## About Amber Puha, PhD

I joined the faculty at CSUSM in 1999 when the university was just 10 years young. Before joining CSUSM, I earned a BA in Mathematics at UCSD in 1993 and a PhD in Mathematics at UCLA under the supervision of Professor Thomas Liggett in 1998. My expertise is in probability theory and stochastic processes with a focus on the modeling and analysis of stochastic networks. Since joining CSUSM, I have spent three yearlong sabbaticals at UCSD pursuing various projects related to my research interests. More information is available through the Research tab above. I also spent two years as an Associate Director at the Institute for Pure and Applied Mathematics, a federally funded mathematics research institute on the UCLA campus. I served a three-year elected term on the American Mathematical Society Council, the main governing body of the society. I have also served on the INFORMS Applied Probability Society Prize Committee as well as the Institute for Mathematical Statistics Travel Awards Committee and Nominations and Elections Committee. I am an avid surfer, having been a competitive surfer in my younger years, which has motivated me to serve as the Faculty Advisor for the CSUSM Surf Team since its inception in 2002.

**Administrative Support Coordinator**

Jennifer Johnson

Email: jejohnson@csusm.edu

Phone: (760)750-8059

**Links**Department of Mathematics

College of Science and Mathematics

## Research

My training is in probability theory, stochastic processes, and their applications. These days I primarily work in the area of stochastic processing networks. A stochastic network model captures the inherent randomness in a variety of networks, including those that arise in modern computing and communications, as well as transportation and hi-tech manufacturing. The structure of the network is typically deterministic and the service discipline is usually specified. Randomness manifests itself in customer exogenous arrival times, service times, routing, etc. In general, such networks are complicated and involve feedback and non-head-of-the-line (HL) service disciplines. Consequently, they often evade closed form analysis, and tractable approximations are needed. Fluid approximations can be regarded as first-order deterministic (dynamical systems) approximations that yield insights about average network performance. A diffusion approximation is then a second-order stochastic approximation that captures the dominant effects of randomness. My work has centered on proving such approximation theorems for a variety of non-HL service discipline that arise in modern networks. Measure-valued stochastic processes are a key tool employed in my work to handle the infinite dimensional nature of these state-spaces.

### Awards

- 2021-25 NSF Grant DMS-2054505, $232,443
- 2015-19 NSF Grant DMS-1510198, $180,000
- 2015-16 Presidents Outstanding Faculty Award for Scholarship and Creative Activity
- 2007 INFORMS Applied Probability Society Best Publication Award, Co-Recipient

### Publications

Click on the highlighted word to download either a PDF or Postscript Version for personal scientific non-commercial use only.

- Chunxu Ji and Amber L. Puha. Heavy Traffic Scaling Limits for Shortest Remaining Processing Time Queues with Light Tailed Processing Time Distributions. Submitted, October 2023.
- Angelos Aveklouris, Amber L. Puha, and Amy R. Ward. A Fluid Approximation for a Matching Model with General Reneging Distributions. Queueing Systems: Theory and Applications, 106, 199-238, 2024. DOI
- Sayan Banerjee, Amarjit Budhiraja, and Amber L. Puha. Heavy Traffic Scaling Limits for Shortest Remaining Processing Time Queues with Heavy Tailed Processing Time Distributions. Annals of Applied Probability, 32:4, 2587-2651, 2022. DOI
- Yueyang Zhong, Amy R. Ward, and Amber L. Puha. Asymptotically Optimal Idling in the GI/GI/N+GI Queue. Operations Research Letters, 34:3, 362-369, 2022.
- Amber L. Puha and Amy R. Ward. Fluid Limits for Multiclass Many Server Queues with General Reneging Distribution and General Head-of-the-Line Scheduling Policies. Mathematics of Operations Research, 47:2, 847-1705, 2022.
- David Aldous, Pietro Caputo, Rick Durrett, Paul Jung, Alexander E. Holroyd, and Amber L. Puha. The Life and Mathematical Legacy of Thomas M. Liggett. Notices of the American Mathematical Society, January 2021.
- Amber L. Puha and Amy R. Ward. Scheduling an Overloaded Multiclass Many-Server Queue with Impatient Customers. Tutorials in Operations Research, Published online: 02 Oct 2019; 189--217. Presented by Ward at INFORMS 2019.
- Justin A. Mulvany, Amber L. Puha and Ruth J. Williams. Asymptotic Behavior of a Critical Fluid Model for a Multiclass Processor Sharing Queue via Relative Entropy. Queueing Systems, 93: 351--397, 2019.
- Amber L. Puha and Ruth J. Williams. Asymptotic Behavior of a Critical Fluid Model for a Processor Sharing Queue via Relative Entropy. Stochastic Systems, 6, 251-300, 2016.
- Amber L. Puha. Diffusion limits for shortest remaining processing time queues under nonstandard spatial scaling. Annals of Applied Probability, 25, 3381-3404, 2015.
- Otis Jennings and Amber L. Puha. The fluid limit of an overloaded FIFO queue with general abandonment distribution. Stochastic Systems, 3, 262-321, 2013.
- H. Christian Gromoll, Lukasz Kruk, and Amber L. Puha. The diffusion limit of an SRPT queue. Stochastic Systems, 1, 1-16, 2011.
- Douglas Down, H. Christian Gromoll, and Amber L. Puha. Fluid limits for shortest remaining processing time queues. Mathematics of Operations Research, 34, 880 - 911, November 2009.
- Douglas Down, H. Christian Gromoll, and Amber L. Puha. State-dependent response times via fluid limits for shortest remaining processing time queues. San Diego ACM-Sigmetrics Performance Evaluation Review, 27, 75-76, September 2009.
- A. L. Puha, A. L. Stoylar, and R. J. Williams. The Fluid Limit of an Overloaded Processor Sharing Queue. Mathematics of Operations Research, 31, 316-350, 2006.
- Stan Barrick, Amber Puha, and CSU Information Technology Services Academic Technology Division. CSU Math Success Web, 2004.
- A. L. Puha and R. J. Williams, Invariant States and Rates of Convergence for the Fluid Limit of a Processor Sharing Queue. Annals of Applied Probability, 14, 517-554, 2004.
- H. C. Gromoll, A. L. Puha, and R. J. Williams, The Fluid Limit for a Processor Sharing Queue. The Annals of Applied Probability,12, 797-859, 2002.
- Teaching Developmental Mathematics with ALEKS: An Implementation Guide, S. Barrick and A. L. Puha, McGraw-Hill, 2003.
- A. L. Puha, Critical Exponents for a Reversible Nearest Particle System on the Binary Tree. The Annals of Probability, 28(1), 395-415, 2000.
- A. L. Puha, A Reversible Nearest Particle System on the Homogeneous Tree, Journal of Theoretical Probability, 12(1), 217-254, 1999. View a list of typographical errors that unfortunately found their way into the published version.
- J. T. Chayes, A. L. Puha, and T. Sweet, Independent and Dependent Percolation. In Probability: Theory and Applications, volume 6, of IAS/Park City Mathematics Series, editors E. Hsu and S. R. S. Varadhan, pages 49-166, Amercian Mathematical Society, 1999.
- A. L. Puha, A Reversible Interacting Particle System on the Homogeneous Tree, Dissertation, Department of Mathematics, University of California, Los Angeles, 1998.

## Teaching

- 2009 Greater San Diego Area Mathematics Council Outstanding Post Secondary Mathematics Teacher
- Enrolled students may obtain information about these courses at Cougar Courses.

## Vitae

## Service

### 2024-25 Service and Committees

- Scheduling and Evaluation Coordinator, Department of Mathematics
- Co-Director with Anthony Matranga, MSTI Faculty Champions for Teacher Recruitment (FaCTOR)
- Co-Principle Investigator with Rong-Ji Chen, Optimizing the STEM Teacher Recruitment, Development and Retention Pathway: Aligning STEM and Teaching Identities in the Noyce Community (2024-2029)
- Member, AMS Simons Research Enhancement Grants for Primarily Undergraduate Institutions (PUI) Faculty Committee (2023-26)
- Faculty Advisor, CSUSM Surf Team (since 2002)

### Editorial Work

- Mathematics of Operations Research Associate Editor
- Stochastic Systems Associate Editor

### Conference Coordination

- Coordinator, Southern California Probability Symposium (since 2013)
- Seminar on Stochastic Processes Long Term Science Advisory Board Member (since 2021)

### Conference Organization

- Southern California Probability Symposium 2023: Looking Ahead, UC San Diego, May 20-21, 2023 (w/ Todd Kemp (UCSD) and Ruth Williams (UCSD))
- Interacting Particle Systems, Statistical Mechanics, and Related Topics: A conference to honor the contributions of Thomas Liggett, UC Los Angeles IPAM, March 7-9, 2019 (w/ Marek Biskup (UCLA), Paul Jung (KAIST), and Georg Menz (UCLA))
- Stochastic Networks Conference, UC San Diego, June 20-24, 2016 (w/ Tara Javidi (UCSD Eng) and Ruth Williams (UCSD Math))
- Seminar on Stochastic Processes, UC San Diego, March 26-29, 2014 (w/ Patrick Fitzsimmons, Jason Schweinsberg, and Ruth Williams (UCSD))
- A Workshop for Women in Probability, Duke University, October 14-16, 2012 (w/ Rick Durrett (Duke Univ.) and Tai Melcher (UVA))
- A Workshop for Women in Probability, Cornell Univeristy, Octover 5-7, 2008 (w/ Rick Durrett (Cornell Univ.), Lea Popovik (Concordia Univ.))

## Surf Team

The CSUSM Surf Team was established in January 2002. It was the second Sport Club to be recognized on campus (Women's Soccer was first). It is the longest standing Sport Club at CSUSM. Prof. Puha has served as the Faculty Advisor since its inception. The team competes in the NSSA College Team Season. In 2009, the team earned its first National Championship and then, ten years later in 2019, they earned their second. In 2024, Tanner Vodraska earned the first individual national title in the college men's division. Campus Recreation presently oversees Sport Clubs at CSUSM.

### 2023 Tryouts

Contact: csusmsurf@gmail.comPlease request to be added to our email contact list to keep up with activities of the Surf Team.