Long waiting time has attracted public attention significantly due to the negative effects on patients' satisfaction with health systems. In the United States, waiting time of a patient to see a physician for the first time has been increased by 30% since 2014. This is in part due to the ineffective allocation between physicians and patients, and in part due to growing population needing healthcare and the restriction introduced by insurance policies. There is an urgent need to develop matching mechanisms with the consideration of preferences from both patients and physicians to improve matching results. This paper presents a new allocation framework between physicians and patients to shorten the patient waiting time as well as improve the allocation effectiveness. We leverage the matching theory and extend the conventional deferred acceptance algorithm to a discrete-time stable marriage framework (i.e., discrete deferred acceptance algorithm, DDA) with the consideration of uncertainty constraints introduced by insurance types. We benchmark our proposed algorithm with the current practice (i.e., continuous deferred acceptance scheme, CDA) under different scenarios when the demand-supply ratio (DSR) varies. Experimental results show that when the DSR is more than 1.25, DDA outperforms traditional CDA practices in terms of waiting time and matching regret. The proposed framework shows strong potential to tackle the problem of long waiting time in the healthcare system.