Introduction to Matrix Analytic Methods in Stochastic Modeling

By Tom L. Burr. Technometrics, 2001

1,191 citations recorded by the source corpus.

Subfields: Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/159e8c5962cff91ffbd94a4b4261a11fe5ac256a

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Citations in the corpus

Comparison of Inventory Systems with Service, Positive Lead-Time, Loss, and Retrial of Customers (2007, methodology): “For a detailed discussion of the matrix-analytic method, see [13].”
Monitoring the ratio of population means of a bivariate normal distribution using CUSUM type control charts (2016, methodology): “As proposed by Neuts (1981) and Latouche and Ramaswami (1999), since the number of steps RL until the process reaches the absorbing state is a Discrete PHase-type (or DPH) random variable of parameters (Q,q), the mean (ARL) and the standard-deviation (SDRL) of the run length RL of the one-sided…”
Platoons of connected vehicles can double throughput in urban roads (2015, methodology): “This Markov chain can also be analyzed by matrix-analytic methods (Latouche and Ramaswami (1999)), but the RRR technique is better as it does not require computing the stationary distribution of the chain to determine the average delay (or other performance metrics).”
Monitoring the Coefficient of Variation Using a Variable Sampling Interval EWMA Chart (2017, background): “…number of states L until the process reaches the absorbing state is a discrete phase type (DPT) random variable of parameters (Pt,d) (Neuts (1981), Latouche and Ramaswami (1999)), where d is the (m + 1) × 1 vector of initial probabilities associated with the m + 1 transient states, i.e., d = (d0,…”
Telephone Call Centers: Tutorial, Review, and Research Prospects (2003, neutral): “(For example, see Latouche and Ramaswami [100].”
On the Distribution of the Deficit at Ruin when Claims are Phase-type (2004, background): “A more detailed description of phase-type distributions and their applications can be found in Neuts (1981) and Latouche & Ramaswami (1999).”
Many-server diffusion limits for G/Ph/n+GI queues (2010, neutral): “It is well known [see, e.g., Latouche and Ramaswami (1999)] that P[v ≤ x] = 1 − p′ exp(Fx)e for x ≥ 0.”
Decompositions of binomial ideals (2009, neutral): “It can be constructed by taking the quotient of a univariatepolynomial ring modulo the principal ideal generated by the minimal polyn mial ofξl , thecyclotomic polynomial(Hungerford 1974, Chapter V).”
Monitoring the ratio of two normal variables using Run Rules type control charts (2016, neutral): “…steps RL until the process reaches the absorbing state is a Discrete PHase-type (or DPH) random variable of parameters (Q, q), (see Neuts (1981) or Latouche and Ramaswami (1999)), the mean (ARL) and the standard deviation (SDRL) of the run length RL of the one-sided R R RZ2,3 and R R RZ3,4 charts…”
A Review on Phase-type Distributions and their Use in Risk Theory (2005, background): “For a more elementary textbook, which mainly draws examples from queueing theory, we refer to Latouche and Ramaswami (1999).”
Numerical analysis of a quadratic matrix equation (2000, background): “An excellent reference is the recent book by Latouche & Ramaswami (1999).”
On an (s, S) Inventory Policy with Service Time, Vacation to Server and Correlated Lead Time (2008, background): “For further details one may refer to Latouche and Ramaswami [9].”
Perturbation analysis for denumerable Markov chains with application to queueing models (2004, methodology): “To illustrate our results on singular perturbation we now apply them for quasi-birth-anddeath (QBD) processes; we refer the reader to [19] and [23] for general discussions on QBDs.”
Risk processes analyzed as fluid queues (2005, methodology): “It was in fact mindful of (4.2) that we postulated an exponential form for Ĝu(s): This is related to Theorem 3.2 in Ramaswami [15].”
Quasi-Birth-and-Death Processes with Rational Arrival Process Components (2010, background): “1 of [6] directly as the proof of that theorem is purely analytical relying only on equation (7) and Remark 1 to show that G = e(3,−1,−1).”
Matching Three Moments with Minimal Acyclic Phase Type Distributions (2005, background): “The definition and basic properties of PH distributions are provided in various text books, eg, in Latouche [7] .”