Bounds of the workload in a multiclass retrial queue with exponential services

A multiclass retrial queue with Poisson input and $M$ classes of customers is investigated. For the given retrial system with exponential service times, the lower and upper bounds of the workload are derived. It is shown that the workload in the classical system $M/H_M/1$ with hyperexponential service times is the lower bound for the workload of the given retrial system. The upper bound is the workload in the classical $M/G/1$ system where each customer occupies the server for the given service time and additional time corresponding to the inter-retrial time from the “slowest” orbit. The presented simulation results confirm the theoretical conclusions.