Erlang loss queueing system with batch arrivals operating in a random environment

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).…”

Queueing System Operating in Random Environment as a Model of a Cell Operation

“…All these factors may be random. Account of the influence of some random factors of characteristics of a service system, including telecommunication system, is usually performed via consideration of so called queues operating in the random environment (RE), for recent references see, e.g., (Kim et al, 2009;Kim et al, 2010;Wu et al, 2001;Cordeiro and Kharoufeh, 2012;Yang et al, 2013). The standard assumption in the existing literature about the queues operating in the RE is that the change of the state of the RE instantaneously causes the change of intensities of arrivals, service, retrials, impatience, etc.…”

Analysis of BMAP^(r)/M^(r)/N^(r) Type Queueing System Operating in Random Environment

“…As important early work in the field of queues operating in RE the following publications deserve to be mentioned: Gnedenko and Kovalenko (1966), Neuts (1978), Neuts (1981), O'Cinneide and Purdue (1986), Purdue (1974), Yadin and Syski (1979), Yechialy and Naor (1971). A brief history of the development of theory of queues in the RE, the reference list and real life examples can be found, e.g., in the papers Cordeiro and Kharoufeh (2012), Wu et al (2011), Yang et al (2013, and Kim et al (2009). In Cordeiro and Kharoufeh (2012),an unreliable M/M/1 retrial queue in a Markovian random environment is analyzed via matrix-analytic methods.…”

“…In Kim et al (2009), the BMAP/PH/N/N queue operating in the RE is investigated. The arrival flow is described by the batch Markov arrival process (BMAP).…”

“…In Kim et al (2007), the BMAP/PH/1/1 queue operating in the RE with account of retrials of customers, which do not succeed to get access immediately upon arrival, is investigated. For background information and an overview of the present state of the art in the study of queueing systems operating in the RE, the reader is referred also to the papers Wu et al (2011), Yang et al (2013, Kim et al (2009), Kim et al (2007), Krieger et al (2005), and Takine (2005), as well as references therein.…”