Abstract
We consider a cyclic polling system with general service times, general switch-over times, and simultaneous batch arrivals. This means that at an arrival epoch, a batch of customers may arrive simultaneously at the different queues of the system. For the exhaustive service discipline, we study the batch sojourn-time, which is defined as the time from an arrival epoch until service completion of the last customer in the batch. We obtain exact expressions for the Laplace–Stieltjes transform of the steady-state batch sojourn-time distribution, which can be used to determine the moments of the batch sojourn-time and, in particular, its mean. However, we also provide an alternative, more efficient way to determine the mean batch sojourn-time, using mean value analysis. We briefly show how our framework can be applied to other service disciplines: locally gated and globally gated. Finally, we compare the batch sojourn-times for different service disciplines in several numerical examples. Our results show that the best performing service discipline, in terms of minimizing the batch sojourn-time, depends on system characteristics.
Highlights
Polling models are multi-queue systems in which a single server cyclically visits queues in order to serve waiting customers, typically incurring a switch-over time when moving to the queue
In many applications, these arrival processes are not necessarily independent; customers arrive in batches, and batches of customers may arrive at different queues simultaneously [21]
We study the batch sojourn-time in polling systems with simultaneous arrivals, that is, the time until all the customers in a single batch are served after an arrival epoch
Summary
Polling models are multi-queue systems in which a single server cyclically visits queues in order to serve waiting customers, typically incurring a switch-over time when moving to the queue. After the requested number of products has been produced, including possible demand for the same product from orders that just came in, the machine starts to process the product in the sequence In this way, the machine polls the buffers of the different product categories to check whether production is required. The machine polls the buffers of the different product categories to check whether production is required In this example, the server represents the machine, a customer represents a unit of demand for a given product, and a batch arrival corresponds to the order itself. The web page will be fully loaded when all its file-retrieval requests are executed In this application, the server represents the I/O controller, a customer represents an individual file-retrieval request, a batch of customers who arrive simultaneously corresponds to each web page request, and the batch sojourn-time is the time required to fully load a web page.
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