Steady state analysis of fluid queues driven by birth death processes with rational rates

Kapoor, Shruti; Selvamuthu, Dharmaraja

doi:10.1504/ijor.2020.10027270

Cited by 4 publications

(4 citation statements)

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“…Another study by Li et al [36] used maximum likelihood estimation as a statistical inference for inter-arrival and service rate distribution for general distributions of arrival and ST. Sadu et al [37] used sensitivity analysis to measure system performance for bulk size distribution parameters. Kapoor and Dharmaraja [38] present fluid queues in steady-state with reasonable birth and death rates and find explicit eigenvalues for buffer occupancy. Shone et al [39] discussed literature on stochastic modelling in air traffic queues in light of non-stationarity cases and non-Poisson arrival that the queueing system may never settle down near steady-state conditions.…”

Section: Statistical Inferencing In Queueingmentioning

confidence: 99%

Data-Driven Queueing Science Approach to Manage Secondary Queue Formation of Passenger Flow in Indian Railways: A Case of Overbooking on Vaishali Train

QASIM,

Farooquie

2023

Preprint

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Overbooking has been far and wide embraced to save any system from being idle. Rarely does the literature focuses on the unique queue formation nomenclatures as secondary queue due to overbooking. In this background, deciding the buffer capacity in the secondary queue is a major concern. The hypothetical design of a buffer often leads to wrong decision-making. In this paper, we take a real data-driven approach to explore the passenger flow through the lens of a queueing scientist. The means is to perform the statistical analysis using stationarity (Augmented Dickey-Fuller test), independence (Pearson's correlation) and distribution fitting for the data to validate the queueing system of Advanced Passenger Reservation. Further, what are the unique features of this queueing system in terms of its system primitives, key performance measures, and buffer capacity have been evaluated. What-if analysis has been explored for the different buffer capacities, and operational policy has been suggested for the passenger flow based on different scenarios. Our results show that Inter arrival and service time must be governed by a combination of N and F policies of queueing with suitable channels (servers) to quantify the overbooking.

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Section: Statistical Inferencing In Queueingmentioning

confidence: 99%

Data-Driven Queueing Science Approach to Manage Secondary Queue Formation of Passenger Flow in Indian Railways: A Case of Overbooking on Vaishali Train

QASIM,

Farooquie

2023

Preprint

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“…The study [4] approaches a catastrophic queueing model in random environment over fluid queue investigates the stability of the system. Mao et al [5] and [6] have studied the fluid vacation model expressing Laplacian of the stationary distribution. Kapoor, S., and Dharmaraja, S. [9] have obtained the transient analysis of fluid queue by exploiting the explicit solution of eigenvalue decomposition and subsequently computing the eigenvector interms of bisection algorithm.…”

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.

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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.

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“…Kapoor et al [16] studied the transient distribution of the buffer content of fluid queueing model driven by two distinct restricted state birth-death processes. More works on fluid queueing models with stationary and non-stationary behaviors can be found in Maki [17], Lenin and Parthasarathy [18], Kapoor and Dharmaraja [19], van Doorn and Scheinhardt [20], Parthasarathy and Vijayashree [21], Arunachalama et al [22], and to name a few. In recent years, many researchers investigated on fluid queueing systems subject to catastrophes or vacations.…”

Section: Introductionmentioning

confidence: 99%

“…Maki [17] derivedthe distribution function of a birth and death process in which the denominator and numerator are generic polynomials, where the rates of birth and death are rational functions of the state of the process. Parthasarathy and Vijayashree [21] carried out the distribution of buffer content of a fluid queueing model driven through birth and death process with quadratic arrival and service rates on a limited state space.Kapoor and Dharmaraja [19] established the stationary behaviour of a fluid queueing model with rational birth and death rates driven through a limited birth death process. Kumar et al [35] studied a state-dependent queueing system with catastrophes using continued fraction technique.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Stationary Fluid Queue Driven by State-Dependent Birth-Death Process Subject to Catastrophes

Ammar¹,

Samanta²,

Kilany³

et al. 2022

Scientia Iranica

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This paper investigates an infinite buffer fluid queueing model driven by a state-dependent birth-death process prone to catastrophes.We use the Laplace-Stieltjes transform and continued fraction approaches to establish precise expression for the joint probability of the content of the buffer and the number of customers in an / /1 MM queueing model. The importance of the proposed system is that, in numerous practical situation, the service facility has defence mechanisms in place to deal with long waits. Under the strain of a significant backlog of work, the servers may improve their service rate. Therefore,considering the state-dependent character of queueing systems is of relevance. For example, congestion control technologies prevent long queues forming in computer and communication systems by adjusting packet transmission speeds based on the length of the queue (of packets) at the source or destination. Theoretical results are supported by numerical illustrations.

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Steady state analysis of fluid queues driven by birth death processes with rational rates

Cited by 4 publications

References 0 publications

Data-Driven Queueing Science Approach to Manage Secondary Queue Formation of Passenger Flow in Indian Railways: A Case of Overbooking on Vaishali Train

Data-Driven Queueing Science Approach to Manage Secondary Queue Formation of Passenger Flow in Indian Railways: A Case of Overbooking on Vaishali Train

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

Analysis of Stationary Fluid Queue Driven by State-Dependent Birth-Death Process Subject to Catastrophes

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