Majorization and Extremal PH Distributions

He, Qi–Ming; Zhang, Hanqin; Vera, Juan C.

doi:10.1007/978-1-4614-4909-6_6

Cited by 2 publications

(2 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Such fluid queues have been widely regarded as valuable mathematical tools for modelling, for instance, packet speech, video systems with or without background data, computer networks, including call admission control, traffic shaping and modelling of Traffic Control Protocol (TCP), and production and inventory control. Refer to [7], [8] . The research presented in this article effectively employs the traffic model used in the previous two articles, where a traffic flow is defined by a piecewise-constant rate function.…”

Section: Introductionmentioning

confidence: 99%

An Alleviation of Cloud Congestion Analysis of Fluid Retrial User on Matrix Analytic Method in IoT-based Application

Nandhini

Vidhya

2023

J. Nig. Soc. Phys. Sci.

View full text Add to dashboard Cite

Cloud Computing (CC) and Internet of Things (IoT) are upgrowing human intervention to enhance the daily lifestyle. Currently, the heavy loaded traffic congestion is a very big challenge over IoT-based applications. For that purpose, the researchers approached various ways to overcome the congestion mechanism in recent years. Even though, they have futile to acheive the best resource storage accessing capacity expectation other than, Cloud Computing. Data sharing is a key impediment of Cloud Computing as well as Internet of Things. These are the constituent that give rise to the combination of the IoT and cloud computing paradigm as IoT Cloud. Though, preserving the missed data during the execution time is a key factor to indulge the Retrial Queueing Theory (RQT), who is facing issue upon accessing Cloud Service Provider (CSP) enter into virtual pool to preserve the data for reuse. The paper imposes Markov Fluid analysis with Matrix Analytic Method (MAM) allows the data as continuous length of data rather than individual data to avoid the congestion. The virtual orbit queue follow constant retrial rate discipline, that is, head of the orbital users makes attempt to occupy the server are assumed to be independent and identically distributed (i.i.d). Steady-state expression presented to study the behaviour of congestion. An illustrative analysis is produced to gain deep perception into the system model.

show abstract

Section: Introductionmentioning

confidence: 99%

An Alleviation of Cloud Congestion Analysis of Fluid Retrial User on Matrix Analytic Method in IoT-based Application

Nandhini

Vidhya

2023

J. Nig. Soc. Phys. Sci.

View full text Add to dashboard Cite

show abstract

“…In [11] the minimal SCV of discrete PH distributions was found. In [2] stochastic comparison was utilized in the study of PH distributions, which also led to moment bounds of PH distributions. These results not only Bounds of PH distributions with infinite or finite support 169 deepen our understanding of PH distributions and PH representations, but also facilitate the applications of PH distributions significantly.…”

Section: Introductionmentioning

confidence: 99%

Moment bounds of PH distributions with infinite or finite support based on the steepest increase property

Horväth

Horváth

et al. 2019

Adv. Appl. Probab.

Self Cite

View full text Add to dashboard Cite

The steepest increase property of phase-type (PH) distributions was first proposed in O’Cinneide (1999) and proved in O’Cinneide (1999) and Yao (2002), but since then has received little attention in the research community. In this work we demonstrate that the steepest increase property can be applied for proving previously unknown moment bounds of PH distributions with infinite or finite support. Of special interest are moment bounds free of specific PH representations except the size of the representation. For PH distributions with infinite support, it is shown that such a PH distribution is stochastically smaller than or equal to an Erlang distribution of the same size. For PH distributions with finite support, a class of distributions which was introduced and investigated in Ramaswami and Viswanath (2014), it is shown that the squared coefficient of variation of a PH distribution with finite support is greater than or equal to 1/(m(m + 2)), where m is the size of its PH representation.

show abstract

Majorization and Extremal PH Distributions

Cited by 2 publications

References 13 publications

An Alleviation of Cloud Congestion Analysis of Fluid Retrial User on Matrix Analytic Method in IoT-based Application

An Alleviation of Cloud Congestion Analysis of Fluid Retrial User on Matrix Analytic Method in IoT-based Application

Moment bounds of PH distributions with infinite or finite support based on the steepest increase property

Contact Info

Product

Resources

About