Calling For Help: Using Queueing Theory to Model the Optimal Number of Counselors a University Should Employ

Abstract

This paper will provide a model for universities to use to determine the optimal number of counselors to employ at their counseling center. The model will implement queueing theory and Monte Carlo simulation techniques to minimize the number of students in the queue while also maximizing the usefulness of counselors by ensuring that they don’t sit idle for too long. It bases the model off of one of the original studies of queueing theory done on telephone lines where the students are like callers and the counselors are like telephone lines. By looking at various service time distributions (based on the reasons for seeking therapy), various arrival time distributions (how frequently students need therapy), and various therapists, I was able to develop a model that demonstrates how long on average students spend waiting to see a counselor and how many students on average are stuck waiting. This in turn led to conclusions on how many counselors a university should employ to make sure the needs of the student body are being adequately met.