The M/M/∞ queue in a random environment

Authors:
G. Falin
Affiliations:
Department of Probability, Mechanics and Mathematics Faculty, Moscow State University, Moscow, Russian Federation 119992
Venue:
Queueing Systems: Theory and Applications
Year:
2008

Citing 0
Cited 5

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Markov-modulated stochastic recursive equations with applications to delay-tolerant networks

Performance Evaluation
Markov-modulated infinite-server queues with general service times

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Abstract

We consider the M/M/驴 queueing system with arrival and service rate depending on the state of an auxiliary semi-Markov process (which can be viewed as an external environment) and find the mean number of customers in the system in steady state. In a particular case when the external environment can be only in two states we find the distribution of the number of customers in the system.