Some Results for GIX/M/s/c Queues

We address the time dependent and steady-state analysis of the number of customers in a GIX/M/s/c queuing system at prearrivals of batches. As a corollary, we derive the continuous time steady-state distribution of the number of customers in the system in continuous time. The obtained closed form solutions are easy to compute, as they involve only combinatorial calculations and mixed-Poisson probabilities or mixed-Poisson expected values. Finally, the steady-state distribution of the number of customers seen by customers at their arrival to the system, blocking probability and mean and variance of the waiting times in queue of non-blocked costumers are derived.