Modeling and simulation of M/M/c queuing pharmacy system with adjustable parameters

This paper studies a discrete event simulation (DES) as a computer based modelling that imitates a real system of pharmacy unit. M/M/c queuing theo is used to model and analyse the characteristic of queuing system at the pharmacy unit of Hospital Tuanku Fauziah, Kangar in Perlis, Malaysia. The input of this model is based on statistical data collected for 20 working days in June 2014. Currently, patient waiting time of pharmacy unit is more than 15 minutes. The actual operation of the pharmacy unit is a mixed queuing server with M/M/2 queuing model where the pharmacist is referred as the server parameters. DES approach and ProModel simulation software is used to simulate the queuing model and to propose the improvement for queuing system at this pharmacy system. Waiting time for each server is analysed and found out that Counter 3 and 4 has the highest waiting time which is 16.98 and 16.73 minutes. Three scenarios; M/M/3, M/M/4 and M/M/5 are simulated and waiting time for actual queuing model and experimental queuing model are compared. The simulation results show that by adding the server (pharmacist), it will reduce patient waiting time to a reasonable improvement. Almost 50% average patient waiting time is reduced when one pharmacist is added to the counter. However, it is not necessary to fully utilize all counters because eventhough M/M/4 and M/M/5 produced more reduction in patient waiting time, but it is ineffective since Counter 5 is rarely used.