Fundamentals of queueing theory (2nd ed.).
Fundamentals of queueing theory (2nd ed.).
Queueing systems with vacations—a survey
Queueing Systems: Theory and Applications
The Markov-modulated Poisson process (MMPP) cookbook
Performance Evaluation
Introduction to matrix analysis (2nd ed.)
Introduction to matrix analysis (2nd ed.)
A numerical study of large sparse matrix exponentials arising in Markov chains
Computational Statistics & Data Analysis
On the M(n)/M(n)/s queue with impatient calls
Performance Evaluation
Generalized Polar Decompositions for the Approximation of the Matrix Exponential
SIAM Journal on Matrix Analysis and Applications
Asymptotic Results and a Markovian Approximation for the M(n)/M(n)/s+GI System
Queueing Systems: Theory and Applications
Commissioned Paper: Telephone Call Centers: Tutorial, Review, and Research Prospects
Manufacturing & Service Operations Management
QBD approximations of a call center queueing model with general patience distribution
Computers and Operations Research
Trace data characterization and fitting for Markov modeling
Performance Evaluation
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In this paper, we consider the counting process for a class of Markovian arrival processes (MAPs). We assume that the representing matrices in such MAPs are expanded in terms of matrix representations of the standard generators in the Lie algebra of the special linear group. The primary purpose of this paper is to construct an explicit solution of the time-dependent distribution and factorial moments of the number of arrival events in (0,t] of the counting process for this class of MAPs. Our construction relies on the Baker--Hausdorff lemma and the specific structure of the representing matrices. To investigate the efficiency of CPU usage with the explicit solution, we have conducted numerical experiments on computing the time-dependent distribution of the counting process through the explicit solution and uniformization-based method. We show that the CPU times required to compute the time-dependent distribution of the number of arrival events in (0,t] through the explicit solution have little sensitivity to t, while the consumption of CPU times with the uniformization-based method becomes greater as t increases. For illustrative purposes, we present a system performance analysis of a queueing system for possible use in automatic call distribution (ACD) systems. As an application of the explicit solution, we use it to express the waiting time distribution of the queueing system. Some numerical examples are also given with comparisons to computer simulations.