The M/M/∞ queue in a random environment

Colm Art O’Cinneide · Peter Purdue

73 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 Stochastic processes and statistical mechanics Probability and Risk Models

Abstract

The M/M/∞ queue in a random environment is an infinite-server queue where arrival and service rates are stochastic processes. Here we study the steady-state behavior of such a system. Explicit results are obtained for the factorial moments, the impossibility of a ‘matrix-Poisson' steady-state distribution is demonstrated and two numerical examples are presented.

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 — 73 citations exist upstream.

References

2014Introduction to Stochastic Processes 1978Markov chains with applications in queueing theory, which have a matrix-geometric invariant probability vector

Cited by

2013Markov-modulated infinite-server queues with general service times 2008M/M/∞ queues in semi-Markovian random environment 2015Analysis of the M/G/1 queue in multi-phase random environment with disasters 2008An infinite-server queue influenced by a semi-Markovian environment 2007Erlang loss queueing system with batch arrivals operating in a random environment 2009Heavy-traffic limits for many-server queues with service interruptions 1993The matrix M/M/∞ system: retrial models and Markov Modulated sources 1993The matrix M/M/∞ system: retrial models and Markov Modulated sources

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.