Queue Lengths and Waiting Times for Multiserver Queues with Abandonment and Retrials

We consider a Markovian multiserver queueing model with time dependent parameters where waiting customers may abandon and subsequently retry. We provide simple fluid and diffusion approximations to estimate the mean, variance, and density for both the queue length and virtual waiting time processes arising in this model. These approximations, which are generated by numerically integrating only 7 ordinary differential equations, are justified by limit theorems where the arrival rate and number of servers grow large. We compare our approximations to simulations, and they perform extremely well.