Stationary characteristics of /M/1 systems with hysteretic switching of the service intensity

An [M.sup.X]/M/1 queueing system with two-threshold hysteretic switching of the service intensity at the instants when the number of customers exceeds [h.sub.2] and, then, decreases to the value [h.sub.1] < [h.sub.2] and the same system with the threshold locking of a flow of customers are considered. 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, and the probability of the service of a customer for the system with blocking). Restrictions are imposed on the distribution of the number of incoming customers in a group to facilitate the determination of the stationary characteristics in an explicit form. The results are verified with the help of simulation models developed with the use of the GPSS World tools.