Transient analysis of the MMPP/G/1/K queue

A novel customer batch service discipline for a single server queue is introduced and analyzed. Service to customers is offered in batches of a certain size. If the number of customers in the system at the service completion moment is less than this size, the server does not start the next service until the number of customers in the system reaches this size or a random limitation of the idle time of the server expires, whichever occurs first. Customers arrive according to a Markovian arrival process. An individual customer's service time has a phase-type distribution. The service time of a batch is defined as the maximum of the individual service times of the customers which form the batch. The dynamics of such a system are described by a multi-dimensional Markov chain. An ergodicity condition for this Markov chain is derived, a stationary probability distribution of the states is computed, and formulas for the main performance measures of the system are provided. The Laplace-Stieltjes transform of the waiting time is obtained. Results are numerically illustrated.

show abstract

“…Let us repeat the experiment for the MAP obtained as a result of fitting real world traces (see Chydzinski, 2006 …”

Section: Numerical Resultsmentioning

confidence: 99%

“…These matrices are obtained based on information about the generator of the underlying process ν t and the expression for D 1 as the diagonal matrix presented by Chydzinski (2006). The original matrices are scaled to obtain an M AP having the same fundamental rate λ = 0.6 as the three MAPs of order 2 which were used to build Figs.…”

Section: Numerical Resultsmentioning

confidence: 99%

Analysis of an MAP/PH/1 Queue with Flexible Group Service

Brugno

D’Apice

Dudin

et al. 2017

International Journal of Applied Mathematics and Computer Science

View full text Add to dashboard Cite

show abstract

“…Using one million packet headers from the file FRG-1137208198-1.tsh, recorded at the FGR aggregation point run by PMA (Passive Measurement and Analysis Project [25]), the following MMPP parameteriztion was obtained in [15]: …”

Section: Numerical Illustrationmentioning

confidence: 99%

“…It is important that the autocorrelation function fits the original traffic reasonably well on several time scales (see Fig. 5 in [15]). …”

Section: )mentioning

confidence: 99%

“…Most of the papers are devoted to other queueing characteristics, mainly to queue size distribution or queueing delay (workload). In particular, these characteristics for various MMPP queueing models in the stationary regime can be found by the reader in [7]- [9], while their time-dependent versions in [10]- [15]. There are also some papers in which approximation techniques for analysis of MMPP queues are shown, for instance [16]- [18].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Time to Buffer Overflow in an MMPP Queue

Chydziñski

2007

NETWORKING 2007. Ad Hoc and Sensor Networks, Wireless Networks, Next Generation Internet

Self Cite

View full text Add to dashboard Cite

Abstract. In this report we deal with the time to buffer overflow in a finite-buffer queue with MMPP (Markov-modulated Poisson process) arrivals. The results include a closed-form formula for the transform of the distribution of the time to buffer overflow. The main benefit of this formula is that, using properties of the transform, we can easily compute the average overflow time and all the moments (variance etc). Moreover, by means of an inversion algorithm, we can obtain the probability density function and cumulative distribution function of the overflow time. Analytical results are illustrated by a numerical example based on MMPP parameterization fitted to an IP traffic trace file.

show abstract

Batch Markovian Arrival Processes (BMAP)

Cordeiro

Kharoufeh

2011

Wiley Encyclopedia of Operations Research and Management Science

View full text Add to dashboard Cite

This article describes the batch Markovian arrival process (BMAP), a point process that is characterized by Markov‐modulated batch arrivals of random size. The BMAP is a generalization of many well‐known processes including the Markovian arrival process (MAP), the Poisson process, and the Markov‐modulated Poisson process. It provides a common framework for modeling arrival processes in a variety of applications. We formally define the continuous‐ and discrete‐time BMAP, review a few basic results for each, and show how these processes generalize many common point processes. Additionally, we provide suggestions for further reading on the subject.

show abstract

Transient analysis of the MMPP/G/1/K queue

Cited by 19 publications

References 29 publications

Analysis of an MAP/PH/1 Queue with Flexible Group Service

Analysis of an MAP/PH/1 Queue with Flexible Group Service

Time to Buffer Overflow in an MMPP Queue

Batch Markovian Arrival Processes (BMAP)

Contact Info

Product

Resources

About