Time to Reach Buffer Capacity in a BMAP Queue

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 expli...

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Bibliographic Details
Published in:Stochastic models Vol. 23; no. 2; pp. 195 - 209
Main Author: Chydzinski, Andrzej
Format: Journal Article
Language:English
Published: Philadelphia, PA Taylor & Francis Group 08.05.2007
Taylor & Francis
Subjects:
BMAP/G/1/b queue
Buffer overflow time
Distribution theory
Exact sciences and technology
Inference from stochastic processes; time series analysis
Mathematics
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
Statistics
Stochastic analysis
Stochastic processes
Transient analysis
Stochastic model
Probability theory
Arrival time
68M20; 90B22; 60K25
Time distribution
Service time
Arrival process
Distribution function
Stream
Laplace transformation
Buffer overflow time; BMAP/G/1/b queue; Transient analysis
Application
Batch arrival
Queue
ISSN:1532-6349, 1532-4214
Online Access:Get full text
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Summary: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.
ISSN:1532-6349
1532-4214
DOI:10.1080/15326340701300746