Queueing systems with vacations—a survey
Queueing Systems: Theory and Applications
M/M/1 queues with working vacations (M/M/1/WV)
Performance Evaluation
Analysis on queueing systems with synchronous vacations of partial servers
Performance Evaluation
Role of oxidizer in the chemical mechanical planarization of the Ti/TiN barrier layer
Microelectronic Engineering
Proceedings of the 10th ACM Symposium on Modeling, analysis, and simulation of wireless and mobile systems
Stochastic decompositions in the M/M/1 queue with working vacations
Operations Research Letters
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This paper introduces the CPP/M/c model with working vacations to describe queueing phenomena that arise in an advanced computing environment of virtualized servers operated by the infrastructure owners. In the proposed queue the inter-arrival times of jobs requesting servers follow a Generalized Exponential distribution. To model a maintenance activity, we assume that a certain number of servers simultaneously goes to a maintenance state for a random period when they complete the service of requests and find no further jobs in the waiting line. We derive an expression for the steady-state probabilities and prove a conditional stochastic decomposition property. By a relatively simple model we are able to prove a property which has a significant impact on the organization of maintenance activities of virtualized servers. It means that instead of migrating virtual servers to expensive physical backup servers during software maintenance, a wise and simple strategy based on the vacation approach can be used. Moreover, it is theoretically proved that the system is not overloaded if we organize the maintenance according to the vacation model. We believe that our model can be useful for administrators to choose an appropriate parameter set for the maintenance activities.