Some results for the actual waiting time in batch arrival queueing systems

The article deals with the queueing system of GI/G/1 type with individual service and batch arrival of customers. The method of integral equations on a half-axis [0, ∞) is applied to obtain new results for the actual waiting time wⁿ of the nth arriving customer. The transient and steady state as n tends to infinity are considered. Some simplifications and numerical results for M/M/1, M/E²/1, and M²/M/1 queueing systems are derived as well.