Poisson and Gaussian Approximations for Multi-Server Queues with Batch Arrivals and Batch Abandonment

In this paper, we consider nonstationary multi-server queues and multiserver loss queues with batch arrivals and where we allow customer abandonment to also occur as a Markovian batch process. To estimate the performance of the system, we develop two new approximations that take advantage of the functional Kolmogorov forward equations. The first approximation we develop uses the Poisson distribution, which is motivated from the infinite server queue offered load process. The second approximation uses a Gaussian distribution, which is motivated by the many server heavy traffic limit theorems of Mandelbaum et al [13]. We compare our results with Monte Carlo simulation and show that our approximations provide accurate estimates of the mean, variance, probability of delay, and the probabilty of blocking for the queueing process.