Utility Analysis of an Emergency Medical Service Model Using Queuing Theory

Aims/ Objectives: To use queuing model to deter mine the optimum waiting and service cost in a hospital ICU emergency service.

Study Design: Modeling and Simulation.

Place and Duration of Study: ICU Emergency Service Department, Moi Teaching and Referral Hospital (MTRH), Uasin Gishu - County, between June 2016 and July 2016.

Methodology: Use of M/M/s queuing model to analyze ICU services using secondary data of MTRH emergency patients arrival and service rates together with estimated service cost of available 6 beds. Waiting cost estimated using formulated Modified Normal Loss function.

Results: With an average individual tolerance of τ=0.083 hrs and average response time of =0.083 hrs, the present scenario of 6 ICU beds in MTRH is operating at a service cost of Ksh 60 and patient queuing cost of Ksh 415.53 per hour. The length of the queue is 1.4 hr or approximately 34 patients per day. The optimum number of beds required for the facility to operate with zero response time and zero quality tolerance is 18 beds. This will facilitate the reduction of queuing cost to 153.98 and total cost to 333.98.

Conclusion: The current status of ICU emergency services at MTRH is costly to both the health facility and the patients. Individuals seeking such services may either opt to get similar services elsewhere at an opportunity cost of Ksh 641.39 per hour of delay. With 1.4 patients waiting in the queue every hour, this accumulates to 34 patients per day. Increasing ICU beds to 18 minimizes the length of the queue to 6 patients per day and queuing cost by 76% and reduces the total cost by 65%. This will reduce the financial burden of the patients and increase the chances of saving lives during emergency cases. These predictors, however, need further work and inclusion of related services to give a bigger and better picture of the facility.