Numerical analysis of a discrete-time finite capacity queue with a burst arrival

We study a discrete-time, multi-server, finite capacity queue with a burst arrival. Once the first job of a burst arrives at the queue, the successive jobs will arrive every time slot until the last job of the burst arrives. The number of jobs and the inter-arrival time of bursts are assumed to be generally distributed, and the service time is assumed to be equal to one slot. We propose an efficient numerical method to exactly obtain the job loss probability, the waiting time distribution and the mean queue length using an embedded Markov chain at the arrival instants of bursts.