A transient <i>M</i><SUP align="right">[<i>X</i>]</SUP>/<i>M</i><SUP align="right">(<i>k</i>, <i>K</i>)</SUP>/1 queue with reneging and setup time for service

In this paper, we analyse a transient queuing model, in which tasks arrival in bulks of varying sizes with compound Poisson process. There is a single server serving batches of tasks with limited sizes with a minimum and a maximum, according with exponential distribution, with setup times for service with also exponential distribution, and impatient tasks that may renege while the server is busy with also exponential distribution. The transient probability generating function for the number in the system, special cases to verify it and some performance measures have been found.