This study reviewed the works done on queuing systems in several situations where customers had to wait in a queue to receive the services they needed. Statistical tools such as the repeated measure ANOVA, correlation analysis and chi square of Goodness of fit for Poisson distribution were employed to analyze the data collected across three designated points concerning the service times of patients, waiting times and inter- arrival time at the OPD of Bolgatanga Regional Hospital . These analysis were to assist to achieve the objectives of determining whether there is a significant linear relationship between the service times and waiting times of patients, establish whether the service times of patients across the three points in the department are the same and the waiting times as well, and finally, to ascertain whether the inter-arrival times follow a Poisson distribution. Results shown that the minimum and maximum service times at the first point were 2.22 minutes and 35.17 minutes respectively with a corresponding mean service time of 10.4545 minutes. The minimum and maximum waiting times at the vital taking point were 0.27 minutes and 16.082 minutes respectively with a mean waiting time of 3.3949 minutes. The correlation coefficient was -0.378 with a p-value of 0.000. For the Mauchly’s test of sphericity for service times the Greenhouse Geisser and Huynh Feldt test statistics were 0.705 and 0.712 respectively whiles that of the waiting time were 0.544 and 0.546 respectively. The F-ratio and the Partial Eta squared values for the service times were 83.221 and 0.457 respectively ant that of the waiting times were 44.952 and 0.312. Finally, the results gave a chi square test statistic value of 451.132.
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