Asymptotic analysis of multiserver retrial queueing system with \(\pi\)-defeat of negative arrivals under heavy load

The paper studies a multiserver retrial queuing system with \(\pi\)-defeat as a mathematical model of cloud services. The arrival processes of “positive” calls are Poisson. The system has a finite number of servers and the service time for calls at the servers is exponentially distributed. When all servers are busy, calls entering the system transfer to an orbit, where they experience a random delay. After the delay, calls from the orbit attempt to access the service unit according to a multiple access policy. The system also receives a stream of negative calls. Negative calls do not require the service. An negative call “deletes” a random number of calls is the service unit. For the considered model, the Kolmogorov equations are written in the steady state. The method of asymptotic analysis under a heavy load condition is applied for deriving the stationary probability distribution of the number of calls in the orbit. The results of the numerical analysis are presented.