An alternative method for computing system-length distributions of BMAP/R/1 and BMAP/D/1 queues using roots

Gupta, Umesh C.; Singh, Gagandeep; Chaudhry, M. L.

doi:10.1016/j.peva.2015.11.001

Cited by 17 publications

(10 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We obtain these unknowns from (3.28) using the roots method given in Chaudhry et al [13], Gupta et al [18] and Pradhan and Gupta [22]. For this, we first obtain the expressions for A * r (x), a ≤ r ≤ b, by considering commonly used service-time distributions.…”

Section: Computing Process To Obtain the Distributions At Various Epochsmentioning

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

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.

show abstract

Section: Computing Process To Obtain the Distributions At Various Epochsmentioning

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

show abstract

“…[ 8 ], Gupta et al. [ 14 ], Pradhan and Gupta [ 23 ], Kumar and Gupta [ 18 , 20 ]. The literature shows that distributions having L.-S.T.…”

Section: Computing Process To Obtain the Distributions At Various Epochsmentioning

confidence: 99%

“…If there are repeated roots, a slight modification is needed in the computing process, see, e.g., Gupta et al. [ 14 ], Pradhan and Gupta [ 23 ].…”

Section: Computing Process To Obtain the Distributions At Various Epochsmentioning

confidence: 99%

“…[ 28 ], Gupta et al. [ 14 ], Pradhan and Gupta [ 23 ], Bank and Samanta [ 4 ]. The method is analytically quite simple and easy to implement.…”

Section: Introductionmentioning

confidence: 99%

“…It is shown in Gupta et al. [ 14 ], Singh et al. [ 28 ], Bank and Samanta [ 4 ] that the computation time using the roots method for different values of the parameters remains almost the same, whereas the MAM requires more computation time and is dependent on the parameter like lag-correlation and traffic intensity.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Computational and Numerical Investigation of the Batch Markovian Arrival Process Subject to Renewal Generated Geometric Catastrophes

Kumar

Gupta

Singh

2021

Int. J. Appl. Comput. Math

Self Cite

View full text Add to dashboard Cite

In this paper, we consider a stochastic model in which the population grows according to the batch Markovian arrival process and is subjected to renewal generated geometric catastrophes. Our analytical work starts from the vector generating function (VGF) of the population size at post-catastrophe epoch. We develop a methodology for extracting the population size distribution at post-catastrophe epoch from the VGF, which is based on the inversion of VGF using the roots method. The method is analytically quite simple and easy to implement. Further, we obtain the population size distribution at arbitrary, pre-catastrophe and pre-arrival epochs along with their factorial moments. To show the applicability and correctness of the proposed methodology, we match our results with the available ones in special cases and present several numerical examples for different inter-catastrophe time distributions. Moreover, we investigate the effect of key parameters on the system performance and display the results in the form of graphs along with a detailed description.

show abstract

Analysis of BMAP∕R∕1 Queues Under Gated-Limited Service with the Server’s Single Vacation Policy

Ghosh

Banik

Chaudhry

2020

Infosys Science Foundation Series

View full text Add to dashboard Cite

This paper deals with the finite-buffer single server vacation queues with batch Markovian arrival process (BMAP ). The server follows gated-limited service discipline, i.e., the server can serve a maximum of L customers out of those that are waiting at the start of the busy period or all the waiting customers, whichever is minimum. It has been assumed that the server can take only one vacation, i.e., if no customers are found at the end of a vacation, the server remains idle until a batch of customers arrives. The service time and vacation time distributions are considered to possess rational Laplace-Stieltjes transform. The queue-length distribution at postdeparture, arbitrary, and pre-arrival epochs has been obtained. Various performance measures like mean queue-length, mean waiting time of an arbitrary customer, and mean length of busy and idle periods have been derived for this model. Numerical results have been presented based on the analysis done.

show abstract

An alternative method for computing system-length distributions of BMAP/R/1 and BMAP/D/1 queues using roots

Cited by 17 publications

References 18 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

Computational and Numerical Investigation of the Batch Markovian Arrival Process Subject to Renewal Generated Geometric Catastrophes

Analysis of BMAP∕R∕1 Queues Under Gated-Limited Service with the Server’s Single Vacation Policy

Contact Info

Product

Resources

About

An alternative method for computing system-length distributions of BMAP/R/1 and BMAP/D/1 queues using roots

Cited by 17 publications

References 18 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

Computational and Numerical Investigation of the Batch Markovian Arrival Process Subject to Renewal Generated Geometric Catastrophes

Analysis of BMAP∕R∕1 Queues Under Gated-Limited Service with the Server’s Single Vacation Policy

Contact Info

Product

Resources

About

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