Modeling parallel and distributed systems with finite workloads

Summary form only given. In studying or designing parallel and distributed systems one should have available a robust analytical model that includes the major parameters that determine the system performance. Jackson networks have been very successful in modeling parallel and distributed systems. However, they have their limitations. In particular, the product-form solution of Jackson networks assumes steady state and exponential service centers or certain specialized queueing disciplines. We use a transient model studying distributed systems with finite workload (no new arrivals). Using some nonexponential distributions we show to what extent the exponential distribution can be used to approximate other distributions. When the number of tasks to be executed is large enough, the model approaches the product-form solution in those cases where the Jackson networks can be applied. We also study some cases where Jackson networks can't be applied (the nonexponential servers have queueing). The model can be used for reliability analysis of systems that allow failures without repair (fail-stop).

[1]  Tao Zhang,et al.  On The Performance Of Parallel Computers: Order Statistics, Amdahl's Law and Their Applications , 1996, Int. CMG Conference.

[2]  YONG YAN,et al.  An Effective and Practical Performance Prediction Model for Parallel Computing on Nondedicated Heterogeneous NOW , 1996, J. Parallel Distributed Comput..

[3]  Kishor S. Trivedi.  Probability and Statistics with Reliability, Queuing, and Computer Science Applications , 1984 .

[4]  Lester Lipsky,et al.  Efficient Data Allocation for a Cluster of Workstations , 2003, PDCS.

[5]  Lester Lipsky,et al.  Queueing Theory: A Linear Algebraic Approach , 1992 .

[6]  Lester Lipsky,et al.  Long-lasting transient conditions in simulations with heavy-tailed workloads , 1997, WSC '97.

[7]  Lester Lipsky,et al.  Transient Model for Jackson Networks and Its Approximation , 2003, OPODIS.

[8]  Rajkumar Buyya,et al.  High Performance Cluster Computing , 1999 .

[9]  Lester Lipsky,et al.  Buffer Problems in Telecommunications Networks , 1997 .

[10]  Ahmed M. Mohamed,et al.  Transient performance model for parallel and distributed systems , 2004, Proceedings. Tenth International Conference on Parallel and Distributed Systems, 2004. ICPADS 2004..

[11]  Ami Marowka,et al.  The GRID: Blueprint for a New Computing Infrastructure , 2000, Parallel Distributed Comput. Pract..

[12]  Ian Foster,et al.  The Grid 2 - Blueprint for a New Computing Infrastructure, Second Edition , 1998, The Grid 2, 2nd Edition.

[13]  Tao Zhang,et al.  On The Performance of Parallel Computers: Order Statistics and Amdahl's Law , 1996 .

[14]  Cosimo Anglano,et al.  Predicting parallel applications performance on non-dedicated cluster platforms , 1998, ICS '98.

[15]  James R. Jackson,et al.  Jobshop-Like Queueing Systems , 2004, Manag. Sci..

[16]  Ray Jinzhu Chen.  A Hybrid Solution of Fork/Join Synchronization in Parallel Queues , 2001, IEEE Trans. Parallel Distributed Syst..

[17]  Jeffrey P. Buzen,et al.  Computational algorithms for closed queueing networks with exponential servers , 1973, Commun. ACM.

[18]  Gianfranco Balbo,et al.  Computational algorithms for closed queueing networks , 1980 .

[19]  Lester Lipsky,et al.  Performance Modeling of a Cluster of Workstations , 2003, Communications in Computing.

[20]  K. Mani Chandy,et al.  Open, Closed, and Mixed Networks of Queues with Different Classes of Customers , 1975, JACM.

[21]  A. Tehranipour,et al.  The generalized M/G/C//N-queue as a model for time-sharing systems , 1990, Proceedings of the 1990 Symposium on Applied Computing.

[22]  Jeffrey P. Buzen,et al.  Queueing Network Models of Multiprogramming , 1971, Outstanding Dissertations in the Computer Sciences.

[23]  Reda A. Ammar,et al.  Micro Time Cost Analysis of Parallel Computations , 1991, IEEE Trans. Computers.

[24]  Lester Lipsky,et al.  The Importance of Power-Tail Distributions for Modeling Queueing Systems , 1999, Oper. Res..

[25]  Terry Williams,et al.  Probability and Statistics with Reliability, Queueing and Computer Science Applications , 1983 .