$M|G|\infty$ Queue Busy Cycle Renewal Function
Manuel Alberto M. Ferreira
TL;DR
This paper derives formulas for the busy cycle renewal function in the $M|G| ext{infinity}$ queue, which counts busy periods starting within a time interval, crucial for practical queue analysis.
Contribution
It introduces explicit formulas for the busy cycle renewal function in the $M|G| ext{infinity}$ queue, with examples for various service time distributions.
Findings
Formulas for the busy cycle renewal function are provided.
Application examples demonstrate the formulas for different distributions.
The results facilitate practical analysis of $M|G| ext{infinity}$ queues.
Abstract
We present formulas to compute the busy cycle renewal function for the queue and exemplify for some service time distributions. The busy cycle renewal function value in t is the number of busy periods that begin in the interval from 0 till . This number is of crucial importance in practical applications of queue.
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Taxonomy
TopicsAdvanced Queuing Theory Analysis · Probability and Risk Models · Simulation Techniques and Applications