A Multi-Server Retrial Queue with BMAP Arrivals and Group Services


In this paper, we consider a c-server queuing model in which customers arrive according to a batch Markovian arrival process (BMAP). These customers are served in groups of varying sizes ranging from a predetermined value L through a maximum size, K. The service times are exponentially distributed. Any customer not entering into service immediately orbit in an infinite space. These orbiting customers compete for service by sending out signals that are exponentially distributed with parameter θ. Under a full access policy freed servers offer services to orbiting customers in groups of varying sizes. This multi-server retrial queue under the full access policy is a QBD process and the steady state analysis of the model is performed by exploiting the structure of the coefficient matrices. Some interesting numerical examples are discussed.

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Chakravarthy, S.R., Dudin, A.N. A Multi-Server Retrial Queue with BMAP Arrivals and Group Services. Queueing Systems 42, 5–31 (2002). https://doi.org/10.1023/A:1019989127190

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  • batch Markovian arrival process
  • retrials
  • algorithmic probability