Probability in the Engineering and Informational Sciences



THRESHOLD POLICIES FOR A SINGLE-SERVER QUEUING NETWORK


P. S.  Ansell a1, K. D.  Glazebrook a2 and I.  Mitrani a3
a1 Department of Statistics, University of Newcastle upon Tyne, Newcastle upon Tyne NE1 7RU, United Kingdom, E-mail: p.s.ansell@newcastle.ac.uk
a2 Department of Statistics, University of Newcastle upon Tyne, Newcastle upon Tyne NE1 7RU, United Kingdom, E-mail: kevin.glazebrook@newcastle.ac.uk
a3 Department of Computing Science, University of Newcastle upon Tyne, Newcastle upon Tyne NE1 7RU, United Kingdom, E-mail: isi.mitrani@newcastle.ac.uk

Abstract

We consider a single-server queuing system with two job classes under service policies of threshold type. The server switches from type 1 to type 2 when either the former queue is empty or the latter reaches size T; it switches from type 2 to type 1 when the former queue size drops below T and the latter is not empty. The joint queue-length distribution is determined for preemptive and nonpreemptive implementations using both analytic techniques and the power series algorithm.