Stochastic analysis of multiserver systems

This paper presents an overview of research in the stochastic analysis of multiserver systems, where scheduling often play a critical role. Our primary focus is on the stochastic analysis and optimization of multiserver systems in general, since most of this research directly investigates scheduling issues and all of this research provides the methods and results that have been and will continue to be used to study existing and future multiserver scheduling issues.

[1]  Panganamala Ramana Kumar,et al.  A network information theory for wireless communication: scaling laws and optimal operation , 2004, IEEE Transactions on Information Theory.

[2]  Mark S. Squillante,et al.  Analysis of optimal scheduling in distributed parallel queueing systems , 1996 .

[3]  J. W. Cohen,et al.  Boundary value problems in queueing theory , 1988, Queueing Syst. Theory Appl..

[4]  Knut Sydsæter,et al.  SUFFICIENT CONDITIONS IN OPTIMAL CONTROL THEORY , 1977 .

[5]  Alan Scheller-Wolf,et al.  Exploring Threshold-based Policies for Load Sharing , 2004 .

[6]  N. K. Jaiswal,et al.  Priority queues , 1968 .

[7]  W. Whitt,et al.  Blocking when service is required from several facilities simultaneously , 1985, AT&T Technical Journal.

[8]  G. Fayolle,et al.  Random Walks in the Quarter-Plane: Algebraic Methods, Boundary Value Problems and Applications , 1999 .

[9]  Devavrat Shah,et al.  Optimal throughput-delay scaling in wireless networks - part I: the fluid model , 2006, IEEE Transactions on Information Theory.

[10]  Mark S. Squillante,et al.  Analysis of Stochastic Online Bin Packing Processes , 2005 .

[11]  F. Kelly.  Blocking probabilities in large circuit-switched networks , 1986, Advances in Applied Probability.

[12]  Lisa Fleischer,et al.  Efficient Algorithms for Separated Continuous Linear Programs: The Multicommodity Flow Problem with Holding Costs and Extensions , 2005, Math. Oper. Res..

[13]  S. L. Bell,et al.  Dynamic Scheduling of a Parallel Server System in Heavy Traffic with Complete Resource Pooling: Asymptotic Optimality of a Threshold Policy , 2005 .

[14]  Mark S. Squillante,et al.  Optimal capacity planning in stochastic loss networks with time-varying workloads , 2007, SIGMETRICS '07.

[15]  Marcel F. Neuts,et al.  Matrix-geometric solutions in stochastic models - an algorithmic approach , 1982 .

[16]  Mark S. Squillante,et al.  Modeling and analysis of dynamic coscheduling in parallel and distributed environments , 2002, SIGMETRICS '02.

[17]  Emre Telatar,et al.  Information-theoretic upper bounds on the capacity of large extended ad hoc wireless networks , 2005, IEEE Transactions on Information Theory.

[18]  J. Tsitsiklis,et al.  Performance of Multiclass Markovian Queueing Networks Via Piecewise Linear Lyapunov Functions , 2001 .

[19]  Armand M. Makowski,et al.  Interpolation Approximations for Symmetric Fork-Join Queues , 1994, Perform. Evaluation.

[20]  Marios C. Papaefthymiou,et al.  Stochastic Analysis of Gang Scheduling in Parallel and Distributed Systems , 1996, Perform. Evaluation.

[21]  Mark S. Squillante,et al.  Analysis of task assignment with cycle stealing under central queue , 2003, 23rd International Conference on Distributed Computing Systems, 2003. Proceedings..

[22]  D. Gaver.  A Waiting Line with Interrupted Service, Including Priorities , 1962 .

[23]  D. Yao,et al.  Fundamentals of Queueing Networks: Performance, Asymptotics, and Optimization , 2001, IEEE Transactions on Automatic Control.

[24]  Adam Wierman,et al.  Multi-Server Queueing Systems with Multiple Priority Classes , 2005, Queueing Syst. Theory Appl..

[25]  Alan Scheller-Wolf,et al.  Analysis of cycle stealing with switching times and thresholds , 2005, Perform. Evaluation.

[26]  Mark S. Squillante,et al.  ANALYSIS OF PARALLEL-SERVER QUEUES UNDER SPACESHARING AND TIMESHARING DISCIPLINES , 2002 .

[27]  Mark S. Squillante.  Issues in Shared-Memory Multipro-cessor Scheduling: A Performance Evaluation , 1990 .

[28]  G. Fayolle,et al.  Two coupled processors: The reduction to a Riemann-Hilbert problem , 1979 .

[29]  Mark S. Squillante,et al.  Optimal stochastic scheduling in multiclass parallel queues , 1999, SIGMETRICS '99.

[30]  J. Harrison,et al.  Brownian motion and stochastic flow systems , 1986 .

[31]  Onno Boxma,et al.  Queueing-theoretic solution methods for models of parallel and distributed systems , 1994 .

[32]  Florin Avram,et al.  Fluid models of sequencing problems in open queueing networks; an optimal control approach , 1995 .

[33]  Mark S. Squillante,et al.  Cycle stealing under immediate dispatch task assignment , 2003, SPAA '03.

[34]  F. Baccelli,et al.  The fork-join queue and related systems with synchronization constraints: stochastic ordering and computable bounds , 1989, Advances in Applied Probability.

[35]  Devavrat Shah,et al.  Optimal Throughput–Delay Scaling in Wireless Networks—Part II: Constant-Size Packets , 2006, IEEE Transactions on Information Theory.

[36]  M. Bramson.  Instability of FIFO Queueing Networks , 1994 .

[37]  J. Dai.  On Positive Harris Recurrence of Multiclass Queueing Networks: A Unified Approach Via Fluid Limit Models , 1995 .

[38]  Alan Scheller-Wolf,et al.  Analysis of cycle stealing with switching cost , 2003, SIGMETRICS '03.

[39]  J. Michael Harrison,et al.  Dynamic Scheduling of a Multiclass Queue in the Halfin-Whitt Heavy Traffic Regime , 2004, Oper. Res..

[40]  Mark S. Squillante,et al.  Scalability of wireless networks , 2007, TNET.

[41]  Ivo J. B. F. Adan,et al.  Analysis of the symmetric shortest queue problem , 1990 .

[42]  Mor Harchol-Balter,et al.  Analysis of multi-server systems via dimensionality reduction of markov chains , 2005 .

[43]  Marcel F. Neuts,et al.  Structured Stochastic Matrices of M/G/1 Type and Their Applications , 1989 .

[44]  L. Flatto,et al.  Two parallel queues created by arrivals with two demands. II , 1984 .

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

[46]  Asser N. Tantawi,et al.  Approximate Analysis of Fork/Join Synchronization in Parallel Queues , 1988, IEEE Trans. Computers.

[47]  G. Fayolle,et al.  Topics in the Constructive Theory of Countable Markov Chains , 1995 .

[48]  Sean P. Meyn.  Dynamic Safety-Stocks for Asymptotic Optimality in Stochastic Networks , 2005, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[49]  Randolph D. Nelson,et al.  An Approximation for the Mean Response Time for Shortest Queue Routing with General Inerarrival and Service Times , 1993, Perform. Evaluation.

[50]  Sean P. Meyn.  Sequencing and Routing in Multiclass Queueing Networks Part II: Workload Relaxations , 2003, SIAM J. Control. Optim..

[51]  Yves Dallery,et al.  On Decomposition Methods for Tandem Queueing Networks with Blocking , 1993, Oper. Res..

[52]  Michael Mitzenmacher,et al.  Computational Complexity of Loss Networks , 1994, Theor. Comput. Sci..

[53]  Ronald J. Williams,et al.  Dynamic scheduling of a system with two parallel servers in heavy traffic with resource pooling: asymptotic optimality of a threshold policy , 2001 .

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

[56]  Martin I. Reiman,et al.  An Interpolation Approximation for Queueing Systems with Poisson Input , 1988, Oper. Res..

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

[58]  H. Kushner.  Numerical Methods for Stochastic Control Problems in Continuous Time , 2000 .

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

[60]  Sanjeev R. Kulkarni,et al.  Upper bounds to transport capacity of wireless networks , 2004, IEEE Transactions on Information Theory.

[61]  Mark S. Squillante,et al.  Buffer Scalability of Wireless Networks , 2006, Proceedings IEEE INFOCOM 2006. 25TH IEEE International Conference on Computer Communications.

[62]  Hong Chen,et al.  Dynamic Scheduling of a Multiclass Fluid Network , 1993, Oper. Res..

[63]  Richard L. Tweedie,et al.  Markov Chains and Stochastic Stability , 1993, Communications and Control Engineering Series.

[64]  P. R. Kumar,et al.  Re-entrant lines , 1993, Queueing Syst. Theory Appl..

[65]  Sean P. Meyn.  Sequencing and Routing in Multiclass Queueing Networks Part I: Feedback Regulation , 2001, SIAM J. Control. Optim..

[66]  Ivo J. B. F. Adan,et al.  Queueing Models with Multiple Waiting Lines , 2001, Queueing Syst. Theory Appl..

[67]  Panganamala Ramana Kumar,et al.  RHEINISCH-WESTFÄLISCHE TECHNISCHE HOCHSCHULE AACHEN , 2001 .