Markovian Analysis of Coordination Strategies in Tandem Polling Queues with Setups

TL;DR

This paper provides an exact Markovian analysis of tandem polling queues with setups, comparing synchronized and out-of-sync strategies to determine performance differences, stability conditions, and when each strategy is preferable.

Contribution

It introduces a decomposition approach for analyzing tandem polling queues with setups, offering insights into performance and stability under different strategies and network configurations.

Findings

SP outperforms OP in symmetric networks

OP can outperform SP in asymmetric networks

Network stability depends on downstream bottlenecks

Abstract

We analyze a network of tandem polling queues with two stations operating under synchronized polling (SP) and out-of-sync polling (OP) strategies, and with nonzero setups. We conduct an exact analysis using a decomposition approach to compare the performance in terms of throughput and mean waiting times to investigate when one strategy might be preferred over the other. We also numerically investigate the condition for network stability operating under the two strategies and show that polling network is unstable when there is bottleneck at downstream stations. We find that the SP strategy outperforms the OP strategy in case of product and station symmetric networks while under certain settings of product and station asymmetry, OP strategy outperforms the SP strategy.