Polling system

[1] The model has applications in computer networks and telecommunications,[2] manufacturing[3][4] and road traffic management.

[11] A group of n queues are served by a single server, typically in a cyclic order 1, 2, …, n, 1, ….

New jobs arrive at queue i according to a Poisson process of rate λi and are served on a first-come, first-served basis with each job having a service time denoted by an independent and identically distributed random variables Si.

[14] For gated service, the expected waiting time at node i is[12] and for exhaustive service where Ci is a random variable denoting the time between entries to node i and[15] The variance of Ci is more complicated and a straightforward calculation requires solving n2 linear equations and n2 unknowns,[16] however it is possible to compute from n equations.

[17] The workload process can be approximated by a reflected Brownian motion in a heavily loaded and suitably scaled system if switching servers is immediate[18] and a Bessel process when switching servers takes time.