Approximate evaluation for mixed delay and loss systems with renewal and Poisson inputs

An approximate evaluation is proposed for the individual mean waiting time, and loss probability for mixed delay and loss (nondelay) systems with renewal and Poisson inputs handled by servers with exponential service time. The approximation is based on the GI approximation previously proposed by H. Akimaru, et al. (1983, 1985), in which the mixed input process is regarded as renewal. The systems with mixed delay renewal and nondelay Poisson inputs, and ones with mixed nondelay renewal and delay Poisson inputs are analyzed. Approximate formulas for the mean waiting time and loss probability for the respective inputs are presented in simple closed form, and comparisons to simulations show good accuracy. The formulas are expected to be useful for analysis and optimum design of the mixed delay and loss systems