A matrix analytic solution to a hysteretic queueing system with random server capacity

Tadj, Lotfi

doi:10.1016/s0096-3003(99)00254-4

Cited by 4 publications

(3 citation statements)

References 50 publications

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“…The proof of Equation (11) is given later (see Equations (13) and (14) below). Here, we give its interpretation.…”

Section: Relations Between Arbitrary-and Departure-epoch Probabilitiesmentioning

confidence: 99%

“…However, these articles only dealt with the queue with uncorrelated arrivals. (see also [2,4,8,9,13] for references on such type of queues and their variations in continuous time. ) Here, we discuss the distribution of the number of customers in the queue at various epochs and performance measures such as the average number of customers in the queue and the loss probability of customers.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of a Discrete-Time Finite-Capacity Single-Server Queue with Markovian-Arrival Process and Random-Bulk-Service: D-MAP/G^Y/1/M

Chaudhry

Yoon

Kim

2010

Stochastic Analysis and Applications

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In this article, we consider a single-server, finite-capacity queue with random bulk service rule where customers arrive according to a discrete-time Markovian arrival process (D-MAP). The model is denoted by D-MAP/G Y /1/M where server capacity (bulk size for service) is determined by a random variable Y at the starting point of services. A simple analysis of this model is given using the embedded Markov chain technique and the concept of the mean sojourn time of the phase of underlying Markov chain of D-MAP. A complete solution to the distribution of the number of customers in the D-MAP/G Y /1/M queue, some computational results, and performance measures such as the average number of customers in the queue and the loss probability are presented.

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“…The proof of Equation (11) is given later (see Equations (13) and (14) below). Here, we give its interpretation.…”

Section: Relations Between Arbitrary-and Departure-epoch Probabilitiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analysis of a Discrete-Time Finite-Capacity Single-Server Queue with Markovian-Arrival Process and Random-Bulk-Service: D-MAP/G^Y/1/M

Chaudhry

Yoon

Kim

2010

Stochastic Analysis and Applications

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“…Lam et al [15] derived some queueing characteristics of the system and reliability indices of the service station. Tadj [22] used matrix analytical solution to investigate N-policy in a queueing system. Jain et al [11] also used matrix method to suggest N-policy for a machine repair system.…”

mentioning

confidence: 99%

N-Policy Machine Repair System with Mixed Standbys and Unreliable Server

Jain¹,

Bhargava²

2009

Quality Technology & Quantitative Management

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This paper is concerned with machine repair system having on line units along with mixed standby units under the care of single unreliable server. Whenever any unit fails, it is immediately replaced by a standby unit if available. In case when all standbys are used, the failure of remaining on line units occurs in degraded fashion. The server is turned on when there are N or more failed units present in the system; it is turned off when the system has no failed unit. The server is subject to breakdowns and repairs. The life time and repair time of failed units and the server are exponentially distributed. The governing equations are constructed using appropriate birth-death rates. After taking Laplace transform of set of equations, we employ matrix method to determine transient probabilities. Various performance indices such as expected number of standby units, expected number of failed units, probability of server being idle, busy or broken etc. are determined. Expressions for the system reliability and mean time to system failure are established in terms of transient probabilities. Cost function is also facilitated which may be helpful for system designer to achieve effective system descriptors. Numerical results are provided for various system characteristics to examine the effects of different parameters.

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On the time to reach a certain orbit level in multi-server retrial queues

Apaolaza

Artalejo

2005

Applied Mathematics and Computation

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A matrix analytic solution to a hysteretic queueing system with random server capacity

Cited by 4 publications

References 50 publications

Analysis of a Discrete-Time Finite-Capacity Single-Server Queue with Markovian-Arrival Process and Random-Bulk-Service: D-MAP/G^Y/1/M

Analysis of a Discrete-Time Finite-Capacity Single-Server Queue with Markovian-Arrival Process and Random-Bulk-Service: D-MAP/G^Y/1/M

N-Policy Machine Repair System with Mixed Standbys and Unreliable Server

On the time to reach a certain orbit level in multi-server retrial queues

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A matrix analytic solution to a hysteretic queueing system with random server capacity

Cited by 4 publications

References 50 publications

Analysis of a Discrete-Time Finite-Capacity Single-Server Queue with Markovian-Arrival Process and Random-Bulk-Service: D-MAP/GY/1/M

Analysis of a Discrete-Time Finite-Capacity Single-Server Queue with Markovian-Arrival Process and Random-Bulk-Service: D-MAP/GY/1/M

N-Policy Machine Repair System with Mixed Standbys and Unreliable Server

On the time to reach a certain orbit level in multi-server retrial queues

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Product

Resources

About

Analysis of a Discrete-Time Finite-Capacity Single-Server Queue with Markovian-Arrival Process and Random-Bulk-Service: D-MAP/G^Y/1/M

Analysis of a Discrete-Time Finite-Capacity Single-Server Queue with Markovian-Arrival Process and Random-Bulk-Service: D-MAP/G^Y/1/M