The long waiting time in the public health sector in many countries has motivated the government to shift public sectors' waiting lists to the private sector, by setting a price cap and subsidizing switching patients in private services. In this paper,  we propose a novel queuing model incorporating choice behavior of heterogeneous time-sensitive customers. The optimal admission and pricing policy with price discrimination to maximize the private sectors' revenue will exam the effect of subsidy and price cap in a government regulated market. We find that price discrimination plays an important role in providing incentive for the private sector to admit switching patients. There is an upper bound for the take up rate of the private sector. In addition, we find the increase in the subsidy simultaneously exhibits positive effect and negative effect. The price cap is an effective approach to restrain the negative effect of the subsidy.