A Restless Time-Fractional Multiclass Queue

Abstract We study a single-server priority queue with a finite number of classes, in which the arrivals follow a fractional Poisson process of index $$\alpha \in (0,1]$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>∈</mml:mo> <mml:mo>(</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo>]</mml:mo> </mml:mrow> </mml:math> and the service completions are triggered by an independent fractional Poisson process of index $$\beta