Mθ/G/1/m and Mθ/G/1 queues with operating parameters depending on the queue length

Mθ/G/1/m and Mθ/G/1 queues are considered in the case when the service time and input flow parameters depend on the queue length and are determined at the instants of completion of the service of customers. With the help of an approach based on the idea of Korolyuk’s potential method, the Laplace transforms are found for the distribution of the number of customers in a system within the busy period and for the distribution function of the busy period. The mean duration of the busy period and the stationary distribution of the number of customers in a system are determined. An Mθ/G/1 system with one threshold of functioning mode switching is considered as a particular case. The obtained results are verified with the help of simulation models developed with the use of the GPSS World tools.