Departure process of a single server queueing system with Markov renewal input and general service time distribution

Lim, Siyeong; Hur, Sun; Noh, Seung J.

doi:10.1016/j.cie.2006.08.011

Cited by 13 publications

(2 citation statements)

References 14 publications

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“…Heindl proposed a numerical approach whereby the output process of an MMPP/G/1/(K) queue was approximated by a semi‐Markov model, which was then converted to an MMPP 2 , this approach is computationally expensive. Lim et al gave a general framework for the calculation of the Laplace transform of the interdeparture times for a single server queue with Markov renewal input and general service time distribution (MAP/G/1), which is also on the basis of the computationally expensive matrix‐geometric solution. No closed‐form solution was given.…”

Section: The Departure Process Of Mmpp2/m/1 Queuementioning

confidence: 99%

Analysis and efficient provisioning of access networks with correlated and bursty arrivals

Tian

2013

Int J Communication

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SUMMARY The statistical multiplexer problem was analyzed extensively in the discrete‐time case within the context of ATM access networks or Internet. Despite the vast literature on ATM multiplexer, this problem has not been satisfactorily analyzed in the continuous‐time case. In this paper, a statistical multiplexer consisting of a single server queue is modeled and analyzed. N identical interrupted Poisson process arrivals flow into the multiplexer are considered, the service time is assumed to be exponentially distributed, and the queue size is infinite. We developed an efficient way to approximate the superposition of n interrupted Poisson process (or n MMPP 2) arrival process by an MMPP 2 through moments and index of dispersion count (IDC) matching. We then find the closed‐form Laplace transform of the departure process of an MMPP 2/M/1 queue. Our results prove that the departure process of an MMPP 2/M/1 queue is not an MMPP 2, which closes the long open problem that whether the departure process of an MMPP/M/1 can be a MMPP. Using Laplace transform matching, we approximated the departure process of an MMPP 2/M/1 by an MMPP 2. These results permit us to analyze a number of statistical multiplexer linked in series as they arise in an access network. Numerical experiments show that approximate analytical results match the simulation results very well. Copyright © 2013 John Wiley & Sons, Ltd.

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Section: The Departure Process Of Mmpp2/m/1 Queuementioning

confidence: 99%

Analysis and efficient provisioning of access networks with correlated and bursty arrivals

Tian

2013

Int J Communication

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“…In the past, several papers studied the autocorrelation of the departure process at a single server queue ( [3], [5], [6], [25], [10], [9], [17] and references therein). In this section, we study the impact of the additional waiting times for a release authorization on the autocorrelation of the M/M/1 departure process.…”

Section: Autocorrelation Of Departure Processmentioning

confidence: 99%

The Consequences of Time-Phased Order Releases on Two M/M/1 Queues in Series

Claerhout

Vandaele²

2009

SSRN Journal

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A key characteristic of MRP applications includes the coordination of assembly and purchased component requirements by time-phased order releases. In the literature on order review and release strategies, timephased order releases are described as a worthy alternative to load limited release mechanisms. This paper initializes the development of a stochastic model that quanti…es the consequences of time-phased order releases on the stochastic system behavior. This is done by introducing them in an open queueing network composed of two M/M/1 stations. The core of the analysis is focused on the modi…ed ‡ow variability which is speci…ed by the second-order stationary departure process at the …rst station in the routing. It is a process characterized by a negligible autocorrelation. Based on the stationary-interval method and the asymptotic method, we propose an approximating renewal process for the modi…ed departure process. The modelling e¤orts provide interesting conclusions and practical insights on some coordination issues in stochastic multi-echelon systems. Contrary to the SCV [D n ] expression in section 5, this analytical expression for Dn (1) does not allow a P-value equal to 100%. Figure 18 reproduces Dn (1)

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The structure of departure process and optimal control strategy N* for Geo/G/1 discrete-time queue with multiple server vacations and Min(N, V)-Policy

Lan

Tang

2017

J Syst Sci Complex

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Departure process of a single server queueing system with Markov renewal input and general service time distribution

Cited by 13 publications

References 14 publications

Analysis and efficient provisioning of access networks with correlated and bursty arrivals

Analysis and efficient provisioning of access networks with correlated and bursty arrivals

The Consequences of Time-Phased Order Releases on Two M/M/1 Queues in Series

The structure of departure process and optimal control strategy N* for Geo/G/1 discrete-time queue with multiple server vacations and Min(N, V)-Policy

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