A single server queue with a varying gate mechanism

Abstract

A Markovian single server queue in a varying environment with gate mechanism is studied. Exact expressions for the duration of the nth batch and the number served are obtained by exploiting the connection between queues, branching processes and continued fractions. Numerical illustrations are presented.

Keywords:

• continued fractions
• branching processes
• busy period
• gated service

2000 AMS Subject Classification: :

• 60K25

Acknowledgements

The authors thank Prof. Wolfgang Stadje, University of Osnabrück, Germany for useful discussions. The authors thank the referees for their useful suggestions. The work of P.R. Parthasarathy has been supported by the Alexander von Humboldt Foundation, Germany.