Unreliable multi-server system with controllable broadcasting service

Consideration was given to the multi-server queuing system with an infinite buffer. The customer arrivals obey a Markov arrival flow, the time of customer service having a phasetype distribution. service may be done with errors. If at the instant of customer arrival the number of busy servers is less than some threshold, then the customer is copied to all free servers which service it. If at that instant the number of busy servers is not less than some threshold, then the customer is serviced by a single server. The stationary distribution of the number of customers and their sojourn time were determined. The impact of the threshold value on the probability of successful service of the customer was studied numerically.