Batch sojourn time in polling systems on a circle
arXiv:2308.12793 · doi:10.1017/S0269964824000238
Abstract
In this paper, we analyze a polling system on a circle. Random batches of customers arrive at a circle, where each customer, independently, obtains a uniform location. A single server cyclically travels over the circle to serve all customers. Using mean value analysis, we derive the expected number of waiting customers within a given distance of the server and a closed form expression for the mean batch sojourn time.