Outpatient services have become an important component of healthcare especially during the era of pandemic (Covid-19). The amount of time a patient spends waiting in an outpatient setting may have an impact on their satisfaction with the service(s) provided. In this research, an attempt was made to investigate the arrival and service rates of patients for the period of one month between the hours of 9:00am and 2:00pm at the University College Hospital (UCH), Ibadan during Covid-19 using Poisson Process in order to deduce traffic intensity (ρ), expected number of patients at a steady rate (L), expected queue length (Lq), expected waiting time (Wq), total patients waiting (W) and mean number of Patients in the system. Results showed that more patients visit the clinic everyday of the week due to the high traffic intensity close to 100% and the high minutes spent in the hospital before being attended to. Conclusively, waiting time on Saturdays and Tuesdays are much compared to the remaining days.