Surprising results on task assignment in server farms with high-variability workloads

This paper investigates the performance of task assignment policies for server farms, as the variability of job sizes (service demands) approaches infinity. Our results reveal that some common wisdoms regarding task assignment are flawed. The Size-Interval-Task-Assignment policy (SITA), which assigns each server a unique size range, was heretofore thought of by some as the panacea for dealing with high-variability job-size distributions. We show SITA to be inferior to the much simpler greedy policy, Least-Work-Left (LWL), for certain common job-size distributions, including many modal, hyperexponential, and Pareto distributions. We also define regimes where SITA's performance is superior, and prove simple closed-form bounds on its performance for the above-mentioned distributions.

[1]  Vaidyanathan Ramaswami,et al.  Introduction to Matrix Analytic Methods in Stochastic Modeling , 1999, ASA-SIAM Series on Statistics and Applied Mathematics.

[2]  Zahir Tari,et al.  Task assignment strategy for overloaded systems , 2003, Proceedings of the Eighth IEEE Symposium on Computers and Communications. ISCC 2003.

[3]  Paul Barford,et al.  Generating representative Web workloads for network and server performance evaluation , 1998, SIGMETRICS '98/PERFORMANCE '98.

[4]  Mor Harchol-Balter,et al.  On Choosing a Task Assignment Policy for a Distributed Server System , 1998, J. Parallel Distributed Comput..

[5]  Mor Harchol-Balter.  Task assignment with unknown duration , 2002, JACM.

[6]  Zahir Tari,et al.  A least flow-time first load sharing approach for distributed server farm , 2005, J. Parallel Distributed Comput..

[7]  Vishal Misra,et al.  Optimal state-free, size-aware dispatching for heterogeneous M/G/-type systems , 2005, Perform. Evaluation.

[8]  Mor Harchol-Balter,et al.  Evaluation of Task Assignment Policies for Supercomputing Servers: The Case for Load Unbalancing and Fairness , 2004, Cluster Computing.

[9]  Hagit Sarfati,et al.  Analysis of size interval task assignment policies , 2008, PERV.

[10]  Alan Scheller-Wolf,et al.  Further delay moment results for FIFO multiserver queues , 1999, Queueing Syst. Theory Appl..

[11]  Anees Shaikh,et al.  Load-sensitive routing of long-lived IP flows , 1999, SIGCOMM '99.

[12]  John A. Buzacott,et al.  Stochastic models of manufacturing systems , 1993 .

[13]  A. P. Zwart,et al.  Waiting-Time Asymptotics for the M/G/2 Queue with Heterogeneous Servers , 2002, Queueing Syst. Theory Appl..

[14]  Ward Whitt,et al.  The impact of a heavy-tailed service-time distribution upon the M/GI/s waiting-time distribution , 2000, Queueing Syst. Theory Appl..

[15]  Azer Bestavros,et al.  Self-similarity in World Wide Web traffic: evidence and possible causes , 1996, SIGMETRICS '96.

[16]  Timothy J. O'Donnell,et al.  Analysis of the early workload on the Cornell Theory Center IBM SP2 , 1996, SIGMETRICS '96.

[17]  Pablo Molinero-Fernández,et al.  Systems with multiple servers under heavy-tailed workloads , 2005, Perform. Evaluation.

[18]  Zahir Tari,et al.  Task assignment with work-conserving migration , 2006, Parallel Comput..

[19]  Leonard Kleinrock,et al.  Queueing Systems: Volume I-Theory , 1975 .

[20]  Philip S. Yu,et al.  The state of the art in locally distributed Web-server systems , 2002, CSUR.

[21]  Alan Scheller-Wolf,et al.  Delay moments for FIFO GI/GI/s queues , 1997, Queueing Syst. Theory Appl..

[22]  Nigel Thomas,et al.  Comparing job allocation schemes where service demand is unknown , 2008, J. Comput. Syst. Sci..

[23]  Bacel Maddah,et al.  Allocation of Service Time in a Multiserver System , 2006, Manag. Sci..

[24]  Gianfranco Ciardo,et al.  EQUILOAD: a load balancing policy for clustered web servers , 2001, Perform. Evaluation.

[25]  Kazumasa Oida,et al.  Characteristics of deterministic optimal routing for a simple traffic control problem , 1999, 1999 IEEE International Performance, Computing and Communications Conference (Cat. No.99CH36305).

[26]  Alan Scheller-Wolf,et al.  New bounds for expected delay in FIFO M/G/c queues , 1997, Queueing Syst. Theory Appl..

[27]  Alan Scheller-Wolf,et al.  Structural interpretation and derivation of necessary and sufficient conditions for delay moments in FIFO multiserver queues , 2006, Queueing Syst. Theory Appl..

[28]  Serguei Foss,et al.  Heavy Tails in Multi-Server Queue , 2006, Queueing Syst. Theory Appl..