On Erlang Queue with Multiple Arrivals and its Time-changed Variant

R. B. Pote; K. K. Kataria

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arXiv · 2501.08789

On Erlang Queue with Multiple Arrivals and its Time-changed Variant

R. B. Pote·K. K. Kataria

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Abstract

We introduce and study a queue with the Erlang service system and whose arrivals are governed by a counting process in which there is a possibility of finitely many arrivals in an infinitesimal time interval. We call it the Erlang queue with multiple arrivals. Some of its distributional properties are obtained that includes the state-phase probabilities, the mean queue length and the distribution of busy period etc. Also, we study a time-changed variant of it by subordinating it with an independent inverse stable subordinator where we obtain its state probabilities and the mean queue length.

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R. B. Pote, K. K. Kataria. 2025-01-15. On Erlang Queue with Multiple Arrivals and its Time-changed Variant. https://arxiv.org/abs/2501.08789

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