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 .
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 in the queueing literature, such as cyclic exhaustive, gated andl -limited policies, Stochastic Largest Queue policy, One Machine policy and Gittins Index policy for polling systems .