Waiting-time analysis of D-$${ BMAP}{/}G{/}1$$BMAP/G/1 queueing system

Samanta, S. K.

doi:10.1007/s10479-015-1974-6

Cited by 12 publications

(5 citation statements)

References 24 publications

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“…Here π + (n, 1) = φ + (n), n ≥ 0. One may note that the waiting-time analysis of D-MAP/G/1 queue can be obtained from those of Samanta [24] by considering D n = 0, n ≥ 2.…”

Section: D-map/g/1/∞ Queuementioning

confidence: 99%

Complete analysis of a discrete-time batch service queue with batch-size-dependent service time under correlated arrival process: D-MAP/G_n^(a,b)/1

et al. 2021

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Discrete-time queueing models find a large number of applications as they are used in modeling queueing systems arising in digital platforms like telecommunication systems and computer networks. In this paper, we analyze an infinite-buffer queueing model with discrete Markovian arrival process. The units on arrival are served in batches by a single server according to the general bulk-service rule, and the service time follows general distribution with service rate depending on the size of the batch being served. We mathematically formulate the model using the supplementary variable technique and obtain the vector generating function at the departure epoch. The generating function is in turn used to extract the joint distribution of queue and server content in terms of the roots of the characteristic equation. Further, we develop the relationship between the distribution at the departure epoch and the distribution at arbitrary, pre-arrival and outside observer's epochs, where the first is used to obtain the latter ones. We evaluate some essential performance measures of the system and also discuss the computing process extensively which is demonstrated by some numerical examples.

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“…Here π + (n, 1) = φ + (n), n ≥ 0. One may note that the waiting-time analysis of D-MAP/G/1 queue can be obtained from those of Samanta [24] by considering D n = 0, n ≥ 2.…”

Section: D-map/g/1/∞ Queuementioning

confidence: 99%

Complete analysis of a discrete-time batch service queue with batch-size-dependent service time under correlated arrival process: D-MAP/G_n^(a,b)/1

et al. 2021

View full text Add to dashboard Cite

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“…, mean (v)=3.333333 and hence H(x) = 0.15 + 0.15x 0.65 − 0.35x . The joint distribution at service completion and arbitrary epochs along with some performance measures are displayed in Tables [2][3][4][5] . Example 2: In this example, the service time has been considered as negative binomial (NB) distribution with pmf…”

Section: Numerical Illustrationmentioning

confidence: 99%

“…Consequently, those systems can be adequately modeled and analyzed using discrete-time queues which have notable diverse spectrum of applications in modern telecommunication/wireless systems, see e.g. Bruneel and Kim [1], Alfa [2], Samanta et al [3,4,5], Gupta et al [6,7], Claeys et al [8] and references therein. Batch-service queues are ubiquitous in several practical situations such as automatic manufacturing technology (very large-scale integrated (VLSI) circuits), blood pooling, ovens in manufacturing system, mobile crowdsourcing app for smart cities, recreational devices in amusement park etc.…”

Section: Introductionmentioning

confidence: 99%

On the joint distribution of an infinite-buffer discrete-time batch-size-dependent service queue with single and multiple vacation

Nandy,

Pradhan

2020

Preprint

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Due to the widespread applicability of discrete-time queues in wireless networks or telecommunication systems, this paper analyzes an infinite-buffer batch-service queue with single and multiple vacation where customers/messages arrive according to the Bernoulii process and service time varies with the batch-size.The foremost focal point of this analysis is to get the complete joint distribution of queue length and server content at service completion epoch, for which first the bivariate probability generating function has been derived. We also acquire the joint distribution at arbitrary slot. We also provide several marginal distributions and performance measures for the utilization of the vendor. Transmission of data through a particular channel is skipped due to the high transmission error. As the discrete phase type distribution plays a noteworthy role to control this error, we include numerical example where service time distribution follows discrete phase type distribution. A comparison between batch-size dependent and independent service has been drawn through the graphical representation of some performance measures and total system cost.

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“…Here π + (n, 1) = φ + (n), n ≥ 0. One may note that the waiting-time analysis of D-M AP/G/1 queue can be obtained from those of Samanta [21] by considering D n = 0, n ≥ 2.…”

Section: D-map/g/1/∞ Queuementioning

confidence: 99%

Analysis of an infinite-buffer batch-size-dependent service queue with discrete-time Markovian arrival process: D-$MAP/G_n^{(a,b)}/1$

Gupta,

Kumar,

Pradhan

et al. 2020

Preprint

View full text Add to dashboard Cite

Discrete-time queueing models find huge applications as they are used in modeling queueing systems arising in digital platforms like telecommunication systems, computer networks, etc. In this paper, we analyze an infinite-buffer queueing model with discrete Markovian arrival process. The units on arrival are served in batches by a single server according to the general bulk-service rule, and the service time follows general distribution with service rate depending on the size of the batch being served. We mathematically formulate the model using the supplementary variable technique and obtain the vector generating function at the departure epoch. The generating function is in turn used to extract the joint distribution of queue and server content in terms of the roots of the characteristic equation. Further, we develop the relationship between the distribution at the departure epoch and the distribution at arbitrary, pre-arrival and outside observer's epoch, which is used to obtain the latter ones. We evaluate some essential performance measures of the system and also discuss the computing process extensively which is demonstrated by few numerical examples.

show abstract

Waiting-time analysis of D-$${ BMAP}{/}G{/}1$$BMAP/G/1 queueing system

Cited by 12 publications

References 24 publications

Complete analysis of a discrete-time batch service queue with batch-size-dependent service time under correlated arrival process: D-MAP/G_n^(a,b)/1

Complete analysis of a discrete-time batch service queue with batch-size-dependent service time under correlated arrival process: D-MAP/G_n^(a,b)/1

On the joint distribution of an infinite-buffer discrete-time batch-size-dependent service queue with single and multiple vacation

Analysis of an infinite-buffer batch-size-dependent service queue with discrete-time Markovian arrival process: D-$MAP/G_n^{(a,b)}/1$

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Waiting-time analysis of D-$${ BMAP}{/}G{/}1$$BMAP/G/1 queueing system

Cited by 12 publications

References 24 publications

Complete analysis of a discrete-time batch service queue with batch-size-dependent service time under correlated arrival process: D-MAP/Gn(a,b)/1

Complete analysis of a discrete-time batch service queue with batch-size-dependent service time under correlated arrival process: D-MAP/Gn(a,b)/1

On the joint distribution of an infinite-buffer discrete-time batch-size-dependent service queue with single and multiple vacation

Analysis of an infinite-buffer batch-size-dependent service queue with discrete-time Markovian arrival process: D-$MAP/G_n^{(a,b)}/1$

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Product

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Complete analysis of a discrete-time batch service queue with batch-size-dependent service time under correlated arrival process: D-MAP/G_n^(a,b)/1

Complete analysis of a discrete-time batch service queue with batch-size-dependent service time under correlated arrival process: D-MAP/G_n^(a,b)/1