2026-06-29T08:03:21Zhttps://docta.ucm.es/rest/oai/requestoai:docta.ucm.es:20.500.14352/574232023-08-10T23:06:20Zcom_20.500.14352_14col_20.500.14352_15
The stationary distribution of a Markovian process arising in the theory of multiserver retrial queueing systems
Gómez-Corral, Antonio
Ramalhoto, M.F.
519.216
multiserver queue
repeated attempt
stationary distribution
closed form formulae
Procesos estocásticos
1208.08 Procesos Estocásticos
In this paper, we introduce a bivariate Markov process {X(t), t greater than or equal to 0} = {(C(t), Q(t)), t greater than or equal to 0} whose state space is a lattice semistrip E = {0, 1, 2, 3} x Z(+). The process {X(t), t greater than or equal to 0} can be seen as the joint process of the number of servers and waiting positions occupied, and the number of customers in orbit of a generalized Markovian multiserver queue with repeated attempts and state dependent intensities. Using a simple approach, we derive closed form expressions for the stationary distribution of {X(t), t greater than or equal to 0} when a sufficient condition is satisfied. The stationary analysis of the M/M/2/2 + 1 and M/M/3/3 queues with linear retrial rates is studied as a particular case in this process.
DGICYT
INTAS
JNICT
Depto. de Estadística e Investigación Operativa
Fac. de Ciencias Matemáticas
TRUE
pub
2023-06-20T16:55:09Z
2023-06-20T16:55:09Z
1999-04-03
journal article
https://hdl.handle.net/20.500.14352/57423
0895-7177
10.1016/S0895-7177(99)00138-7
eng
PB95-0416
96-0828
134-94
restricted access
application/pdf
Pergamon-Elsevier Science LTD