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

TL;DR

This paper introduces a new Erlang queue model with multiple arrivals and explores its properties, including state probabilities and mean queue length, as well as a time-changed variant using inverse stable subordination.

Contribution

It presents a novel queue model with multiple arrivals and analyzes its distributional properties, also extending to a time-changed version with inverse stable subordination.

Findings

Derived state-phase probabilities for the queue

Calculated mean queue length for both models

Analyzed the distribution of busy periods

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.