Queueing system \(\text{G}^{\kappa}|\text{G}|1\) with customers arriving in batches. (English. Ukrainian original) Zbl 0998.60087

Ezhov, I. I.; Kadankov, V. F.

Theory Probab. Math. Stat. 64, 19-36 (2002); translation from Teor. Jmovirn. Mat. Stat. 64, 18-34 (2001).

The authors find distributions of the following characteristics of \(\text{G}^{\kappa}|\text{G}|1\) queueing system (index \(\kappa\) shows that customers arrive as groups of random size \(\kappa\)): the length of the queue under transition and stationary regime, service time, virtual waiting time, etc. The proposed method of investigation is based on the analysis of the difference between two renewal processes and useful factorization expansions of the corresponding generating functions.

Reviewer: N.M.Zinchenko (Kyïv)

MSC:

60K20	Applications of Markov renewal processes (reliability, queueing networks, etc.)
60K25	Queueing theory (aspects of probability theory)
90B22	Queues and service in operations research

Keywords:

queueing system; renewal process; distributions of functionals; generating function; factorization