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Expected move request waiting times in single-device, polling-based material handling systems

We present an analytical approach to approximate the expected waiting times of move requests (customers) served by a single handling device (server) that operates according to the First-Encountered-First-Served (FEFS) rule, which is a common rule employed for polling-based material handling systems. Under the FEFS rule, the device inspects each station according to a prespecified polling sequence and serves the first move request it encounters. Polling resumes as soon as the device completes serving a move request. The expected waiting times are important for estimating the expected Work-In-Process (WIP) levels at individual stations and to gauge the overall performance of the system. Moreover, the polling sequence itself can affect the expected waiting times. If the device meets the throughput requirement under more than one polling sequence, the results we present can also be used to evaluate alternative polling sequences. In fact, using the analytical results and a numerical example, we show that alternative polling sequences, even if they impose the same ``workload factor'' on the device, can lead to significantly different expected WIP levels.