Methods of investigation of queueing network with jumps of service rate

The equilibrium and the non-equilibrium behaviours of the uniform tandem with jump-like service rate in each queue are examined. The uniform tandem represents a specific multiplicative queueing network and involves a sequence of queues being identical with respect to customer's services. It is a suitable mathematical model providing analysis of the effect of the jump-like service rate on the probability-temporal measures related, in particular, to transient processes.
For the equilibrium behaviour, the state space structure is determined, and the Laplace–Stieltjes transform of the cycle times distribution is obtained. For the non-equilibrium behaviour, the recurrence solution of the Kolmogorov differential equations is developed, the transient process time is evaluated, the integral and the phase trajectories for the respective Markov process are investigated.