A note on \(M/G/1\) vacation systems with sojourn time limits. (English) Zbl 1255.90055

Summary: We deal with an \(M/G/1\) vacation system with the sojourn time (wait plus service) limit and two typical vacation rules, i.e. multiple and single vacation rules. Using the level crossing approach, we derive recursive equations for the steady-state distributions of the virtual waiting times in \(M/G/1\) vacation systems with a general vacation time and two vacation rules.


90B25 Reliability, availability, maintenance, inspection in operations research
60K25 Queueing theory (aspects of probability theory)
60G17 Sample path properties
45D05 Volterra integral equations
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