An Elementary Derivation of Mean Wait Time in Polling Systems
For queueing theory practitioners and educators, this offers a simpler method to compute average wait times, though it is an incremental simplification of existing results.
The authors provide an elementary derivation for the mean wait time in polling systems using only algebra and Poisson process properties, avoiding complex tools like Laplace transforms. This simplifies the calculation for practical use and teaching.
Polling systems are a well-established subject in queueing theory. However, their formal treatments generally rely heavily on relatively sophisticated theoretical tools, such as moment generating functions and Laplace transforms, and solutions often require the solution of large systems of equations. We show that, if you are willing to only have the average waiting of a system time rather than higher moments, it can found through an elementary derivation based only on algebra and some well-known properties of Poisson processes. Our result is simple enough to be easily used in real-world applications, and the simplicity of our derivation makes it ideal for pedagogical purposes.