A polynomial factorization approach for the discrete time \(\text{GI}^X/ \text{G}/1/K\) queue
The stationary queue size of the discrete time \(\text{GI}^X/\text{G}/1/(K)\) queue is analyzed. The analysis uses a two-component state model at the arrival and departure instants of customers. The steady-state probabilities are obtained with the help of a polynomial factorization approach, thus representing the distribution of the queue size as a superposition of a geometrical series with complex-valued parameters. The only restriction to polynomial factorization is that the interarrival-time distribution, the service-time distribution, and the batch-size distribution are of finite support. Special attention is paid to finite capacity queues.
scientific article; zbMATH DE number 2085811
scientific article