Analysis and optimization of vacation and polling models with retrials

TL;DR

This paper analyzes queueing models with retrials and glue periods, providing insights into queue length behavior at various time points and optimizing system performance.

Contribution

It introduces a novel queueing model with deterministic glue periods and retrials, and offers analytical methods for queue length analysis and optimization.

Findings

Queue length distributions at key time points derived.

Impact of glue period duration on system performance quantified.

Analytical framework applicable to similar queueing systems.

Abstract

We study a vacation-type queueing model, and a single-server multi-queue polling model, with the special feature of retrials. Just before the server arrives at a station there is some deterministic glue period. Customers (both new arrivals and retrials) arriving at the station during this glue period will be served during the visit of the server. Customers arriving in any other period leave immediately and will retry after an exponentially distributed time. Our main focus is on queue length analysis, both at embedded time points (beginnings of glue periods, visit periods and switch- or vacation periods) and at arbitrary time points.