Spectral Expansion Solution Methodology for QBD-M Processes and Applications in Future Internet Engineering

Quasi Simultaneous-Multiple Births and Deaths (QBD-M) Processes are used to model many of the traffic, service and related problems in modern communication systems. Their importance is on the increase due to the great strides that are taking place in telecommunication systems and networks. This paper presents the overview of the Spectral Expansion (SE) for the steady state solution of QBD-M processes and applications in future Internet engineering.

[1]  L. P. Seelen An algorithm for Ph/Ph/c queues , 1986 .

[2]  Winfried K. Grassmann,et al.  The Use of Eigenvalues for Finding Equilibrium Probabilities of Certain Markovian Two-Dimensional Queueing Problems , 2003, INFORMS J. Comput..

[3]  Tien Van Do An efficient solution to a retrial queue for the performability evaluation of DHCP , 2010, Comput. Oper. Res..

[4]  Ram Chakka,et al.  Heterogeneous Multiprocessor Systems with Breakdowns: Performance and Optimal Repair Strategies , 1994, Theor. Comput. Sci..

[5]  Enver Ever,et al.  Joint-State Modeling for Open Queuing Networks with Breakdowns, Repairs and Finite Buffers , 2007, 2007 15th International Symposium on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems.

[6]  Enver Ever,et al.  A mathematical model for performability of Beowulf clusters , 2006, 39th Annual Simulation Symposium (ANSS'06).

[7]  Udo R. Krieger,et al.  Analysis of a versatile multi-class delay-loss system with a superimposed Markovian arrival process , 1998, Eur. J. Oper. Res..

[8]  Tien Van Do,et al.  The MM sum(k=1 to K of CPPk/GE/c/L) G-queue with heterogeneous servers: Steady state solution and an application to performance evaluation , 2007, Perform. Evaluation.

[9]  최영식,et al.  자기잡음제거 전압제어발진기 이용한 위상고정루프 , 2010 .

[10]  Giuseppe Serazzi,et al.  Processor Saving Scheduling Policies for Multiprocessor Systems , 1998, IEEE Trans. Computers.

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

[12]  Ram Chakka,et al.  Performance and reliability modelling of computing systems using spectral expansion , 1995 .

[13]  Marcel F. Neuts,et al.  Matrix-Geometric Solutions in Stochastic Models , 1981 .

[14]  Tien Van Do,et al.  Performance modeling of an Apache Web server with a dynamic pool of service processes , 2008, Telecommun. Syst..

[15]  Peter G. Harrison,et al.  The MMCPP/GE/c Queue , 2001, Queueing Syst. Theory Appl..

[16]  Ram Chakka,et al.  Multiprocessor Systems with General Breakdowns and Repairs , 1992, SIGMETRICS.

[17]  Peter G. Harrison,et al.  A Markov modulated multi-server queue with negative customers – The MM CPP/GE/c/L G-queue , 2001, Acta Informatica.

[18]  Srinivas R. Chakravarthy,et al.  Matrix-Analytic Methods in Stochastic Models , 1996 .

[19]  Winfried K. Grassmann,et al.  A numerically stable algorithm for two server queue models , 1991, Queueing Syst. Theory Appl..

[20]  Demetres Kouvatsos,et al.  An Information Theoretic Approach for the Performance Evaluation of Multihop Wireless Ad Hoc Networks , 2004 .

[21]  Ram Chakka,et al.  Spectral expansion solution for some finite capacity queues , 1998, Ann. Oper. Res..

[22]  H. R. Gail,et al.  Spectral analysis of M/G/1 and G/M/1 type Markov chains , 1996, Advances in Applied Probability.

[23]  Dietmar Wagner,et al.  Analysis of a multi-server delay-loss system with a general Markovian arrival process , 1994 .

[24]  Demetres D. Kouvatsos,et al.  A Maximum Entropy Analysis of the G/G/1 Queue at Equilibrium , 1988 .

[25]  Ram Chakka,et al.  A Generalized Markovian Queue and Its Applications to Performance Analysis in Telecommunications Networks , 2004 .

[26]  Udo R. Krieger,et al.  Analysis of a Finite FIFO Buffer in an Advanced Packed-Switched Network , 1998 .

[27]  Peter G. Harrison,et al.  An integrated analytical model for computation and comparison of the throughputs of the UMTS/HSDPA user equipment categories , 2007, MSWiM '07.

[28]  Richard V. Evans Geometric Distribution in Some Two-Dimensional Queuing Systems , 1967, Oper. Res..

[29]  Adam Wierman,et al.  How many servers are best in a dual-priority M/PH/k system? , 2006, Perform. Evaluation.

[30]  Winfried K. Grassmann,et al.  An analytical solution for a tandem queue with blocking , 2000, Queueing Syst. Theory Appl..

[31]  Tien Van Do,et al.  A new performability model for queueing and FDL-related burst loss in optical switching nodes , 2010, Comput. Commun..

[32]  Isi Mitrani,et al.  Approximate solutions for heavily loaded Markov-modulated queues , 2005, Perform. Evaluation.

[33]  Victor L. Wallace The solution of quasi birth and death processes arising from multiple access computer systems , 1969 .

[34]  Winfried K. Grassmann,et al.  An Eigenvalue Approach to Analyzing a Finite Source Priority Queueing Model , 2002, Ann. Oper. Res..

[35]  Ram Chakka,et al.  Spectral Expansion Solution for a Class of Markov Models: Application and Comparison with the Matrix-Geometric Method , 1995, Perform. Evaluation.

[36]  Enver Ever,et al.  Analytical modelling and simulation of small scale, typical and highly available Beowulf clusters with breakdowns and repairs , 2009, Simul. Model. Pract. Theory.

[37]  Tien Van Do,et al.  A Performance Model of MPLS Multipath Routing with Failures and Repairs of the LSPs , 2006 .

[38]  Tien Van Do,et al.  Performance Evaluation of the High Speed Downlink Packet Access in Communications Networks Based on High Altitude Platforms , 2008, ASMTA.

[39]  Tien Van Do,et al.  A Markovian queue with varying number of servers and applications to the performance comparison of HSDPA user equipment , 2011, Acta Informatica.

[40]  Ram Chakka,et al.  The MM \sum\limits_{k = 1}^K {} CPPk/GE/c/L G-Queue and Its Application to the Analysis of the Load Balancing in MPLS Networks , 2002 .

[41]  Hung T. Tran,et al.  COMPUTATIONAL ASPECTS FOR STEADY STATE ANALYSIS OF QBD PROCESSES , 2000 .