A discrete-time infinite-server batch arrival queue with application to serverless computing
Abstract
Serverless computing systems behave like an infinite server queue, dynamically expanding the number of instances to handle incoming batch tasks. In serverless computing, to leverage its scalability, efficiency, and cost-effectiveness, it is essential to apply an infinite server queue with batch task arrival. The model is used to estimate resource usage and to optimize cost-performance trade-offs. This paper analyzes a discrete-time infinite-server batch/single-arrival queue with application to a serverless computing system. We obtain the probability-generating function of the system size, which characterizes a functional equation; we then solve it recursively to find state probabilities at various epochs and some performance measures. Unlike existing discrete-time infinite-server models, this paper explicitly compares the late-arrival system with delayed access and the early-arrival system policies in the context of batch arrivals, and establishes convergence to their continuous-time counterparts. The model's numerical results have been presented in graphs and tables to illustrate the impact of batch-size distributions and system parameters.
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