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Required Readings

Amazon logo Shwartz, Adam, and Alan Weiss. Large Deviations for Performance Analysis: Queues, Communications, and Computing. New York, NY: Chapman and Hall, 1995, chapters 1 and 3. ISBN: 0412063115.

Amazon logo Resnick, Sidney. Adventures in Stochastic Processes. Boston, MA: Birkhäuser, 1992, chapter 6. ISBN: 0817635912.

Amazon logo Harrison, J. Michael. Brownian Motion and Stochastic Flow Systems. Malabar, FL: Robert E. Krieger Pub. Co., 1990, chapter 4. ISBN: 0894644556.

Amazon logo Chen, Hong, and David D. Yao. Fundamentals of Queuing Networks: Performance, Asymptotics, and Optimization. New York, NY: Springer, 2001, sections 6.1-6.5 and 7.1-7.9. ISBN: 0387951660.

Reiman, Martin I. "Open Queueing Networks in Heavy Traffic." Mathematics of Operations Research 9, no. 3 (1984): 441-458.

Gamarnik, David, and Assaf Zeevi. "Validity of Heavy Traffic Steady-State Approximations in Generalized Jackson Networks." Annals of Applied Probability 16, no. 1 (2006): 56-90.

Harrison, J. M., and R. J. Williams. "Brownian Models of Open Queueing Networks with Homogeneous Customer Populations." Stochastics 22 (1987): 77-115.

———. "Multidimensional Reflected Brownian Motions Having Exponential Stationary Distributions." Annals of Probability 15, no. 1 (1987): 115-137.

Supplemental Reading References

Amazon logo Grimmett, Geoffrey R., and David R. Stirzaker. Probability and Random Processes. New York, NY: Oxford University Press, 2001. ISBN: 0198572220.

Amazon logo Durrett, Richard. Probability: Theory and Examples. Belmont, CA: Thomson Brooks/Cole, 2005. ISBN: 0534424414.

Amazon logo Billingsley, Patrick. Weak Convergence of Measures: Applications in Probability. Philadelphia, PA: Society for Industrial and Applied Mathematics, 1971. ISBN: 0898711762.