Algorithmic methods for multi-server queues with group arrivals and exponential services

We discuss algorithms for the computation of the steady-state features of the c-server queue with exponential service times and bounded group arrivals. While our methods are valid for general interarrival time distributions, we treat in detail the simplifications obtained by using a distribution of phase type. Oueue length densities at times prior to arrivals and at arbitrary times are obtained in a modified matrix-geometric form. Their means and variances are found in computationally tractable forms. We also present algorithmic methods for the waiting time and the virtual waiting time distributions of a customer in a group and obtain the means and variances of these distributions in tractable forms. Numerical examples show that the effects of changing various parameters of the queuing model may so be examined at a small computational cost.