Queueing systems with vacations—a survey
Queueing Systems: Theory and Applications
State dependence in M/G/1 server-vacation models
Operations Research
Workloads and waiting times in single-server systems with multiple customer classes
Proceedings of the workshop held at the Mathematical Sciences Institute Cornell University on Mathematical theory of queueing systems
Conditional and unconditional distributions for M/G/1 type queues with server vacations
Queueing Systems: Theory and Applications
Queueing analysis of polling models: progress in 1990-1994
Frontiers in queueing
Queueing Systems: Theory and Applications
Analysis of Alternating-Priority Queueing Models with (Cross) Correlated Switchover Times
Queueing Systems: Theory and Applications
On a generic class of lÉvy-driven vacation models
Probability in the Engineering and Informational Sciences
On Lévy-driven vacation models with correlated busy periods and service interruptions
Queueing Systems: Theory and Applications
Maintenance of infinite-server service systems subjected to random shocks
Computers and Industrial Engineering
Marginal queue length approximations for a two-layered network with correlated queues
Queueing Systems: Theory and Applications
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Single-server queues in which the server takes vacations arise naturally as models for a wide range of computer, communication, and production systems. In almost all studies on vacation models, the vacation lengths are assumed to be independent of the arrival, service, workload, and queue length processes. In the present study, we allow the length of a vacation to depend on the length of the previous active period (viz. the period since the previous vacation). Under rather general assumptions regarding the offered work during active periods and vacations, we determine the steady-state workload distribution, both for single and multiple vacations. We conclude by discussing several special cases, including polling models, and relate our findings to results obtained earlier.