On the Power of (Even a Little) Resource Pooling

We propose and analyze a multi-server model that captures a performance trade-off between centralized and distributed processing. In our model, a fraction p of an available resource is deployed in a centralized manner (e.g., to serve a most-loaded station) while the remaining fraction 1 − p is allocated to local servers that can only serve requests addressed specifically to their respective stations. Using a fluid model approach, we demonstrate a surprising phase transition in the steady-state delay scaling, as p changes: in the limit of a large number of stations, and when any amount of centralization is available (p > 0), the average queue length in steady state scales as log11−p11−λ when the traffic intensity λ goes to 1. This is exponentially smaller than the usual M/M/1-queue delay scaling of 11−λ, obtained when all resources are fully allocated to local stations (p = 0). This indicates a strong qualitative impact of even a small degree of resource pooling. We prove convergence to a fluid limit, and ...

[1]  G. J. Foschini,et al.  A Basic Dynamic Routing Problem and Diffusion , 1978, IEEE Trans. Commun..

[2]  Leandros Tassiulas,et al.  Dynamic server allocation to parallel queues with randomly varying connectivity , 1993, IEEE Trans. Inf. Theory.

[3]  William C. Jordan,et al.  Principles on the benefits of manufacturing process flexibility , 1995 .

[4]  R. L. Dobrushin,et al.  Queueing system with selection of the shortest of two queues: an assymptotic approach , 1996 .

[5]  Avishai Mandelbaum,et al.  On Pooling in Queueing Networks , 1998 .

[6]  Maury Bramson,et al.  State space collapse with application to heavy traffic limits for multiclass queueing networks , 1998, Queueing Syst. Theory Appl..

[7]  J. Michael Harrison,et al.  Heavy traffic resource pooling in parallel‐server systems , 1999, Queueing Syst. Theory Appl..

[8]  Ronald J. Williams,et al.  Dynamic Scheduling of a System with Two Parallel Servers in Heavy Traffic with Resource Pooling: Asy , 2001 .

[9]  Michael Mitzenmacher,et al.  The Power of Two Choices in Randomized Load Balancing , 2001, IEEE Trans. Parallel Distributed Syst..

[10]  Ramesh K. Sitaraman,et al.  The power of two random choices: a survey of tech-niques and results , 2001 .

[11]  Stephen C. Graves,et al.  Process Flexibility in Supply Chains , 2003, Manag. Sci..

[12]  Saif Benjaafar,et al.  Modeling and analysis of flexible queueing systems , 2004 .

[13]  S. Foss,et al.  AN OVERVIEW OF SOME STOCHASTIC STABILITY METHODS( Network Design, Control and Optimization) , 2004 .

[14]  Alexander L. Stolyar,et al.  Scheduling Flexible Servers with Convex Delay Costs: Heavy-Traffic Optimality of the Generalized cµ-Rule , 2004, Oper. Res..

[15]  Heriot-Watt University.  AN OVERVIEW OF SOME STOCHASTIC STABILITY METHODS , 2004 .

[16]  Ward Whitt,et al.  A Staffing Algorithm for Call Centers with Skill-Based Routing , 2005, Manuf. Serv. Oper. Manag..

[17]  Seyed M. R. Iravani,et al.  Structural Flexibility: A New Perspective on the Design of Manufacturing and Service Operations , 2005, Manag. Sci..

[18]  S. Ethier,et al.  Markov Processes: Characterization and Convergence , 2005 .

[19]  M. Alanyali,et al.  On power-of-choice in downlink transmission scheduling , 2008, 2008 Information Theory and Applications Workshop.

[20]  B. Brogliato,et al.  Numerical Methods for Nonsmooth Dynamical Systems: Applications in Mechanics and Electronics , 2008 .

[21]  Douglas G. Down,et al.  On Accommodating Customer Flexibility in Service Systems , 2009, INFOR Inf. Syst. Oper. Res..

[22]  Yi Lu,et al.  Randomized load balancing with general service time distributions , 2010, SIGMETRICS '10.

[23]  Bruno Gaujal,et al.  Mean field limit of non-smooth systems and differential inclusions , 2010, PERV.

[24]  D. Gamarnik,et al.  Steady-state $\mathit{GI}/\mathit{GI}/\mathit{n}$ queue in the Halfin-Whitt regime , 2011, 1103.1709.

[25]  David Simchi-Levi,et al.  Understanding the Performance of the Long Chain and Sparse Designs in Process Flexibility , 2012, Oper. Res..

[26]  Ramandeep S. Randhawa,et al.  A Little Flexibility is All You Need: On the Asymptotic Value of Flexible Capacity in Parallel Queuing Systems , 2012, Oper. Res..

[27]  Kuang Xu.  On the Power of Centralization in Distributed Processing , 2012, ArXiv.