A queue with starter and a queue with vacations: delay analysis by decomposition
Operations Research
Queueing systems with vacations—a survey
Queueing Systems: Theory and Applications
Control policies for the MX/g/1 queueing system
Management Science
Stochastic models in queueing theory
Stochastic models in queueing theory
A Poisson input queue under N-policy and with a general start up time
Computers and Operations Research
Batch arrival queue with N-policy and single vacation
Computers and Operations Research
A batch arrival queue with a vacation time under single vacation policy
Computers and Operations Research
Analysis of a Multiserver Queue with Setup Times
Queueing Systems: Theory and Applications
Computers and Industrial Engineering
Equilibrium customer strategies in a single server Markovian queue with setup times
Queueing Systems: Theory and Applications
A discrete-time single-server queue with a modified N-policy
International Journal of Systems Science
Discrete-time GeoX/G/1 queue with unreliable server and multiple adaptive delayed vacations
Journal of Computational and Applied Mathematics
Performance Evaluation
An algorithmic analysis of multi-server vacation model with service interruptions
Computers and Industrial Engineering
On departure process in the batch arrival queue with single vacation and setup time
Annales UMCS, Informatica
Green Networking With Packet Processing Engines: Modeling and Optimization
IEEE/ACM Transactions on Networking (TON)
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This paper deals with an MX/G/1 queueing system with a vacation period which comprises an idle period and a random setup period. The server is turned off each time when the system becomes empty. At this point of time the idle period starts. As soon as a customer or a batch of customers arrive, the setup of the service facility begins which is needed before starting each busy period. In this paper we study the steady state behaviour of the queue size distributions at stationary (random) point of time and at departure point of time. One of our findings is that the departure point queue size distribution is the convolution of the distributions of three independent random variables. Also, we drive analytically explicit expressions for the system state probabilities and some performance measures of this queueing system. Finally, we derive the probability generating function of the additional queue size distribution due to the vacation period as the limiting behaviour of the MX/M/1 type queueing system.