On the use of second‐order descriptors to predict queueing behavior of MAPs

Allan T. Andersen · Bo Friis Nielsen

18 citations0/0 files storedNaval Research Logistics (NRL)

No readable copy stored yet — this record is metadata only.

No open-access location is known for this record yet.

Literature note Cite in a project Citation map

Advanced Queuing Theory Analysis Probability and Statistical Research Network Traffic and Congestion Control

Abstract

Abstract The contributions of this paper are the following: We derive a formula for the IDI (Index of Dispersion for Intervals) for the Markovian Arrival Process (MAP). We show that two‐state MAPs with identical fundamental rate, IDI and IDC (Index of Dispersion for Counts), define interval stationary point processes that are stochastically equivalent; this is true for the time stationary point processes they define too. Special cases of the two‐state MAP are frequently used as source models in the literature. The result shows that, fitting to the rate, IDC and IDI of a source completely determine the interval stationary and time stationary behavior of the two‐state model. We give various illustrative numerical examples on the merits in predicting queueing behavior on the basis of first‐ and second‐order descriptors by considering queueing behavior of MAPs with constant fundamental rate and IDC, respectively, constant fundamental rate and IDI. Disturbing results are presented on how different the queueing behavior can be with these descriptors fixed. Even MAPs with NO correlations in the counting process, i.e., IDC(t) = 1 are shown to have very different queueing behavior. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 391–409, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10015

Paper brief

Loading…

Cite this work

Citation unavailable for this work.

BibTeX RIS CSL-JSON

No public copy is stored for this record, so only the metadata is cited.

Citations in this library

Citation map →

Stored only when both papers are in the corpus — 18 citations exist upstream.

References

1986A Markov Modulated Characterization of Packetized Voice and Data Traffic and Related Statistical Multiplexer Performance 1991New results on the single server queue with a batch markovian arrival process 1993The Markov-modulated Poisson process (MMPP) cookbook 1990A single-server queue with server vacations and a class of non-renewal arrival processes 1994Asymptotics for steady-state tail probabilities in structured markov queueing models 1989Measurements and approximations to describe the offered traffic and predict the average workload in a single-server queue 1983The SPP/G/1 queue: A single server queue with a switched Poisson process as input process

Cited by

2011Building accurate workload models using Markovian arrival processes 2024Call center data modeling: a queueing science approach based on Markovian arrival process 2008Interarrival Times Characterization and Fitting for Markovian Traffic Analysis 2004On the Time Reversal of Markovian Arrival Processes

Explore the map →

Papers that cite the same references — the relational fallback while embeddings are still backfilling.

Imported from OpenAlex (CC0) — nothing here is generated.