Dynamic, Transient and Stationary Behavior of the $M/GI/1$ Queue Via Martingales

François Baccelli · Armand M. Makowski

21 citations0/0 files storedThe Annals of 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 Stochastic processes and statistical mechanics

Abstract

An exponential martingale is associated with the Markov chain of the number of customers in the $M/GI/1$ queue. With the help of arguments from renewal theory, this martingale provides a unified probabilistic framework for deriving several well-known generating functions for the $M/GI/1$ queue, such as the Pollaczek-Khintchine formula, the transient generating function of the number of customers at departure epochs and the generating function of the number of customers served in a busy period.

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 — 21 citations exist upstream.

References

2014Introduction to Stochastic Processes 1963Introduction to the Theory of Queues.1983The Single Server Queue 1983The Single Server Queue.1983Calculation of the Laplace Transform of the Length of the Busy Period for the M|G|1 Queue Via Martingales

Cited by

2004Scale functions of Lévy processes and busy periods of finite-capacity M/GI/1 queues 2000A new approach to the busy period of the M/M/1 queue

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.