In this article, we study the home healthcare (HHC) admission problem. HHC offers an interesting compromise between reduced health costs, sufficient quality of care and increased comfort for the patient. However, HHC providers encounter variability in both patients length of stay and arrival rate, making it difficult to determine an admission policy that ensures sufficient activity for the HHC provider to be economically viable without relying too heavily on overtime from its employees. We present a memoryless discrete-time model that encompasses this variability. This model was solved by a Markov chain approach, giving us exact results on small instances, and hinting some analytical results. The results obtained by this method allow us to analyze and compare performances from different admission policies.