Special Issue on the Workshop on MAthematical performance Modeling and Analysis (MAMA 2000) M a r k S. Squillante 1 The complexity of computer systems, networks and applications, as well as the advancements in computer technology, continue to grow at a rapid pace. Mathematical analysis, modeling and optimization are playing an important role in research studies to investigate fundamental issues and tradeoffs at the core of performance problems in the design and implementation of complex computer systems, networks and applications. On June 17-18, 2000, the Second Workshop on MAthematical performance Modeling and Analysis (MAMA 2000) was held in Santa Clara, CA, USA, sponsored by and held in conjunction with ACM SIGMETRICS 2000. This workshop seeks to bring together researchers working on the mathematical, methodological and theoretical aspects of performance analysis, modeling and optimization. It is intended to provide a forum at SIGMETRICS conferences for talks on early research in the more mathematical areas of computer performance analysis. These talks tend to be based on very recent research results (including work in progress) or on new research results that will be otherwise submitted only to a journal (or recently have been submitted to a journal). Thus, part of the goal is to complement and supplement the SIGMETRICS conference program with such talks without removing any theoretical contributions from the main program. The MAMA 2000 workshop consisted of 15 presentations by Eitan Bachmat, C.S. Chang, Ed Coffman, Edmundo de Souza e Silva, Paulo Fernandes, David Gamarnik, Peter Haas, Mor Harchol-Balter, Jean-Michel Ilie, Lei Kuang, John Lui, VT Rajan, Don Towsley, Joel Wolf and Li Zhang. This special issue of Performance Evaluation Review consists of extended abstracts relating to these presentations (arranged in the order of their presentation), which cover a wide range of topics in the area of mathematical performance analysis, modeling and optimization. The abstract by Harchol-Balter considers the classical problem of job placement in a distributed server system, where the job service time distribution has a "heavy-tailed property". Golubchik and Lui present some of their recent work on multiclass, multiserver threshold-based queueing systems and discuss some open problems in this area. The abstract by Coffman and Jelenkovi6 studies the fraction of time a single resource is in use in a reservation system under a greedy policy of threshold type. Wolf and Yu propose an approach l IBM Research Division, T.J. Watson Research Center, Yorktown Heights, NY 10598, USA. mss@watsot~ibm~com to optimally balance the load on the servers of a clustered web farm. The abstract by de Souza e Silva, Le~o and Diniz presents algorithms to efficiently obtain various performance measures directly from the model of the source feeding the queueing system. Bu and Towsley study the problem of modeling and analyzing the behavior of a large population of infinite duration TCP flows traversing a network of routers which implement active queue management. The abstract by Chang, Chiu and Song considers stochastic bounds on the performance characteristics of a work conserving link with a large number of independent regulated inputs. Kuang and Makowski discuss how the notion of convex stability for a sequence of non-negative random variables can be exploited to yield insights in the context of several applications. The abstract by Bachmat reports on two recent results which relate performance and modeling issues in disks and disk arrays to the theory of metric spaces and the theory of graph evolution and phase transition. Hogstedt et al. introduce a number of heuristic graph algorithms for use in solving the problem of optimally allocating the components of a distributed program over several computers. The abstract by Fernandes and Plateau presents an algorithm based on LU decomposition to solve linear systems expressed by a matrix stored in a tensor product format. Capra et al. propose a method to exploit partially symmetric behavior of systems for efficient performance evaluation. The abstract by Haas addresses the estimation of long-run delay characteristics in non-regenerative discrete-event stochastic systems. Gamarnik demonstrates the fundamental reason for the absence of stability characterizations for two types of queueing systems, establishing undecidability results for addressing such stability issues. Finally, the abstract by Squillante, Woo and Zhang considers the approximation of dependent arrival processes based on web server access logs and the analysis of the corresponding queueing system. I sincerely thank each of the speakers and co-authors for their presentation and participation at the MAMA 2000 workshop, as well as each of the other attendees. I also sincerely thank the program committee members: Ed Coffman, Nick Duffield, Dick Epema, David Gamarnik, Erol Gelenbe, Leana Golubchik, Ulrich Herzog, John Lewis, Zhen Liu, Raymond Russell, Perwez Shahabuddin, Don Towsley and Li Zhang. Without all of the work and support from both of these groups of people, the MAMA 2000 workshop would not have been possible. I also thank ACM SIGMETRICS for all of its support, and Scott Leutenegger for all of his assistance with this special issue of PER.

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