Matrix Analytic Methods

Grassmann, Winfried K.; Stanford, David A.

doi:10.1007/978-1-4757-4828-4_6

Cited by 36 publications

(40 citation statements)

References 31 publications

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“…R 0,k (s) and R k (s) increase as s → ∞. This can be verified by examining (6). We take R k (s) as an example to reveal this property.…”

Section: Setmentioning

confidence: 63%

“…Such a transition probability matrix is said to have the rowrepeating property in this paper. The Markov chain defined in (4) [6,14]. We notice that both (2) and (3) …”

Section: Characteristics Of the R Measuresmentioning

confidence: 99%

“…In addition, as shown in [6,19], the steady probability vector π for the GI/G/1-type Markov chain satisfies…”

Section: Characteristics Of the R Measuresmentioning

confidence: 99%

“…In other words, R 0,k (s) and R k (s) must converge to some limit value R * 0,k and R * k , respectively, as s → ∞. The limit values of R * 0,k and R * k can be considered as the exact solution for the system of equations (6).…”

Section: Setmentioning

confidence: 99%

“…It is known that there is no general solution for this type of Markov chain, where the block elements of the transition probability matrix have infinite dimensions. The matrix-analytic methods [6] can handle the case only when the block elements are of finite size. In this paper, we develop an analytical solution for the problem.…”

Section: Introductionmentioning

confidence: 99%

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A matrix-analytic solution for the DBMAP/PH/1 priority queue

Zhao¹,

Li²,

Cao

et al. 2006

Queueing Syst

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Priority queueing models have been commonly used in telecommunication systems. The development of analytically tractable models to determine their performance is vitally important. The discrete time batch Markovian arrival process (DBM AP ) has been widely used to model the source behavior of data traffic, while phase-type (P H) distribution has been extensively applied to model the service time. This paper focuses on the computation of the DBM AP/P H/1 queueing system with priorities, in which the arrival process is considered to be a DBM AP with two priority levels and the service time obeys a discrete P H distribution. Such a queueing model has potential in performance evaluation of computer networks such as video transmission over wireless networks and priority scheduling in ATM or TDMA networks. Based on matrix-analytic methods, we develop computation algorithms for obtaining the stationary distribution of the system numbers and further deriving the key performance indices of the DBM AP/P H/1 priority queue.

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“…R 0,k (s) and R k (s) increase as s → ∞. This can be verified by examining (6). We take R k (s) as an example to reveal this property.…”

Section: Setmentioning

confidence: 63%

“…Such a transition probability matrix is said to have the rowrepeating property in this paper. The Markov chain defined in (4) [6,14]. We notice that both (2) and (3) …”

Section: Characteristics Of the R Measuresmentioning

confidence: 99%

“…In addition, as shown in [6,19], the steady probability vector π for the GI/G/1-type Markov chain satisfies…”

Section: Characteristics Of the R Measuresmentioning

confidence: 99%

Section: Setmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A matrix-analytic solution for the DBMAP/PH/1 priority queue

Zhao¹,

Li²,

Cao

et al. 2006

Queueing Syst

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Level‐Independent Quasi‐Birth‐and‐Death Processes

Latouche

2011

Wiley Encyclopedia of Operations Research and Management Science

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M/G/1-Type Markov Processes: A Tutorial

Riska

Smirni

2002

Performance Evaluation of Complex Systems: Techniques and Tools

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M/G/1-type processes are commonly encountered when modeling modern complex computer and communication systems. In this tutorial, we present a detailed survey of existing solution methods for M/G/1-type processes, focusing on the matrix-analytic methodology. From first principles and using simple examples, we derive the fundamental matrix-analytic results and lay out recent advances. Finally, we give an overview of an existing, state-of-the-art software tool for the analysis of M/G/1-type processes.

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Matrix Analytic Methods

Cited by 36 publications

References 31 publications

A matrix-analytic solution for the DBMAP/PH/1 priority queue

A matrix-analytic solution for the DBMAP/PH/1 priority queue

Level‐Independent Quasi‐Birth‐and‐Death Processes

M/G/1-Type Markov Processes: A Tutorial

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