Fast Simulation of the Customer Blocking Probability in a Queueing System with Poisson Input Flow Controlled by a Semi-Markov Process

A multichannel queueing system with a Poisson input flow is considered. The input flow rate depends on the current state of the semi-Markov process. This state also determines the type of the customer. Each channel contains several service lines. To be serviced, a customer requires several lines depending on the respective distribution. If the channel does not have sufficient service lines, it is possible to redirect this customer to another channel. The service time has a general distribution function depending on the customer's type and the number of lines required for servicing. A fast simulation method is proposed to evaluate the blocking probability of customers of a certain type demanding a given number of service lines. A comparison with the Monte Carlo method is made using a numerical example, and the change in the relative error of the estimate as the blocking probability decreases is analyzed.