Telecommunication networks: protocols, modeling and analysis
Telecommunication networks: protocols, modeling and analysis
Numerical recipes: the art of scientific computing
Numerical recipes: the art of scientific computing
Fundamentals of queueing theory (2nd ed.).
Fundamentals of queueing theory (2nd ed.).
Probability, statistics, and queueing theory with computer science applications
Probability, statistics, and queueing theory with computer science applications
Exact and approximate numerical solutions of steady-state distributions arising in the queue GI/G/1
Queueing Systems: Theory and Applications - Numerical computations in queues
Combined Elapsed Time and Matrix-Analytic Method for the Discrete Time GI/G/1 and GIX/G/1 Systems
Queueing Systems: Theory and Applications
Performance evaluation of a single node with general arrivals and service
ASMTA'11 Proceedings of the 18th international conference on Analytical and stochastic modeling techniques and applications
An approximate solution for Ph/Ph/1 and Ph/Ph/1/N queues
ICPE '12 Proceedings of the 3rd ACM/SPEC International Conference on Performance Engineering
Approximations and bounds for the variance of steady-state waiting times in a GI/G/1 queue
Operations Research Letters
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This paper focuses on easily computable numerical approximations for the distribution and moments of the steady-state waiting times in a stable GI/G/1 queue. The approximation methodology is based on the theory of Fredholm integral equations and involves solving a linear system of equations. Numerical experimentation for various M/G/1 and GI/M/1 queues reveals that the methodology results in estimates for the mean and variance of waiting times within \pm1% of the corresponding exact values. Comparisons with competing approaches establish that our methodology is not only more accurate, but also more amenable to obtaining waiting time approximations from the operational data. Approximations are also obtained for the distributions of steady-state idle times and interdeparture times. The approximations presented in this paper are intended to be useful in rough-cut analysis and design of manufacturing, telecommunications, and computer systems as well as in the verification of the accuracies of inequalities, bounds, and approximations.