Asymptotic behavior of a multiplexer fed by a long-range dependent process

Zhen Liu · Philippe Nain · Don Towsley · Zhi-Li Zhang

55 citations0/0 files storedJournal of Applied Probability

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 Probability and Risk Models

Abstract

In this paper we study the asymptotic behavior of the tail of the stationary backlog distribution in a single server queue with constant service capacity c, fed by the so-called M/G/∞ input process or Cox input process. Asymptotic lower bounds are obtained for any distribution G and asymptotic upper bounds are derived when G is a subexponential distribution. We find the bounds to be tight in some instances, e.g. when G corresponds to either the Pareto or lognormal distribution and c − ρ < 1, where ρ is the arrival rate at the buffer.

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 — 55 citations exist upstream.

References

1997Modelling Extremal Events 1996Statistics for Long-Memory Processes.1994A storage model with self-similar input 1976Stochastic Processes in Queueing Theory 1997Statistics for Long-Memory Processes 1995Large deviations and overflow probabilities for the general single-server queue, with applications 1975On the tails of waiting-time distributions 1986Convolution tails, product tails and domains of attraction

Cited by

1999Subexponential loss rates in a GI/GI/1 queue with applications 2001Steady-State Distribution of the Buffer Content for M/G/ infinity Input Fluid Queues 2000Overflow behavior in queues with many long-tailed inputs 2003Queueing systems with long-range dependent input process and subexponential service times 2002Asymptotic analysis of GPS systems fed by heterogeneous long-tailed sources 2003Asymptotic loss probability in a finite buffer fluid queue with hetergeneous heavy-tailed on--off 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.