The Virtual Waiting Time for the Batch Arrival Queueing Systems

Abstract

In the article the G ^η I/G/1-type batch arrival system with infinite waiting-room is considered. The explicit formulae for the distribution of the virtual waiting time at any fixed moment t and as t → ∞ are obtained. The study is based on generalization of Korolyuk's method for semi-markov random walks.

Key Words:

• Batch arrival G ^η I/G/1 queueing system
• FIFO service discipline
• Virtual waiting time
• Canonical factorization

Mathematics Subject Classification:

• Primary 60K25
• Secondary 60K15, 60K20