Approximation of the non-stationary M(t)/M(t)/c(t)-queue using stationary queueing models: The stationary backlog-carryover approach

This paper proposes a new approach for the time-dependent analysis of stochastic and non-stationary queueing systems. The analysis of a series of stationary queueing models leads to a new approximation of time-dependent performance measures. Based on a stationary backlog-carryover (SBC) approximation of the time-dependent expected utilization, different approximations of the time-dependent expected queue length and the number of customers in the system are discussed. Limiting results are given for the case of constant rates. The accuracy of the SBC approach is shown for non-stationary M(t)/M(t)/c(t) queueing systems with time-dependent and piecewise constant arrival rates. In numerical experiments we demonstrate the reliability of this approach and compare it with the (lagged) stationary independent period by period (SIPP) approach. In addition, the approximation is applied to temporarily overloaded systems that cannot be analyzed by the variants of the SIPP approach.