Robertazzi, T.G., Computer Networks and Systems: Queueing Theory and Performance Evaluation, Springer-Verlag, N.Y., 1990. Second edition: 1994. Third edition: 2000.
Contains sixty pages dealing with the algebraic topological structure of Markov chains of queueing and stochastic Petri networks.
Lazar, A.A. and Robertazzi, T.G., "The Geometry of Lattices for Markovian Queueing Networks," Columbia University Tech. Rep., 1984, SUNY at Stony Brook CEAS Tech. Rep. 471. Part A , Part B
Original work on this subject.
(1) Lazar, A.A. and Robertazzi, T.G., "The Geometry of Lattices for Multiclass Markovian Queueing Networks," Proceedings of the 1984 Information Sciences and Systems Conference, Princeton University, Princeton, March 1984, pp. 164-168.
(2) Lazar, A.A. "An Algebraic Topological Approach to Markovian Queueing Networks", Proceedings of the 1984 Information Sciences and Systems Conference, Princeton University, Princeton, March 1984, pp. 437-442,
(3) Wang, I.Y. and Robertazzi, T.G., "The Probability Flux Circulation of Certain Communication and Computation State Models," Proc. of 1986 Information Sciences and Systems Conf., Princeton University, Princeton, N.J., March 1986, pp. 865-870. Some corrections to this paper appear in the book above.
(4) Hamilton, R.L. and Coyle, E.J., "A Two-Hop Packet Radio Network with Product Form Solution", Proc. of 1986 Information Sciences and Systems Conf., Princeton University, Princeton, N.J., March 1986, pp. 871-876.
(5) Hamilton, R.L., Modeling and Analysis of Multihop and Priority Random Access Computer Networks, Ph.D. Dissertation, School of Electrical Engineering, Purdue University, 1986.
(6) Lazar, A.A. and Robertazzi, T.G., "The Algebraic and Geometric Structure of Markovian Petri Network Lattices," Twenty-Fourth Annual Allerton Conf. on Communication, Control and Computing, Urbana-Champaigne, Illinois, 1986.
(7) Ferrandiz, J.M. and Lazar, A.A., "Geometric Analysis of Quasi-Birth- and-Death Processes by Flow Redirection", Proc. of 1987 Information Sciences and Systems Conf., Johns Hopkins University, Baltimore Md., March 1987. pp. 865-870.
(8) Lazar, A.A. and Robertazzi, T.G., "Markovian Petri Net Protocols with Product Form Solution", IEEE INFOCOM '87, San Francisco, CA., March 1987. Journal version appears in Performance Evaluation, Vol. 12, 1991, pp. 67-77.
(9) Wang, I.Y. and Robertazzi, T.G., "Recursive Computation of Steady State Probabilities of Non Product Form Queueing Networks Associated with Computer Network Models", 30th Midwest Symposium on Circuits and Systems, Syracuse N.Y., Aug. 1987. Corrected and Revised Version in IEEE Transactions on Communications, Vol. 38, No. 1, Jan. 1990, pp. 155-117.
(10) Lazar, A.A. and Robertazzi, T.G., "The Lattice Structure of a Bus Oriented Multiprocessor System", Twenty-Fifth Annual Allerton Conf. on Communication, Control and Computing, Urbana-Champaigne, Illinois, 1987.
(11) Cheng, Y.C. and Robertazzi, T.G., "The Lattice Geometry of Petri Network Protocol Models of Multihop Radio Networks", 22nd Annual Conference on Information Sciences and Systems, Princeton N.J., March 1988, pp. 251-256.
(12) Hamilton Jr., R. L. and Yu, H.-C., "Analysis of a Two-Hop Packet Radio Network under Window Flow Control", 22nd Annual Conference on Information Sciences and Systems, Princeton N.J., March 1988, pp. 239-244.
(13) Jalloul, L, Hamilton Jr., R.L. and Yu, H-C., Product Form Solution for a Buffered Two-Node Slotted-Aloha Network", Tech. Rep. 1988-2, Dept. of Electrical Engineering, Ohio State University, July 1988.
(14) Hamilton Jr., R. L. and Yu, H.-C., "Improving the Performance of Packet Radio Networks with Adaptive Array Antennas", IEEE International Conference on Communications, Philadelphia PA, June 1988, pp. 189-193.
(15) Yu, H.-C., and Hamilton Jr., R.L., "A New Technique for the Analysis of a Buffered Two-Node Packet Radio Network", IEEE Globecom '88, Hollywood, Florida, Dec. 1988, pp. 1090-1094.
(16) Ni, R.-X., and Robertazzi, T.G., "Performance Evaluation of Three Related Protocols", 23rd Annual Conference on Information Sciences and Systems, Johns Hopkins University, Baltimore Md., March 1989.
(17) Robertazzi. T.G., "Recursive Solution of a Class of Non-Product Form Protocol Models", IEEE INFOCOM'89, Ottawa, Canada, April 1989, pp. 38-46.
(18) Yu, C. and Hamilton, R.L., A Buffered Two Node Packet Radio Network with Product Form Solution", IEEE INFOCOM'89, Ottawa, Canada, April 1989, pp. 520-528.
(19) Wang, I.Y. and Robertazzi, T.G., "Service Stage Petri Net Protocols with Product Form Solution", International Conference on Measurement and Modeling of Computer Systems, Berkeley CA, May 1989, one page abstract in Performance Evaluation Review, Special Issue Vol. 17, No. 1, May 1989, pg. 233. Extended version appears in Queueing Systems, 1990, pp. 355-374.
(20) Wang, I. and Hong, C.K., "A Decomposition Algorithm for the State Transition Lattices of Certain Non-Product Form Queueing Protocols", Proceedings of the 27th Annual Allerton Conference On Communication, Control and Computing, University of Illinois, Urbana-Champaign Ill., Oct. 1989.
(21) Pareek, S. and Robertazzi, T.G., "An Algorithm for the Exact Decomposition of a Class of Non-Product Form Queueing Models", Proceedings of the 1990 Conference on Information Sciences and Systems, Princeton N.J., March 1990.
(22) Yu, H-C., and Hamilton. R.L., "A Buffered Two-Node Packet Radio Network with Product Form Solution", IEEE Transactions on Communications, Vol. 39, No. 1, Jan. 1991, pp. 62-75.
(23) Robertazzi, T.G., "Why Most Stochastic Petri Nets are Non-Product Form Nets", SUNY at Stony Brook College of Engineering and Applied Science Tech. Rep. 598, March 8, 1991. Presented as a short paper at the 1991 Conference on Information Sciences and Systems, The Johns Hopkins University, Baltimore MD, March 1991. Also in the 1994 2nd ed. of the book above.
(24) Wang, I., "Decomposing Non-product Form Queueing Lattices Through Simulated Annealing", Proceedings of the 1991 Conference on Information Sciences and Systems, The Johns Hopkins University, Baltimore MD, March 1991 (short paper).
(25) Foo, E. and Robertazzi, T.G., "An Algebraic Topological Interpretation of Queueing Networks with Positive and Negative Customers", Proceedings of the 1996 Conference on Information Sciences and Systems, Princeton University, Princeton NJ, March 1996.
(26) Robertazzi, T.G., "Twinflow Markov Chain Decomposition for Tandem Queues with Blocking," Proceedings of the 2002 Conference on Information Sciences and Systems, Princeton University, Princeton NJ, March 2002 (paper available on this homepage).
(27) Caraballo, W. and Robertazzi, T.G., "Markov Chain Flow Decomposition for a Two Class Priority Queue," Proceedings of the 2003 Conference on Information Sciences and Systems, The Johns Hopkins Univesrity, Baltimore Maryland, March 2003 (paper available on this homepage).