Optimization of polling systems with Bernoulli schedules

Optimization;Polling Systems;Queueing Theory;operations research

The power-series algorithm applied to polling systems with a dormant server

Polling Systems;Queueing Theory

Towards a unifying theory on branching-type polling models in heavy traffic

htmlabstractFor a broad class of polling models the evolution of the system at specific embedded polling instants is known to constitute a multi-type branching process (MTBP) with immigration. In this paper we derive heavy-traffic limits for general MTBP-type of polling models. The results generalize and unify many known results on the waiting times in polling systems in heavy traffic, and moreover, lead to new exact results for classical polling models that have not been observed before. To demonstrate the usefulness of the results, we derive closed-form expressions for the LST of the waiting-time distributions for models with cyclic globally-gated polling regimes, and for cyclic polling models with general branching-type service policies. As a by-product, our results lead to a number of asymptotic insensitivity properties, providing new fundamental insights in the behavior of polling models

Towards a unifying theory on branching-type polling systems in heavy traffic

For a broad class of polling models the evolution of the system at specific embedded polling instants is known to constitute a multi-type branching process (MTBP) with immigration. In this paper we derive heavy-traffic limits for general MTBP-type of polling models. The results generalize and unify many known results on the waiting times in polling systems in heavy traffic, and moreover, lead to new exact results for classical polling models that have not been observed before. To demonstrate the usefulness of the results, we derive closed-form expressions for the LST of the waiting-time distributions for models with cyclic globally-gated polling regimes, and for cyclic polling models with general branching-type service policies. As a by-product, our results lead to a number of asymptotic insensitivity properties, providing new fundamental insights in the behavior of polling models

A queueing theory approach to Pareto-optimal bags-of-tasks scheduling on clouds

Cloud hosting services offer computing resources which can scale along with the needs of users. When access to data is limited by the network capacity this scalability also becomes limited. To investigate the impact of this limitation we focus on bags{of{tasks where task data is stored outside the cloud and has to be transferred across the network before task execution can commence. The existing bags-of-tasks estimation tools are not able to provide accurate estimates in such a case. We introduce a queuing{network inspired model which successfully models the limited network resources. Based on the Mean{Value Analysis of this model we derive an efficient procedure that results with an estimate of the makespan and the executions costs for a given configuration of cloud virtual machines. We compare the calculated Pareto set with measurements performed in a number of experiments for real-world bags-of-tasks and validate the proposed model and the accuracy of the estimated configurations