Abstract: The aim of this paper is to derive the analytical solution of the
queue: / a,b / /
k H M C N with balking and reneging in which (i) units arrive according to
a hyper-Poisson distribution with k independent branches, (ii) the queue discipline is
FIFO; and (iii) the units are served in batches according to a general bulk service rule.
The steady-state probabilities, recurrence relations connecting various probabilities
introduced are found and the expected number of units in the queue is derived in an
explicit form. Also, some special cases are obtained.