The truncated queues with bulk arrivals and hyperexponential service time distribution with reneging

This paper deals with the steady-state solution of the queueing system: MX/Hk /1/N with reneging in which (i) units arrive in batches of random size with the interarrival times of batches following negative exponential distribution, (ii) the batches are served in order of their arrival; and (iii) the service time distribution is hyperexponential with k branches. Recurrence relations connecting the various probabilities introduced are found. Some measures of effectiveness are deduced and some special cases are also obtained.