Artalejo Rodríguez, Jesús ManuelLi, Quan-Lin2023-06-202023-06-202010-090924-670310.1007/s10626-009-0075-6https://hdl.handle.net/20.500.14352/42138In this paper, we introduce a new discrete block state-dependent arrival (D-BSDA) distribution which provides fresh insights leading to a successful generalization of the discrete-time Markovian arrival process (D-MAP). The D-BSDA distribution is related to structured Markov chains and the method of stages. The consideration of this new discrete-time state-dependent block description gives one the ability of construct new stochastic models. The retrial queue analyzed in this paper gives an example of application of the D-BSDA distribution to construct more general and sophisticated models. We assume that the primary arrivals and the retrials follow the D-BSDA description and the service times are of discrete phase-type (PH). We study the underlying level dependent Markov chain of M/G/1-type at the epochs immediately after the slot boundaries. To this end, we employ the UL-type RG-factorization which provides an expression for the stationary probabilities. We also perform an analysis of waiting times. Numerical experiments are presented to study the system performance.engjournal articlehttp://www.springerlink.com/content/3522g14536j4351v/fulltext.pdfhttp://www.springerlink.comrestricted access517ServiceSystemQueueingDiscrete-timeStructured Markov chainRetrialLU-factorizationsWaiting timeAnálisis matemático1202 Análisis y Análisis Funcional