The BMAP/PH/N retrial queueing system operating in Markovian random environment

Single server retrial queue with group admission of customers

“…First papers where single server retrial queues with the BMAP and arbitrary distribution of service time were analyzed are [10] and [11] where the BMAP=G=1 and the BMAP=SM=1 retrial queues, respectively, were under study. Multi-server retrial queues with the BMAP and phase (PH) type distribution of service time were studied in [7,8,[16][17][18][19]22,23].…”

Analysis of Multiserver Retrial Queueing System with Varying Capacity and Parameters

“…Early research in this topic was done by Gnedenko and Kovalenko [1], Yechiali and Naor [2], Yadin and Syski [3], O'Cinneide and Purdue [4], Purdue [5], Neuts [6,7], and others. A brief history of the development of theory of queues in the RE, the reference list, and real life examples of queues in the RE can be found, for example, in the papers [8][9][10][11][12]. In [8], an unreliable / /1 retrial queue in a Markovian random environment is analyzed via matrix-analytic methods.…”

“…In particular, it is demonstrated that reasonable engineering approximations of performance measures of the system may be very poor. In [12], the BMAP/PH/ retrial queue operating in the RE is investigated. As in the previously described model, the system does not have a buffer.…”

Analysis of an MMAP/PH1, PH2/N/∞ queueing system operating in a random environment

“…Some references to the literature about systems operating in a random environment can be found, e.g., in the works of Dudin et al (2013a); Kim et al (2010a;2010b) or Krieger et al (2005).…”