Abstract
We deal with finite‐buffer queueing systems fed by a Markovian point process. This class includes the queues of type M/G/1/N, MX/G/1/N, PH/G/1/N, MMPP/G/1/N, MAP/G/1/N, and BMAP/G/1/N and is commonly used in the performance evaluation of network traffic buffering processes. Typically, such queueing systems are studied in the stationary regime using matrix‐analytic methods connected with M/G/1‐type Markov processes. Herein, another method for finding transient and stationary characteristics of these queues is presented. The approach is based on finding a closed‐form formula for the Laplace transform of the time‐dependent performance measure of interest. The method can be used for finding all basic characteristics like queue size distribution, workload distribution, loss ratio, time to buffer overflow, and so forth. To demonstrate this, several examples for different combinations of arrival processes and characteristics are presented. In addition, the most complex results are illustrated via numerical calculations based on an IP traffic parameterization.
Highlights
Since the beginning of the 1990s, when the strong auto-correlation of the Internet traffic was discovered, a variety of processes have been developed or adapted for proper teletraffic modeling
Fractional Brownian motion 1, chaotic maps 2, FARIMA 3, and multifractal wavelets 4 have been applied in wide range of tasks connected with performance evaluation of buffering processes, traffic predictability, congestion and admission control, buffer sizing, and so forth
We deal with the finite-buffer queue whose arrival process is given by a Markovian point process from the class N. Such queueing systems have been solved typically in their stationary regime using matrix-analytic methods connected with M/G/1-type Markov chains 13–16 this set of papers is not intended to be exhaustive, the literature devoted to the subject is vast
Summary
Since the beginning of the 1990s, when the strong auto-correlation of the Internet traffic was discovered, a variety of processes have been developed or adapted for proper teletraffic modeling. None of the aforementioned processes suits as well for the teletraffic modeling as the famous class N of Markovian point processes 5 or one of its well-known reparameterizations or subclasses MMPP, MAP, BMAP, etc First of all, this is connected with the fact that N processes are analytically tractable. We deal with the finite-buffer queue whose arrival process is given by a Markovian point process from the class N Such queueing systems have been solved typically in their stationary regime using matrix-analytic methods connected with M/G/1-type Markov chains 13–16 this set of papers is not intended to be exhaustive, the literature devoted to the subject is vast.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
