Stationary characteristics of MX/M/1 systems with two-speed service

An MX/M/1 queueing system with threshold switching of service regimes at the instant of a change in the number of customers and the same system with threshold blocking of the flow of customers are considered. For these systems, an algorithm is proposed for determination of the stationary distribution of the number of customers and stationary characteristics (the mean queue length, the mean time of waiting in a queue, the variance of the queue length, the probability of the customer service for a system with blocking). For the case when the minimal number of incoming customers in a group is comparable with threshold value h, the stationary characteristics are found in an explicit form. For the system with threshold switching of service regimes (without blocking), two problems of optimal synthesis are solved. In these problems, the optimal values of threshold h and of the service intensity in the post-threshold regime are determined. The obtained results are verified with the help of simulation models developed with the help of the GPSS World software.