Explicit Formulae for the Queue Length Distribution of Batch Arrival Systems

Abstract

A G ^θ I/G/1-type batch arrival system is considered. Explicit formulae for the distribution of queue length both at the fixed time t and as t → ∞ are obtained. The study is based on the generalization of Korolyuk's method for semi-markov random walks.

Key Words:

• Batch arrival queueing system
• Queue length
• Busy period
• Steady-state distribution
• Canonical factorization

Acknowledgments