Advanced search
Publication Cover
Stochastic Models Volume 23, 2007 - Issue 2
Submit an article Journal homepage
79
Views
20
CrossRef citations to date
0
Altmetric
Original Articles

Time to Reach Buffer Capacity in a BMAP Queue

Andrzej Chydzinski Silesian University of Technology, Institute of Computer Sciences, Gliwice, PolandCorrespondence[email protected]
Pages 195-209 | Received 01 Jul 2005, Accepted 01 Sep 2006, Published online: 26 Aug 2010
 
Sample our Mathematics & Statistics journals, sign in here to start your FREE access for 14 days

Abstract

In this paper a detailed study is presented on the first time to reach buffer capacity in a queue with batch arrivals and general service time distribution. A flexible analytical model of the input stream, which is the Batch Markovian Arrival Process (BMAP), is assumed. The results include the explicit formula for the Laplace transform of the distribution of the first buffer overflow time and discussion of its computational aspects. In addition, the popular special case of the BMAP queue, which is the batch Poisson arrival queue, is studied. Theoretical results are illustrated via numerical calculations based on IP traffic data.

Mathematics Subject Classification:

ACKNOWLEDGMENTS

This material is based upon work supported by the Polish Ministry of Scientific Research and Information Technology under Grant No. 3 T11C 014 26.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related Research Data

New results on the single server queue with a batch markovian arrival process
Source: Informa UK Limited
On the Queue Length Distribution in BMAP Systems
Source: The Croatian Communications and Information Society (CCIS) in cooperation with Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, University of Split
Limits of First Passage Times to Rare Sets in Regenerative Processes
Source: The Institute of Mathematical Statistics
Calculating the loss probability in a BMAP/G/1/N+1 queue
Source: Informa UK Limited
First-passage-time and busy-period distributions of discrete-time Markovian queues: Geom(n)/Geom(n) /1/ N
Source: Springer Science and Business Media LLC
Exact Buffer Overflow Calculations for Queues via Martingales
Source: Springer Science and Business Media LLC
Introduction to Queuing Theory
Source: Birkhäuser Boston
THE N/G/1 QUEUE AND ITS DETAILED ANALYSIS
Source: Cambridge University Press (CUP)
Transient behaviour of queueing systems with correlated traffic
Source: Informa UK Limited
The n/g/l finite capacity queue
Source: Informa UK Limited
The Markov-modulated Poisson process (MMPP) cookbook
Source: Elsevier BV
Further transient analysis of the BMAP/G/1 Queue
Source: Informa UK Limited
Burst ratio in a single-server queue
Source: Springer Science and Business Media LLC
Modeling IP traffic: joint characterization of packet arrivals and packet sizes using BMAPs
Source: Elsevier BV
A versatile Markovian point process
Source: Cambridge University Press (CUP)
On the self-similar nature of Ethernet traffic (extended version)
Source: Institute of Electrical and Electronics Engineers (IEEE)
The Fourier-series method for inverting transforms of probability distributions
Source: Springer Science and Business Media LLC
Distribution of time to buffer overflow in a finite-buffer manufacturing model with unreliable machine
Source: EDP Sciences
A two-time-scale model for hospital patient flow
Source: Oxford University Press (OUP)
evidence and possible causes
Source: Association for Computing Machinery (ACM)
Distribution of the time to buffer overflow in the M/G/1/N-type queueing model with batch arrivals and multiple vacation policy
Source: Informa UK Limited
The transient BMAP/G/l queue
Source: Informa UK Limited

Linking provided by 

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.