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Successive Superposition: A Technique for the Exact Modeling of Deterministic Packet Queuing Networks
October 1996 (vol. 7 no. 10)
pp. 1106-1120
ASCII Text
x 
 
Dan Picker, Ronald D. Fellman, "Successive Superposition: A Technique for the Exact Modeling of Deterministic Packet Queuing Networks," IEEE Transactions on Parallel and Distributed Systems, vol. 7, no. 10, pp. 1106-1120, October, 1996.
 
 
BibTex
x
 
@article{ 10.1109/71.539741,
author = {Dan Picker and Ronald D. Fellman},
title = {Successive Superposition: A Technique for the Exact Modeling of Deterministic Packet Queuing Networks},
journal ={IEEE Transactions on Parallel and Distributed Systems},
volume = {7},
number = {10},
issn = {1045-9219},
year = {1996},
pages = {1106-1120},
doi = {http://doi.ieeecomputersociety.org/10.1109/71.539741},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Parallel and Distributed Systems
TI - Successive Superposition: A Technique for the Exact Modeling of Deterministic Packet Queuing Networks
IS - 10
SN - 1045-9219
SP1106
EP1120
EPD - 1106-1120
A1 - Dan Picker,
A1 - Ronald D. Fellman,
PY - 1996
KW - Asynchronous transfer mode
KW - interprocessor communication
KW - multiprocessor scheduling
KW - packet multiplexing
KW - packet queuing networks
KW - rate monotonic scheduling algorithm
KW - signal flow graphs.
VL - 7
JA - IEEE Transactions on Parallel and Distributed Systems
ER -
 

Abstract—This paper provides a methodology to decompose a complex network, containing primarily deterministic traffic, into isolated ΣDi/D/1 queuing models. We then present a new technique, Successive Superposition, to analyze the resulting models. In a ΣDi/D/1 queuing system, multiple streams of different bit rate, but constant length packets, arrive at a single high-speed multiplexer. Because of its application to Asynchronous Transfer Mode (ATM) switching nodes, previous ΣDi/D/1 analyses have assumed that stream arrivals are randomly staggered, and packets are served on a first-come-first-served basis. This work was, however, inspired primarily by the need for the accurate assessment of interprocessor communication costs in compile-time multiprocessor scheduling applications. For these applications, streams typically have known arrival times and must often be prioritized. This paper applies primarily to the class of digital signal processing and other applications which can be represented by directed, acyclic precedence graphs. The analysis presented in this paper provides an exact characterization of the traffic, including service start times, queue sizes, and system departure times. We confirm the validity of our approach against simulation results. Finally, we demonstrate the utility of this work in a compile-time multiprocessor scheduling application

[1] S. Banerjee, D. Picker, R.D. Fellman, and P.M. Chau, "Improved Scheduling of Signal Flow Graphs onto Multiprocessor Systems Through an Accurate Network Modelling Technique," VLSI Signal Processing VI, J. Robaey, P. Chau, and J. Eldon, eds., New York: IEEE Press, 1994.
[2] S. Banerjee, P.M. Chau, and R.D. Fellman, "Rapid Prototyping Methodology for Multiprocessor Implementation of Digital Signal Processing Systems," J. VLSI Signal Processing, vol. 11, Oct.-Nov. 1995.
[3] J.C. Bier, E.E. Goei, W.H. Ho, P.D. Lapsley, M.P. O'Reilly, G.C. Sih, and E.A. Lee, "Gabriel: A Design Environment for DSP," IEEE Micro, Oct. 1990.
[4] L.G. Dron, G. Ramamurthy, and B. Sengupta, "Delay Analysis of Continuous Bit Rate Traffic Over an ATM Network," IEEE J. Selected Areas in Comm., Apr. 1991.
[5] A.D. Eckberg, "The Single Server Queue with Periodic Arrival Process and Deterministic Service Times," IEEE Trans. Comm., vol. 27, Mar. 1979.
[6] D. Gustavson, “The Scalable Coherent Interface and Related Standards Projects,” IEEE Micro, Vol. 12, No. 1, Feb. 1992, pp. 10-22.
[7] T.C. Hu, "Parallel Sequencing and Assembly Line Problems," Operations Research, Nov. 1961.
[8] IEEE Std 1596-1992, Scalable Coherent Interface (SCI), IEEE, Piscataway, N.J., 1992.
[9] E.A. Lee and S. Ha, "Scheduling Strategies for Multiprocessor Real-Time DSP," Proc. IEEE Global Telecommunications Conf. (Globecom), Nov. 1989.
[10] D. Picker, R.D. Fellman, and P.M. Chau, "An Extension to the SCI Flow Control Protocol for Increased Network Efficiency," IEEE/ACM Trans. Networking, vol. 4, Feb. 1996.
[11] G. Ramamurthy and B. Sengupta, "Delay Analysis of a Packet Voice Multiplexer by theΣDi/D/1 Queue," IEEE Trans. Comm., vol. 39, July 1991.
[12] B. Sengupta, "A Queue with Superposition of Arrival Streams with an Application to Packet Voice Technology," Proc. Performance '90, 1990.
[13] G.C. Sih and E.A. Lee, “A Compile-Time Scheduling Heuristic for Interconnection-Constrained Heterogeneous Processor Architectures,” IEEE Trans. Parallel and Distributed Systems, vol. 4, no. 2, pp. 175-186, Feb. 1993.
[14] G.C. Sih and E.A. Lee, “Declustering: A New Multiprocessor Scheduling Technique,” IEEE Trans. Parallel and Distributed Systems, vol. 4, no. 6, pp. 625-637, June 1993.
[15] J.T. Virtamo and J.W. Roberts, "Evaluating Buffer Requirements in an ATM Multiplexer," Proc. IEEE Global Telecommunications Conf. (Globecom), Nov. 1989.

Index Terms:
Asynchronous transfer mode, interprocessor communication, multiprocessor scheduling, packet multiplexing, packet queuing networks, rate monotonic scheduling algorithm, signal flow graphs.
Citation:
Dan Picker, Ronald D. Fellman, "Successive Superposition: A Technique for the Exact Modeling of Deterministic Packet Queuing Networks," IEEE Transactions on Parallel and Distributed Systems, vol. 7, no. 10, pp. 1106-1120, Oct. 1996, doi:10.1109/71.539741
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