  This research is about COVID-19, which is a contagious virus that reached
many countries, including Lebanon. Monitoring the outbreak, researchers have
been involved in introducing COVID-19 targeting vaccines. Already facing
financial and political issues, Lebanon was further affected by the COVID-19
outbreak. The hereby research tends to design the optimum vaccination plan to
reach the recommended herd immunity in Lebanon. The scheme is drafted per
application of the queue modeling where the essential parameters revolve around
the arrival rate (the mean of which is 536 people) and service rate. Based on a
two-stage cluster sampling method, this data is collected from six vaccination
centers located in Beirut. The outcomes were computed through R statistical
software after validating the stability condition. Per the results, the mean
number of people in the network queue ranges between 4.1 and 5.2. In contrast,
the time spent by individuals extends from around 5.7 up to 8 minutes, having
an average of 5 servers for system one and 4 servers for system two. Therefore,
the optimization of the vaccination plan followed in Lebanon necessitates the
consistency of arrivals and the decrease of the service time. Furthermore, the
service rate can be maximized by adding servers on both systems of the network
queue. Further studies might include applying queue modeling in other medical
sectors, for instance, the emergency section of hospitals.
