Computing the conditional entry-state distribution in Erlang loss systems

We consider an Erlang loss system with state-dependent arrival rates. Given the system is in steady-state and there are j customers being served, the system operator may wish to know about the distribution of arrival states for the j customers in service. Specifically, they may want the steady-state...

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Bibliographic Details
Published inOperations research letters Vol. 49; no. 3; pp. 345 - 349
Main Authors Nyotta, Bobby S., Bravo, Fernanda, Chen, M. Keith
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.05.2021
Subjects
Birth–death Markov chain
Erlang loss system
M/M/n/n queue
State-dependent arrivals
M/M/n/n queue
State-dependent arrivals
Erlang loss system
Birth–death Markov chain
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Summary:We consider an Erlang loss system with state-dependent arrival rates. Given the system is in steady-state and there are j customers being served, the system operator may wish to know about the distribution of arrival states for the j customers in service. Specifically, they may want the steady-state probability that any given customer entered when the system had i servers busy, given j customers are currently being served. We term this metric the conditional entry-state distribution and develop an algorithm to compute it.
ISSN:0167-6377
1872-7468
DOI:10.1016/j.orl.2021.03.005