Before revision:  We provide conditions for the existence of constant competitive ratio for this system, and also the competitive ratios for several well-studied policies  such as cyclic  exhaustive, gated andl -limited policies, Stochastic Largest Queue policy, One Machine policy and Gittins Index policy for polling systems . We show that any policy with (1) purely static, (2) queue-length based or (3) job-processing-time based routing discipline does not have a competitive ratio smaller than k, where k is the number of queues. Finally, a mixed strategy is provided for a practical scenario where setup time is large but bounded .
After revision:  We provide conditions for the existence of constant competitive ratio for this system, and also the competitive ratios for several well-studied policies such as cyclic exhaustive, gated andl -limited policies, Stochastic Largest Queue policy, One Machine policy and Gittins Index policy for polling systems .