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

Rohini Bhagwanrao Pote () and Kuldeep Kumar Kataria ()
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Rohini Bhagwanrao Pote: Indian Institute of Technology Bhilai
Kuldeep Kumar Kataria: Indian Institute of Technology Bhilai

Methodology and Computing in Applied Probability, 2025, vol. 27, issue 3, 1-36

Abstract: 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 more than one arrival at any instant. We call it the Erlang queue with multiple arrivals. We derive a system of differential equations for its transient probabilities. Its probability generating function is obtained from which the explicit expressions of its transient probabilities are derived. Also, the probability of zero customers at any instant is obtained. Further, we define the queue length process for Erlang queue with multiple arrivals and obtain a system of differential equations for its mean queue length. We derive the explicit expression for the mean queue length and the second moment of the queue length process. Also, we study a time-changed variant of it by subordinating it with an independent inverse stable subordinator for which we obtain its state probabilities, mean queue length and distribution of busy period.

Keywords: Generalized counting process; Erlang service distribution; Transient solution; Queue length; Busy period; Subordinator; Primary 60K15; Primary 60K20; Secondary 60K25; Secondary 26A33 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s11009-025-10200-7

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