Queuing loss models with more alternative heterogeneous groups

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SummaryThis paper considers queuing model with 2 Poisson traffics offered to the primary group, where the rejected demands of one of them are overflowed to the alternative groups in sequence and leave the system without being served when all channels are busy. Here, serving intensity from primary group is changed and gets various values in alternative groups. Generating function technique is used for the analytical solution of steady‐state equations system. Common solution obtained for the state probabilities permits efficient procedure for model parameters calculation. Next, explicit solutions in the case with secondary and tertiary groups are derived. Moreover, obtained solutions for binomial moments are of significant importance for treating more complex models. Some numerical results are also presented through illustrative examples justifying the need to dedicate special attention to the cases where phenomenon of heterogeneous alternative channels or groups is remarked. In addition, as an example, explicit solution for the model with primary group and 3 heterogeneous alternate channels is obtained. This leads to the comparative support when solving 4 channels system with losses and renewal arrivals. These solutions represent a prospective tool applicable in different serving situations, particularly considering traditional and next generation communications networks.