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 fullyear
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 threeyear elected term on the American Mathematical Society Council, the main governing body of the society. I recently served on the INFORMS Applied Probability Society Prize Committee and the Institute for Mathematical Statistics Travel Awards 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
Devin Scattini
Email: dscattini@csusm.edu
Phone: (760)7508059
Links
Department of Mathematics
College of Science and Mathematics
Education
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 hitech 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 nonheadoftheline (HL) service disciplines. Consequently,
they often evade closed form analysis, and tractable approximations are needed. Fluid
approximations can be regarded as firstorder deterministic (dynamical systems) approximations
that yield insights about average network performance. A diffusion approximation is
then a secondorder stochastic approximation that captures the dominant effects of
randomness. My work has centered on proving such approximation theorems for a variety
of nonHL service discipline that arise in modern networks. Measurevalued stochastic processes are a key tool employed in my work to handle the infinite dimensional nature of these
statespaces.
Awards
 202124 NSF Grant DMS2054505, $232,443
 201519 NSF Grant DMS1510198, $180,000
 201516 Presidents Outstanding Faculty Award for Scholarship and Creative Activity
 2007 INFORMS Applied Probability Society Best Publication Award, CoRecipient
Publications
Click on the highlighted word to download either a PDF or Postscript Version for personal
scientific noncommercial use only.
 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, to appear.
 Yueyang Zhong, Amy R. Ward, and Amber L. Puha. Asymptotically Optimal Idling in the GI/GI/N+GI Queue. Operations Research Letters, 34:3, 362369, 2022.
 Amber L. Puha and Amy R. Ward. Fluid Limits for Multiclass Many Server Queues with General Reneging Distribution
and General HeadoftheLine Scheduling Policies. Mathematics of Operations Research, Published online: 21 Dec 2021.
 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 ManyServer Queue with Impatient Customers. Tutorials in Operations Research, Published online: 02 Oct 2019; 189217. 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: 351397, 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, 251300, 2016.
 Amber L. Puha. Diffusion limits for shortest remaining processing time queues under nonstandard spatial
scaling. Annals of Applied Probability, 25, 33813404, 2015.
 Otis Jennings and Amber L. Puha. The fluid limit of an overloaded FIFO queue with general abandonment distribution. Stochastic Systems, 3, 262321, 2013.
 H. Christian Gromoll, Lukasz Kruk, and Amber L. Puha. The diffusion limit of an SRPT queue. Stochastic Systems, 1, 116, 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. Statedependent response times via fluid limits for shortest remaining processing
time queues. San Diego ACMSigmetrics Performance Evaluation Review, 27, 7576, 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, 316350, 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, 517554, 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, 797859, 2002.
 Teaching Developmental Mathematics with ALEKS: An Implementation Guide, S. Barrick and A. L. Puha, McGrawHill, 2003.
 A. L. Puha, Critical Exponents for a Reversible Nearest Particle System on the Binary Tree. The Annals of Probability, 28(1), 395415, 2000.
 A. L. Puha, A Reversible Nearest Particle System on the Homogeneous Tree, Journal of Theoretical Probability, 12(1), 217254, 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 49166, 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.
Courses
 2009 Greater San Diego Area Mathematics Council Outstanding Post Secondary Mathematics
Teacher
 202021, On Sabbatical
 Enrolled students may obtain information about these courses at Cougar Courses.
Service
20212022 Service and Committees
 Department of Mathematics Chair
 Coordinator, Southern California Probability Symposium
 Stochastic Networks, Applied Probability, and Performance (SNAPP) Seminar Advisory
Board
 Mathematics of Operations Research Area Editor
 AMS International Congress of Mathematics 2022 Travel Grants Selection Committee
 Learning Assistant Program Mathematics Coordinator
 Surf Team Faculty Advisor
Conference Organization

Interacting Particle Systems, Statistical Mechanics, and Related Topics: A conference
to honor the contributions of Thomas Liggett, UC Los Angeles IPAM, March 79, 2019 (w/ Marek Biskup (UCLA), Paul Jung (KAIST),
and Georg Menz (UCLA))

Stochastic Networks Conference, UC San Diego, June 2024, 2016 (w/ Tara Javidi (UCSD Eng) and Ruth Williams (UCSD
Math))

Seminar on Stochastic Processes, UC San Diego, March 2629, 2014 (w/ Patrick Fitzsimmons, Jason Schweinsberg, and Ruth Williams (UCSD))

A Workshop for Women in Probability, Duke University, October 1416, 2012 (w/ Rick Durrett (Duke Univ.) and Tai Melcher
(UVA))

A Workshop for Women in Probability, Cornell Univeristy, Octover 57, 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. Campus Recreation presently oversees Sport Clubs at CSUSM.
2021 Tryouts
Contact: csusmsurf@gmail.com
Please request to be added to our email contact list to keep up with activities of
the Surf Team.
2019 National Champions