<abstract xmlns="http://www.w3.org/1999/xhtml"><p>A packet buffer limited to a ﬁxed number of packets (regardless of their lengths) is considered. The buffer is described as a ﬁnite FIFO queuing system fed by a Markovian Arrival Process (MAP) with service times forming a Semi-Markov (SM) process (MAP /SM /1/b in Kendall’s notation). Such assumptions allow us to obtain new analytical results for the queuing characteristics of the buffer. In the paper, the following are considered: the time to ﬁll the buffer, the local loss intensity, the loss ratio, and the total number of losses in a given time interval. Predictions of the proposed model are much closer to the trace-driven simulation results compared with the prediction of the MAP /G/1/b model.</p></abstract>

A packet buffer limited to a ﬁxed number of packets (regardless of their lengths) is considered. The buffer is described as a ﬁnite FIFO queuing system fed by a Markovian Arrival Process (MAP) with service times forming a Semi-Markov (SM) process (MAP /SM /1/b in Kendall’s notation). Such assumptions allow us to obtain new analytical results for the queuing characteristics of the buffer. In the paper, the following are considered: the time to ﬁll the buffer, the local loss intensity, the loss ratio, and the total number of losses in a given time interval. Predictions of the proposed model are much closer to the trace-driven simulation results compared with the prediction of the MAP /G/1/b model.

Transient and stationary characteristics of a packet buffer modelled as an <italic>MAP/SM/1/b</italic> system

Department of Telecommunications AGH University of Science and Technology, al. A. Mickiewicza 30, 30-059 Cracow, Poland

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Transient and stationary characteristics of a packet buffer modelled as an  system

A packet buffer limited to a ﬁxed number of packets (regardless of their lengths) is considered. The buffer is described as a ﬁnite FIFO queuing system fed by...

Transient and stationary characteristics of a packet buffer modelled as an MAP/SM/1/b system

Published Online: Jun 26, 2014

Page range: 429 - 442

Received: May 10, 2013

DOI: https://doi.org/10.2478/amcs-2014-0033

Keywords
router interface, Markovian arrival process, semi-Markov service time, hidden Markov model, ﬁnite-buffer queue, packet loss, ﬁrst passage time

© 2014 Krzysztof Rusek et al.

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Transient and stationary characteristics of a packet buffer modelled as an MAP/SM/1/b system

Published Online: Jun 26, 2014

Page range: 429 - 442

Received: May 10, 2013

DOI: https://doi.org/10.2478/amcs-2014-0033

Keywordsrouter interface, Markovian arrival process, semi-Markov service time, hidden Markov model, ﬁnite-buffer queue, packet loss, ﬁrst passage time

© 2014 Krzysztof Rusek et al.

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
router interface, Markovian arrival process, semi-Markov service time, hidden Markov model, ﬁnite-buffer queue, packet loss, ﬁrst passage time