Piecewise-linear networks with multimode service strategies

Consideration is given to open and closed queueing networks with Markov routing and symmetric service procedures. Single-line nodes can operate in several modes; the switching time from one mode to another is of exponential distribution. The switching occurs only to nearby modes. The quantity of work on service of the arriving customer is a random quantity with an arbitrary distribution function. For open networks, the input flow is the simplest. The invariancy of the stationary distribution of network states with respect to the functional form of distributions of quantities of works at fixed first moments is established.