Amber L. Puha

Last updated
Amber L. Puha
Born
United States
CitizenshipUnited States
Alma mater University of California, Los Angeles (Ph.D., M.A.)
University of California, San Diego (B.A.)
Scientific career
Fields Probability theory
Stochastic process
Queueing theory
Institutions California State University San Marcos
Thesis
Doctoral advisor Thomas M. Liggett

Amber Lynn Puha is an American mathematician and educator at California State University San Marcos. Her research concerns probability theory and stochastic processes. [1]

Contents

Early life and education

She earned a B.A. in mathematics at University of California, San Diego (UCSD) in 1993 and a Ph.D. in mathematics at University of California, Los Angeles (UCLA) under the supervision of Thomas M. Liggett in 1998. [2]

Career

She joined California State University San Marcos (CSUSM) in 1999. She was appointed an associate professor in 2005 and a full professor in 2010. She has been the chair of the Department of Mathematics at CSUSM since 2021. [3]

Her research has been focused on the modeling and analysis of stochastic networks. [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] Jointly with H. Christian Gromoll and Ruth J. Williams, she developed fluid (law of large numbers) and diffusion (central limit theorem) approximations for processor sharing queues with renewal arrivals and iid service requirements. [16] [17] By removing the Poisson arrival and the exponential service assumptions in previous literatures, this work advanced the state of art of applied probability and has board applications, "from many-server parallel queues that model call centers to bandwidth sharing communications networks that model the Internet." [18]

Professional services

From 2009 to 2011, she served as an associate director at the Institute for Pure and Applied Mathematics, a federally funded mathematics research institute on the UCLA campus. From 2013 to 2015, she served a three-year elected term on the American Mathematical Society Council, the main governing body of the society. [19] From 2016 to 2019, she served on the INFORMS Applied Probability Society Prize Committee. [20] From 2017 to 2020, she served on the Committee On Travel Awards of the Institute for Mathematical Statistics. [21] Since 2013, she has been the coordinator of The Southern California Probability Symposium, an annual gathering of probabilists supported by University of California, Irvine, UCLA, UCSB, UCSD, and University of Southern California. [22]

Since 2019, she has been an associate editor of Mathematics of Operations Research in the area of stochastic models. [23]

From 2013-2015, Puha served as a Council Member at Large for the American Mathematical Society. [24] Since 2016, she has been a life member at American Mathematical Society.

Other services

In addition to her academic work, she served as the faculty advisor for the CSUSM Surf Team, which competes in the National Scholastic Surfing Association (NSSA). She led the team to its first and second National Championship in 2009 [25] and 2019, [26] respectively. She won the NSSA Coach of the Year award in 2019.

Awards

Related Research Articles

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In queueing theory, a discipline within the mathematical theory of probability, Burke's theorem is a theorem asserting that, for the M/M/1 queue, M/M/c queue or M/M/∞ queue in the steady state with arrivals is a Poisson process with rate parameter λ:

  1. The departure process is a Poisson process with rate parameter λ.
  2. At time t the number of customers in the queue is independent of the departure process prior to time t.

In probability theory, a product-form solution is a particularly efficient form of solution for determining some metric of a system with distinct sub-components, where the metric for the collection of components can be written as a product of the metric across the different components. Using capital Pi notation a product-form solution has algebraic form

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<span class="mw-page-title-main">Regenerative process</span>

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<span class="mw-page-title-main">Polling system</span>

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References

  1. 1 2 3 "Amber Puha, PhD | CSUSM". faculty.csusm.edu. Retrieved 2022-04-20.
  2. ↑ "Amber Puha - The Mathematics Genealogy Project". mathgenealogy.org. Retrieved 2022-04-21.
  3. ↑ "Faculty Directory | Department of Mathematics | CSUSM". www.csusm.edu. Retrieved 2022-04-21.
  4. ↑ Puha, Amber (2000). "Critical Exponents for a Reversible Nearest Particle System on the Binary Tree". The Annals of Probability. 28. doi: 10.1214/aop/1019160124 .
  5. ↑ Puha, Amber; Alexander, Stolyar; Ruth, Williams (2006). "The Fluid Limit of an Overloaded Processor Sharing Queue". Mathematics of Operations Research . 31 (2): 316–350. doi:10.1287/moor.1050.0181.
  6. ↑ Down, Douglas; Gromoll, H. Christian; Puha, Amber (2009). "Fluid Limits for Shortest Remaining Processing Time Queues". Mathematics of Operations Research . 34 (4): 880–911. doi:10.1287/moor.1090.0409.
  7. ↑ Down, Douglas; Gromoll, H. Christian; Puha, Amber (2009). "State-dependent response times via fluid limits in shortest remaining processing time queues". ACM SIGMETRICS Performance Evaluation Review. 37 (2): 75–76. doi:10.1145/1639562.1639593. S2CID   2880499.
  8. ↑ Gromoll, H. Christian; Kruk, Lukasz; Puha, Amber (2011). "Diffusion limits for shortest remaining processing time queues". Stochastic Systems. 1: 1–16. arXiv: 1005.1035 . doi: 10.1214/10-SSY016 .
  9. ↑ Jennings, Otis; Puha, Amber (2013). "Fluid Limits for Overloaded Multiclass FIFO Single-Server Queues with General Abandonment". Stochastic Systems. 3: 262–321. arXiv: 1210.0959 . doi: 10.1287/12-SSY085 .
  10. ↑ Puha, Amber (2015). "Diffusion limits for shortest remaining processing time queues under nonstandard spatial scaling". The Annals of Applied Probability. 25 (6). arXiv: 1407.3837 . doi: 10.1214/14-AAP1076 .
  11. ↑ Puha, Amber; Williams, Ruth (2016). "Asymptotic Behavior of a Critical Fluid Model for a Processor Sharing Queue via Relative Entropy". Stochastic Systems. 6 (2): 251–300. doi: 10.1287/15-SSY198 .
  12. ↑ Mulvany, Justin; Puha, Amber; Williams, Ruth (2019). "Asymptotic Behavior of a Critical Fluid Model for a Multiclass Processor Sharing Queue via Relative Entropy". Queueing Systems. 93 (3–4): 351–397. doi: 10.1007/s11134-019-09629-8 .
  13. ↑ Puha, Amber; Ward, Amy (2019). "Scheduling an Overloaded Multiclass Many-Server Queue with Impatient Customers". Tutorials in Operations Research: 189–217. doi:10.1287/educ.2019.0196. ISBN   978-0-9906153-3-0. S2CID   85505491.
  14. ↑ Puha, Amber; Ward, Amy (2021). "Fluid Limits for Multiclass Many Server Queues with General Reneging Distribution and General Head-of-the-Line Scheduling Policies". Mathematics of Operations Research . doi:10.1287/moor.2021.1166. S2CID   202120734.
  15. ↑ Zhong, Yueyang; Ward, Amy; Puha, Amber (2022). "Asymptotically Optimal Idling in the GI/GI/N+GI Queue". Operations Research Letters . 50 (3): 362–369. arXiv: 2106.11407 . doi: 10.1016/j.orl.2022.04.005 .
  16. ↑ Gromoll, H. Christian; Puha, Amber; Williams, Ruth (2002). "The fluid limit of a heavily loaded processor sharing queue". The Annals of Applied Probability. 12 (3). doi: 10.1214/aoap/1031863171 .
  17. ↑ Puha, Amber; Williams, Ruth (2004). "Invariant states and rates of convergence for a critical fluid model of a processor sharing queue". The Annals of Applied Probability. 14 (2). arXiv: math/0405289 . doi: 10.1214/105051604000000017 .
  18. ↑ Dai, J.G. “Jim”; Taylor, Peter; Mandelbaum, Avishai. "INFORMS 2007 Best Publication Award Citation" . Retrieved 6 May 2022.
  19. ↑ "Council Past Members". AMS. Retrieved 18 April 2022.
  20. ↑ "Previous Prize Selection Committee Members". INFORMS. Retrieved 18 April 2022.
  21. ↑ "Institute of Mathematical Statistics | Past Committee Members". imstat.org. Retrieved 2022-05-10.
  22. ↑ "SoCal Probability". scps.pstat.ucsb.edu. Retrieved 2022-04-20.
  23. ↑ "Editorial Board | Mathematics of Operations Research". pubsonline.informs.org. Retrieved 2022-05-10.
  24. ↑ "AMS Committees". American Mathematical Society. Retrieved 2023-03-27.
  25. ↑ Aragon, Janice. "2009 NSSA NATIONAL CHAMPIONSHIP WRAP UP AND RESULTS!". NSSA. Retrieved 18 April 2022.
  26. ↑ NSSA. "2019 NATIONAL CHAMPIONSHIP RESULTS!". NSSA. Retrieved 18 April 2022.
  27. ↑ "APS Best Publication Award: Past Winners". INFORMS. Retrieved 18 April 2022.
  28. ↑ "Previous Awardees: President's Outstanding Faculty Awards". CSUSM. Retrieved 18 April 2022.
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