# Readings

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## Required Readings

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.

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

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

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

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

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

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