TNET.

[6]  Walter Willinger,et al.  Long-range dependence in variable-bit-rate video traffic , 1995, IEEE Trans. Commun..

[7]  K. Meyer.  The Output of a Queueing System , 1981 .

[8]  J. R. Jackson.  Networks of Waiting Lines , 1957 .

[9]  Nick Duffield,et al.  Large deviations and overflow probabilities for the general single-server queue, with applications , 1995 .

[10]  P. Burke.  The Output of a Queuing System , 1956 .

[11]  Nicolas D. Georganas,et al.  On merging and splitting of self-similar traffic in high-speed networks , 1995 .

[12]  Gennady Samorodnitsky,et al.  Performance Decay in a Single Server Exponential Queueing Model with Long Range Dependence , 1997, Oper. Res..

[13]  Sally Floyd,et al.  Wide area traffic: the failure of Poisson modeling , 1995, TNET.

[14]  Mark W. Garrett,et al.  Modeling and generation of self-similar vbr video traffic , 1994, SIGCOMM 1994.

[15]  Walter Willinger,et al.  On the self-similar nature of Ethernet traffic , 1993, SIGCOMM '93.

[16]  Murad S. Taqqu,et al.  On the Self-Similar Nature of Ethernet Traffic , 1993, SIGCOMM.

[17]  Ilkka Norros,et al.  On the Use of Fractional Brownian Motion in the Theory of Connectionless Networks , 1995, IEEE J. Sel. Areas Commun..

[18]  San-qi Li,et al.  The linearity of low frequency traffic flow: an intrinsic I/O property in queueing systems , 1997, TNET.

[19]  B. Mandelbrot,et al.  Fractional Brownian Motions, Fractional Noises and Applications , 1968 .

[20]  Walter Willinger,et al.  Proof of a fundamental result in self-similar traffic modeling , 1997, CCRV.