Abstract
This paper analyzes a single-server discrete-time queueing model with general independent arrivals, where the service process of the server is characterized in two steps. Specifically, the model assumes that (i) each customer represents a random, arbitrarily distributed, amount of work for the server, the service demand, and (ii) the server disposes of a fixed number of work units that can be executed per slot, the service capacity.
For this non-classical queueing model, we obtain explicit closed-form results for the probability generating functions (pgf’s) of the unfinished work in the system and the queueing delay of an arbitrary customer. The pgf of the number of customers is derived explicitly in case of either geometrically distributed service demands, and/or for a geometric arrival distribution. The analysis is complemented by several numerical examples.
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Bruneel, H., Rogiest, W., Walraevens, J., Wittevrongel, S. (2014). On Queues with General Service Demands and Constant Service Capacity. In: Norman, G., Sanders, W. (eds) Quantitative Evaluation of Systems. QEST 2014. Lecture Notes in Computer Science, vol 8657. Springer, Cham. https://doi.org/10.1007/978-3-319-10696-0_17
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DOI: https://doi.org/10.1007/978-3-319-10696-0_17
Publisher Name: Springer, Cham
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