Performance analysis of an infinite-buffer batch-size-dependent bulk service queue with server breakdown and multiple vacation

Pradhan, Sourav; Karan, Prasenjit

doi:10.3934/jimo.2022143

Cited by 8 publications

(3 citation statements)

References 40 publications

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“…where 𝐾 ′ (𝑏) (1), 𝐾 ′′ (𝑏) (1), 𝑀 ′ (1), 𝑀 ′′ (1), 𝐻 ′ (1) and 𝐻 ′′ (1) are the first and second order derivative of 𝐾 (𝑏) (𝑧), 𝑀(𝑧) and 𝐻(𝑧), respectively, evaluated at 𝑧 = 1.…”

Section: Marginal Distributions and Performance Measuresmentioning

confidence: 99%

Stationary queue and server content distribution of a vacation queue with N -policy and set up time

Pradhan

Karan

Nandy

2023

Preprint

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Due to unambiguous applications of bulk service vacation queues with set up time in various fields such as pharmaceutical, aerospace engineering, automobile industries etc., in this article, we analyze an infinite-buffer batch-size-dependent bulk service queue with single and multiple vacations, N-policy and set up time. Customers/packets/units are served by a single server according to general bulk service ( a,b) rule. The service time of a batch dynamically vary with the batch-size and follows the general type of distribution which covers a large scale of distributions. Firstly, we generate the steady-state system equations. The main intend of this study is to obtain the complete joint distribution of queue-length and server content at service completion epoch, for which the bivariate probability generating function has been derived. We extract the joint distribution which is presented in a quite simple form and using those we find the joint distribution at arbitrary epoch beside some marginal distributions and performance measures. Finally, several numerical examples along with graphical sketches have been provided to verify the analytical results and to provide inner feeling to the system designers.

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Section: Marginal Distributions and Performance Measuresmentioning

confidence: 99%

Stationary queue and server content distribution of a vacation queue with N -policy and set up time

Pradhan

Karan

Nandy

2023

Preprint

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“…The existing literature on breakdown queueing theory involves examinations of both the conduct of the client within the queue and the behaviors, and characteristics of the system's servers. These studies present an explanation of queueing systems, including Controlled arrivals, breakdown and repair, Working Breakdown, two-customer and a server subject to breakdown, bulk service queue with server breakdown and multiple vacations, M/M/1 queueing model with working vacation, and two types of server breakdown (6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18) . Gross D introduced steady-state equations and demonstrated them in certain models (19) .…”

Section: Introductionmentioning

confidence: 99%

Poisson Input and Exponential Service Time Finite Capacity Interdependent Queueing Model with Breakdown and Controllable Arrival Rates

Therasal,

Thiagarajan

2024

IJST

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Objectives: This study aims at (i) introducing the finite capacity of the interdependent queueing model with breakdown and controllable arrival rates, (ii) calculating the average number of clients in the system, and identifying the expected waiting period of the clients in the system, (iii) dealing with the model descriptions, steady-state equations, and characteristics, which are expressed in terms of , and (iv) analyzing the probabilities of the queueing system and its characteristics with numerical verification of the obtained results. Methods: While providing the input, the arrival rates through faster and slower arrival rates are controlled using the Poisson process. Also, the service provides an exponential distribution. The server provides the service on an FCFS basis. In this article, two types of models are used: and which are the system’s conditions, where represents the number of units present in the queue in which their probability is and . All probabilities are distributed based on the speed of advent using this concept. Then, the steady-state probabilities are computed using a recursive approach. Findings: This paper discovers the number of clients using the system on average and the expected number of clients in the system using the probability of the steady-state calculation. Little’s formula is used to derive the expected waiting period of the clients in the system. Novelty: There are articles connected to the finite capacity of failed service in functioning and malfunctioning, but this takes the initiative to provide a link in connection with the rates of the controllable arrivals and interdependency in the arrival and service processes. Mathematics Subject allocation: 60K25, 68M20, 90B22. Keywords: M/M/1/K Queue Model, Finite Capacity, Breakdown, Controllable Arrival rates, FCFS Queue Discipline

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“…Various studies have been conducted on queueing systems to elucidate the concept of bulk service. These investigations provide a comprehensive understanding of queueing systems, such as k-stage bulk service, heterogeneous bulk service, group service for impatient customers, performance analysis of dependent bulk service queues with server breakdowns, multiple vacation transient behaviours of bulk service queueing systems with standby servers, and others (11)(12)(13)(14)(15)(16)(17) . Additionally, Anyue Chen, Xiaohan Wu & Jing Zhang (2020) proposed "Markovian bulk-arrival and bulk-service queues with general state-dependent control" (18) .…”

Section: Introductionmentioning

confidence: 99%

M/M(a,b)/1 Model Of Interdependent Queueing With Controllable Arrival Rates

Rahim,

Thiagarajan

2023

IJST

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Objectives: Instead of only providing individualized one-on-one assistance, some studies in the literature on queueing theory describe systems that provide services in batches. This study introduces controllable arrival rates and interdependency in such a system's service and arrival processes and then obtains the queueing system's probabilities and characteristics. It also verified the obtained results numerically. Methods: Controlling the arrival rates by faster and slower arrival rates are expected for the input, with Poisson (each time Poisson occurrence has one arrival) being the default assumption. The general bulk service rule dictates that the service be delivered in batches. Service begins only when the count of customers in the queue approaches or surpasses a and the capacity b (≥a ≥ 1). For brevity, a batch's service time distribution is assumed to be exponential and is not dependent on the batch size. Then, all the steady-state probabilities are derived using a recursive approach. Findings: We used M/M(a,b)/1 as the notation. For this model, steady-state solutions & characteristics are derived and explored. All the probabilities are expressed in terms of P 0,0 (0). The expected count of customers and waiting time depends on the interdependency, service rate, faster arrival rate, and slower arrival rate. According to each parameter, all the results are verified. Novelty: There are works related to bulk service in queuing theory, but this is a new approach to give a bridge between bulk service and controllable arrival rates along with interdependency in the arrival and service process.

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Performance analysis of an infinite-buffer batch-size-dependent bulk service queue with server breakdown and multiple vacation

Cited by 8 publications

References 40 publications

Stationary queue and server content distribution of a vacation queue with N -policy and set up time

Stationary queue and server content distribution of a vacation queue with N -policy and set up time

Poisson Input and Exponential Service Time Finite Capacity Interdependent Queueing Model with Breakdown and Controllable Arrival Rates

M/M(a,b)/1 Model Of Interdependent Queueing With Controllable Arrival Rates

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