The queuing theory is a study of long waiting lines that is used to calculate waiting time and queue lengths. The two main variables in the calculation are the arrival rate and the service rate. The arrival rate is beyond one's control. However, the service rate is dependent on the organization’s representatives available to tend to customer demand (Shortle et al., 2018). For example, the queuing theory can be applied to a small community that has a single police officer on night duty. The average arrival rate is 3 crimes per shift, while an officer can only handle 4 crimes per shift. With these two figures, it is possible to calculate the average waiting time before a criminal is apprehended. One can vary the number of police officers on a night shift, i.e., 2 or 3, and calculate the new average waiting time. When the number of police officers is low, the waiting time increase, and the queues become unnecessarily long. However, very many police officer leads to underutilization of officer and wastage of resources. Therefore, this study will calculate the apprehension time with a variable number of police officers per shift using an online simulator.
Simulation results
When the arrival rate is 3 crimes per shift
Waiting time to apprehension with 3 police officers per shift? Tend to infinity
Waiting time to apprehension with 4 police officers per shift? 360 minutes
Waiting time to apprehension with 5 police officers per shift? 144 minutes
When the arrival rate is 2 crimes per shift
Waiting time to apprehension with 3 police officers per shift? 320 minutes
Waiting time to apprehension with 4 police officers per shift? 120 mins
Waiting time to apprehension with 5 police officers per shift? 64 minutes
Interpretation
From the results, it was established that the waiting time to apprehension increased when the arrival time was high, i.e., 3 crimes per shift compared to when the arrival time was less, i.e., 2 crimes per shift. Though the service rate was the same, i.e., four police officers per shift, more waiting time was recorded when the arrival time was more (Supositorio.com, 2020). For instance, when the arrival time was 2 crimes per shift, the waiting time for apprehension was only 120 minutes when 4 police officers were on duty. On the contrary, when the arrival time was 3 crimes per shift, the waiting time for apprehension was 360 minutes when 4 police officers were on duty.
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When the arrival time was held constant, the waiting time reduced significantly when the more police officers were allocated to desk duty. For instance, when arrival rate was held steady at 3 crimes per shift, and the number of police officers was increased from 4 police officers per shift to 5 officers, the waiting time for apprehension reduced by more than half, i.e., from 360 minutes to 144 minutes (Supositorio.com, 2020). Similarly, when the arrival rate was held constant at 2 crimes per shift, the waiting time reduced from 320 minutes to 120 minutes when the service rate was increased from 3 police officers to 4 officers.
Conclusion
One of the best ways to improve service delivery is to reduce the duration of time spent waiting. However, two significant factors play a critical role in reducing the waiting time, the arrival rate, and the service rate. One way to effectively reduce the waiting time when the arrival time is high is to increase the service rate, i.e., post more officers to address the diverse needs of the customers. However, when the arrival rate is low one does not need to post more employees to duty. A small number of officers is sufficient to handle the low demand.
References
Lin, C. C., Wu, C. C., Chen, C. D., & Chen, K. F. (2019). Could we employ the queueing theory to improve efficiency during future mass causality incidents? Scandinavian journal of trauma, resuscitation, and emergency medicine , 27 (1), 41.
Shortle, J. F., Thompson, J. M., Gross, D., & Harris, C. M. (2018). Fundamentals of queueing theory (Vol. 399). John Wiley & Sons.
Supositorio.com. (2020). Queueing Theory Calculator . Retrieved from https://www.supositorio.com/rcalc/rcalclite.htm
