Poisson input queueing system with startup time and under control-operating policy
Computers and Operations Research
Queueing systems with vacations—a survey
Queueing Systems: Theory and Applications
Computational analysis of steady-state probabilities of M/Ga,b/1 and related nonbulk queues
Queueing Systems: Theory and Applications
Dynamics of the M/G/1 vacation model
Operations Research
State dependence in M/G/1 server-vacation models
Operations Research
Transient solution for a finite capacity M/Ga,b/1 queueing system with vacations to the server
Queueing Systems: Theory and Applications
Control policies for the MX/g/1 queueing system
Management Science
Optimal control of the vacation scheme in a M/G/1 queue
Operations Research
The M/GI/1 Bernoulli feedback queue with vacations
Queueing Systems: Theory and Applications
A Poisson input queue under N-policy and with a general start up time
Computers and Operations Research
ICCAM'92 Proceedings of the fifth international conference on Computational and applied mathematics
Batch arrival queue with N-policy and single vacation
Computers and Operations Research
Optimal control of the MX/G/1/K queue with multiple server vacations
Computers and Operations Research
A continuous approximation for batch arrival queues with threshold
Computers and Operations Research
Queueing systems with state dependent parameters
Frontiers in queueing
A Feedback Queueing System With Batch Arrivals, Bulk Service, and Queue-Dependent Service Time
Journal of the ACM (JACM)
Corrections to: Queues with hysteretic control by vacation and post-vacation periods
Queueing Systems: Theory and Applications
Random walk analysis of parallel queueing stations
Mathematical and Computer Modelling: An International Journal
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The paper investigates the queueing process in stochastic systems with bulk input, batch state dependent service, server vacations, and three post-vacation disciplines. The policy of leaving and entering busy periods is hysteretic, meaning that, initially, the server leaves the system on multiple vacation trips whenever the queue falls below r (\geq1), and resumes service when during his absence the system replenishes to N or more customers upon one of his returns. During his vacation trips, the server can be called off on emergency, limiting his trips by a specified random variable (thereby encompassing several classes of vacation queues, such as ones with multiple and single vacations). If by then the queue has not reached another fixed treshold M (\leq N), the server enters a so-called “post-vacation period” characterized by three different disciplines: waiting, or leaving on multiple vacation trips with or without emergency. For all three disciplines, the probability generating functions of the discrete and continuous time parameter queueing processes in the steady state are obtained in a closed analytic form. The author uses a semi-regenerative approach and enhances fluctuation techniques (from his previous studies) preceding the analysis of queueing systems. Various examples demonstrate and discuss the results obtained.