Two Approximations for the Steady-State Probabilities and the Sojourn-TimeDistribution of the M/D/c Queue with State-Dependent Feedback

摘要

In the paper, two different approximations for the steady-state probabilities andthe sojourn-time distribution of the M/D/c queue with state-dependent feedback are studied. The first approximation is based on an embedded Markov chain and uses the well-known residual-life approximation for the remaining service times of the customers in service. The second approximation is similar to the exact analysis of the ordinary M/D/c queue. Comparison with simulation shows, that both approximations are very accurate for a wide range of system parameters, even for heavily loaded systems.