Queueing system topologies with limited flexibility

We study a multi-server model with n flexible servers and rn queues, connected through a fixed bipartite graph, where the level of flexibility is captured by the average degree, d(n), of the queues. Applications in content replication in data centers, skill-based routing in call centers, and flexible supply chains are among our main motivations. We focus on the scaling regime where the system size n tends to infinity, while the overall traffic intensity stays fixed. We show that a large capacity region (robustness) and diminishing queueing delay (performance) are jointly achievable even under very limited flexibility (d(n) l n). In particular, when d(n) gg ln n , a family of random-graph-based interconnection topologies is (with high probability) capable of stabilizing all admissible arrival rate vectors (under a bounded support assumption), while simultaneously ensuring a diminishing queueing delay, of order ln n/ d(n), as n-> ∞. Our analysis is centered around a new class of virtual-queue-based scheduling policies that rely on dynamically constructed partial matchings on the connectivity graph.

[1]  G. V. Balakin On Random Matrices , 1967 .

[2]  Ward Whitt,et al.  Heavy-Traffic Limits for Queues with Many Exponential Servers , 1981, Oper. Res..

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

[4]  Jean C. Walrand,et al.  Achieving 100% throughput in an input-queued switch , 1996, Proceedings of IEEE INFOCOM '96. Conference on Computer Communications.

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

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

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

[8]  Rayadurgam Srikant,et al.  Analysis and design of an adaptive virtual queue (AVQ) algorithm for active queue management , 2001, SIGCOMM.

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

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

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

[12]  M. Stephanov,et al.  Random Matrices , 2005, hep-ph/0509286.

[13]  Ashvin Goel,et al.  Database replication policies for dynamic content applications , 2006, EuroSys.

[14]  Ward Whitt,et al.  Fluid Models for Overloaded Multi-Class Many-Server Queueing Systems with FCFS Routing , 2007 .

[15]  Eytan Modiano,et al.  Logarithmic delay for N × N packet switches under the crossbar constraint , 2007, TNET.

[16]  Ward Whitt,et al.  Fluid Models for Overloaded Multiclass Many-Server Queueing Systems with First-Come, First-Served Routing , 2008, Manag. Sci..

[17]  J. Tsitsiklis,et al.  Bin Packing with Queues , 2008, Journal of Applied Probability.

[18]  P. Sedgwick Random allocation I , 2009, BMJ : British Medical Journal.

[19]  Albert G. Greenberg,et al.  The nature of data center traffic: measurements & analysis , 2009, IMC '09.

[20]  Shreeshankar Bodas High-performance scheduling algorithms for wireless networks , 2010 .

[21]  Chung-Piaw Teo,et al.  Design for Process Flexibility: Efficiency of the Long Chain and Sparse Structure , 2010, Oper. Res..

[22]  Chung-Piaw Teo,et al.  Process Flexibility Revisited: The Graph Expander and Its Applications , 2011, Oper. Res..

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

[24]  Laurent Massoulié,et al.  Bipartite graph structures for efficient balancing of heterogeneous loads , 2012, SIGMETRICS '12.

[25]  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..

[26]  Gideon Weiss,et al.  A product form solution to a system with multi-type jobs and multi-type servers , 2012, Queueing Syst. Theory Appl..

[27]  John N. Tsitsiklis,et al.  On the Power of (Even a Little) Resource Pooling , 2012 .

[28]  Queueing system topologies with limited flexibility , 2013, SIGMETRICS.