Queueing systems with vacations—a survey
Queueing Systems: Theory and Applications
Analysis of cyclic service systems with limited service: bounds and approximations
Performance Evaluation
A single-server queue with vacations and non-gated time-limited service
Performance Evaluation
Two finite-difference methods for solving MAP(t)/PH(t)/1/K queueing models
Queueing Systems: Theory and Applications
Discrete time analysis of \mathrm{MAP}/\mathrm{PH}/1 vacation queue with gated time-limited service
Queueing Systems: Theory and Applications
Real-time queueing theory: A tutorial presentation with an admission control application
Queueing Systems: Theory and Applications
Research: Analysis of a time-limited polling system
Computer Communications
Level-crossing approach to a time-limited service system with two types of vacations
Operations Research Letters
Analysis of a versatile batch-service queueing model with correlation in the arrival process
Performance Evaluation
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We consider a single-server queue in which the server attends to a queue only for a limited period of time and then goes on to other queues, in which case we say it proceeds on a vacation. We obtain results for the probability densities of the number of customers in the system at an arbitrary time, during vacation, and during service; the customer waiting time distribution; and the amount of work in the system at polling instants and at the start of a vacation. The results are extended to the case of multiple vacations during a cycle. We show that the length of a visit to a time-limited service system has a phase type distribution. The work is carried out in discrete time.