Performance Analysis and Optimal Threshold Policies for Queueing Systems with Several Heterogeneous Servers and Markov Modulated Arrivals

2016 ◽  
pp. 137-156 ◽  
Keyword(s):  
Performance Analysis ◽  
Queueing Systems ◽  
Optimal Threshold ◽  
Heterogeneous Servers ◽  
Threshold Policies ◽  
Markov Modulated

scholarly journals Markov-Modulated Bernoulli-Based Performance Analysis for Gentle BLUE and BLUE Algorithms under Bursty and Correlated Traffic

2016 ◽  
Vol 12 (6) ◽  
pp. 289-299 ◽  
Author(s):  
Adeeb Alsaaidah ◽  
Mohd Zalisham ◽  
Mohd Fadzli ◽  
Hussein Abdel-Jaber
Keyword(s):  
Performance Analysis ◽  
Markov Modulated ◽  
Correlated Traffic

Markov-modulated traffic with nearly complete decomposability characteristics and associated fluid queueing models

1995 ◽  
Vol 27 (04) ◽  
pp. 1144-1185
Author(s):  
Kimon P. Kontovasilis ◽  
Nikolas M. Mitrou
Keyword(s):  
State Space ◽  
Time Scales ◽  
Structural Characteristics ◽  
Queueing Systems ◽  
Queuing Models ◽  
Aggregation Techniques ◽  
Phase Perturbation ◽  
Order Of Magnitude ◽  
Markov Modulated ◽  
The Individual

This paper considers fluid queuing models of Markov-modulated traffic that, due to large differences in the time-scales of events, possess structural characteristics that yield a nearly completely decomposable (NCD) state-space. Extension of domain decomposition and aggregation techniques that apply to approximating the eigensystem of Markov chains permits the approximate subdivision of the full system to a number of small, independent subsystems (decomposition phase), plus an ‘aggregative' system featuring a state-space that distinguishes only one index per subsystem (aggregation phase). Perturbation analysis reveals that the error incurred by the approximation is of an order of magnitude equal to the weak coupling of the NCD Markov chain. The study in this paper is then extended to the structure of NCD fluid models describing source superposition (multiplexing). It is shown that efficient spectral factorization techniques that arise from the Kronecker sum form of the global matrices can be applied through and combined with the decomposition and aggregation procedures. All structural characteristics and system parameters are expressible in terms of the individual sources multiplexed together, rendering the construction of the global system unnecessary. Finally, besides providing efficient computational algorithms, the work in this paper can be recast as a conceptual framework for the better understanding of queueing systems under the presence of events happening in widely differing time-scales.

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