The superposition of two independent Markov renewal processes

Cherry, W. Peter; Disney, Ralph L.

doi:10.4064/am-17-4-567-602

Cited by 9 publications

(12 citation statements)

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“…However, Markov renewal processes find a natural application in many situations and have been particularly useful in modeling queueing situations and providing useful insights (cf. Disney et al (1973), Disney et al (1981)). Further, the special structure of Markov renewal processes allows for computations without undue difficulty.…”

Section: Chapter 4 Mark Dependent Thinning Of Markov Renewal Processementioning

confidence: 99%

Thinning of point processes—covariance analyses

1985

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Cross-covariances between the Bernoulli thinned processes of an arbitrary point process are determined. When the point process is renewal it is shown that zero correlation implies independence. An example is given to show that zero covariance between intervals does not imply zero covariance between counts. Mark-dependent thinning of Markov renewal processes is discussed and the results are applied to the overflow queue. Here we give an example of two uncorrelated but dependent renewal processes, neither of which is Poisson, which yield a Poisson process when superposed. Finally, we study Markov-chain thinning of renewal processes.

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Section: Chapter 4 Mark Dependent Thinning Of Markov Renewal Processementioning

confidence: 99%

Thinning of point processes—covariance analyses

1985

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“…In [1] the superposition state descriptor is a vector consisting of the current state of each component process and the time each process has spent in its current state since its last transition. It is clear that such a characterization results in an enormous state space, since the time a component process spends in a state can be quite large especially when some of the functions s. (x, y, k ) have a long tail.…”

Section: Characterization Of Thementioning

confidence: 99%

“…Cherry and Disney [1] studied the superposition of two continuous-time MRP's. The structure of the interval process resulting from superposing two independent MRP was characterized.…”

Section: Introductionmentioning

confidence: 99%

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The superposition of discrete-time Markov renewal processes with an application to statistical multiplexing of bursty traffic sources

Elsayed

Perros

2000

Applied Mathematics and Computation

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L~this pa per we introduce a methodology for approximately characterizing the superpo sition process of J.V~2 arbitrary discrete-time Markov Renewal Processes (MP2). The superposition process is also a~..,,1RP with a state space that grows exponentially with N. We introduce the arbitrary ani off traffic source model as a special case of the general~. For this special case, we devise an iterative algorithm which can be used to characterize the superposition process in a compact form. Subsequently, a queueing model for a FIFO finite-buffer multiplexer with arbitrary ani off input sources is analyzed. We provide extensive numerical and validation results for the algorithms introduced in the paper. We also study the effect of some of the statistical properties of ani off input sources on the multiplexer's performance.

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“…In particular, they generalized the concepts of renewal functions, renewal equation and the key renewal theorem to the max-position of renewal process. The max-position of two independent Markov renewal processes with countable state space was studied before by Cherry [3], Cherry and Disney [14]. In theses papers, they showed that the max-posed process is again a Markov renewal process defined on a more general state space.…”

Section: Introductionmentioning

confidence: 97%

Analysis of Markov renewal reward process on VLSI cell partitioning

Manikandan¹,

Swaminathan²

2013

ams

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It is well known that various characteristics in risk and queuing process can be formulated as Markov Renewal function. We study the max-position of finitely many Markov Renewal Reward process with countable state space. We define Markov Renewal equation associated with max-posed process. The solutions of the Markov Renewal Reward equation are derived and the asymptotic behaviors of the equations are studied. Also we discuss the idea of delayed Markov renewal reward with state space.

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The superposition of two independent Markov renewal processes

Cited by 9 publications

References 0 publications

Thinning of point processes—covariance analyses

Thinning of point processes—covariance analyses

The superposition of discrete-time Markov renewal processes with an application to statistical multiplexing of bursty traffic sources

Analysis of Markov renewal reward process on VLSI cell partitioning

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