In order to design better communication networks, it is important to be able to evaluate network performance. This area of research focuses on methodologies to model the performance of communication networks. The methodologies may involve applied mathematical analysis, computer simulation studies, empirical measurements, or combinations of these techniques. We have made a rough division of this area into two closely related sub-areas: 1) Traffic characterization and regulation; 2) Queueing models and network performance.

Traffic characterization deals with ways of describing traffic flows mathematically in order to determine their impact on network performance. One of the earliest and simplest traffic models that have been applied to communication networks is the Poisson process, which was used to characterize the arrivals of calls at a telephone exchange by Erlang, Kosten, and others. Modern communication networks are much more complicated than the telephone exchanges of the past. Traffic patterns in data networks, for example, have been seen to exhibit properties such as burstiness, correlation, and self-similarity, which necessitate the development of more sophisticated traffic models. Traffic models can be used to generate synthetic traffic traces to drive simulations of networks and also to perform network resource allocation. The particular application of a traffic model determines the trade-off between model accuracy and complexity. In modern networks, traffic regulation (also called traffic policing) has been developed to simplify traffic characterization and to provide quality-of-service guarantees by enforcing bounds on the resource usage of a given traffic stream. Our work in this area has dealt with formulating new measures of traffic burstiness [MJR97a, MJR97b], developing methods for real-time traffic characterization and regulation [MarkRam96, MarkRam98a, MarkRam98b]. More recently, we have been studying a new class of efficient traffic regulators with constant time implementation [CMS02].

[CMS02] F. Ciucu, B.L. Mark, and R.P. Simon, "The Partially Stopped Leaky
Bucket: An Efficient Traffic Regulator with Constant Time Implementation," in *
Proc. Int. Symp. on Performance Evaluation of Computer and Telecommunication
Systems (SPECTS'02)*, pp. 155-161, San Diego, July 2002.

[MarkRam98b] B.L. Mark and G. Ramamurthy, "Real-time Estimation and Dynamic
Renegotiation of UPC Parameters for Arbitrary Traffic Sources in ATM Networks,"
*IEEE/ACM Trans. on Networking*, Vol. 6, No. 6, pp. 811-827, Dec. 1998.

[MarkRam98a] B.L. Mark and G. Ramamurthy, "Real-time Traffic Characterization for Quality-of-Service Control in ATM Networks," IEICE Trans. on Comm., Vol. E81-B, No. 5, pp. 832-839, May 1998.

[MJR97b] B.L. Mark, D.L. Jagerman and G. Ramamurthy,
"Application of Peakedness Measures to Resource Allocation in
High-Speed Networks,"
in *Proc. 15-th Int. Teletraffic Congress*,
(Washington D.C.), June 1997.

[MJR97a] B.L. Mark, D.L. Jagerman and G. Ramamurthy,
"Peakedness Measures for Traffic Characterization in High-Speed Networks,"
in *Proc. IEEE INFOCOM'97*, (Kobe), April 1997.

[MarkRam96] B.L. Mark and G. Ramamurthy, "UPC-based traffic descriptors for
ATM: How to determine, interpret and use them," *Telecommunications Systems*, Vol.
5, pp. 109-122, 1996.

Queueing or teletraffic theory studies mathematically the interaction between an arrival process (e.g., the traffic) and a server process (e.g., the network). The theory is concerned with calculating measures of delay, loss, and resource usage (e.g., queue length) and has been applied to many areas besides communication networks, e.g., manufacturing, transportation networks, etc. In classical queueing theory, perhaps the simplest system is the M/M/1 queue, a single server queue with Poisson arrivals and exponentially distributed service times with infinite waiting area. More advanced queueing models generalize the arrival process and/or service process to model more complex traffic patterns. Passing from the analysis of a single node to a network of interconnected nodes leads to the study of queueing networks. In recent years, there has been active research on studying network performance from the point of view of computing bounds on network performance rather than attempting to find solutions for specific arrival process. For example, if we assume that the network traffic is regulated deterministically, a so-called network calculus can be developed that allow us to calculate worst-case delay bounds. Our work in this area has dealt with loss network models and their relationship to queueing networks [KobMark94, KobMark95, KobMark97, KobMark02]. More recently, we have been looking at applications of queueing network theory to broadband switch architectures [Lu02, LuMark02a, LuMark02b, LuMark03], and air traffic systems management in collaboration with a group in the Systems Engineering and Operations Research Department at GMU. The study of queueing models and network performance remains an active area of research with many open problems and potential applications.

[LuMark04] X. Lu and B.L. Mark, "Performance Modeling of Optical Burst
Switching with Fiber Delay Lines," *IEEE Trans. on
Communications*, vol. 52, no. 12, pp. 2175-2183, Dec. 2004.

[LuMark03] X. Lu and B.L. Mark, "A New Performance Model of Optical Burst
Switching with Fiber Delay Lines,'' in *Proc. IEEE Int. Conf. on
Comm. 2003*, May 2003.

[Lu02] X. Lu, "Modeling and Performance Evaluation of Broadband Switch Architectures," Ph.D. dissertation, Dept. of Electrical and Computer Engineering, George Mason University, Dec. 2002.

[LuMark02b] X. Lu and B.L. Mark, "Analytical Modeling of Optical Burst
Switching with Fiber Delay Lines,'' in *Proc. IEEE/ACM MASCOTS'2002*, pp. 501-506,
Fort Worth, Texas, Oct. 2002.

[LuMark02a] X. Lu and B.L. Mark, "Analytical Modeling of a Family of Fault-Tolerant Routing Protocols in
k-ary n-cubes," *Proc. Int. Symp. on Performance Evaluation of Computer
and Telecommunication Systems} (SPECTS'02*), pp., 900-907, San Diego, July
2002.

[KobMark02] H. Kobayashi and B. L. Mark, "Generalized Loss Models and Queueing-Loss
Networks," *Int. Trans. in Operational Research*, Vol. 9, No. 1, pp.
97-112, 2002.

[KobMark97] H. Kobayashi and B.L. Mark,
"Product-Form Loss Networks,"
in *Frontiers in Queueing: Models and Applications in
Science and Engineering*, J. Dshalalow, Ed., pp. 147-195, CRC Press, 1997.

[KobMark95] H. Kobayashi and B.L. Mark,
"A Unified Theory for Queuing and Loss Network Models,"
in *Proc. IEEE Malaysia Int. Conf. on Comm.*,
Malaysia, November 1995.

[Paz95] J.M. Paz, B.L. Mark and H. Kobayashi,
"A Maximum Entropy Approach to the Analysis of Loss Systems,"
in *Proc. IEEE Singapore Int. Conf. on Networks*,
Singapore, July 1995.

[MarkKob95] B.L. Mark and H. Kobayashi,
"Blocking in a Class of All-Optical Wavelength Routers,"
in *Proc. 1st IEEE Int. Workshop on Broadband Switching Systems*,
Poznan, Poland, April 1995.

[Kob95] H. Kobayashi, B.L. Mark and Y. Osaki,
"Call Blocking Probability of All-Optical Networks,"
in *Proc. 1st IEEE Int. Workshop on Broadband Switching Systems*,
Poznan, Poland, April 1995.

[KobMark94] H. Kobayashi and B.L. Mark,
"On Queueing Networks and Loss Networks,"
in * Proc. 28th Annual Conf. on Information Sciences and Systems *,
pp. 794-799, Princeton, March 1994.