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

Source: [On Erlang Queue with Multiple Arrivals and its Time-changed Variant](<https://www.sota2.com/research/paper/68fa5cd41e209131ce9d48f0>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T17:52:21.336Z

Authors: R. B. Pote, K. K. Kataria

Published: 2025-01-15T13:24:37.000Z

## 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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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2501.08789>)

[PDF](<https://arxiv.org/pdf/2501.08789.pdf>)