[Tip: Study the MC, QT, and Little's law lectures together: CTMC (MC lecture), M/M/1 queue (QT lecture), Little's law lecture (when deriving the mean response time from mean number of customers), DTMC (MC lecture), M/M/1 queue derivation using DTMC analysis, derive distribution of response time in M/M/1 queue (QT lecture), relation between Markov property and mem-oryless property (MC lecture), ...

It has been proven that the batch renewal process is the least biased choice of traffic process given the infinite sets of measures of the traffic correlation, (i.e. indices of dispersion, covariances or correlation functions) in the discrete time domain. The same conclusion is expected to hold in the continuous time domain. That motivates the study and comparison of similar queues, fed by batc...

This paper treats a discrete-time single-server finite-buffer exhaustive (singleand multiple-) vacation queueing system with discrete-time Markovian arrival process (D-MAP). The service and vacation times are generally distributed random variables and their durations are integral multiples of a slot duration. We obtain the queue-length distributions at departure, service completion, vacation te...