Myths of Adding Staff: Why Math Says It Doesn't Always Reduce Queues

The common assumption that adding more doctors will automatically shorten hospital waiting lines may be flawed, according to a mathematical simulation conducted using Maple software. The research, exploring the dynamics of patient queues, suggests that simply increasing medical staff does not guarantee a reduction in wait times if the overall service efficiency does not improve.

The simulation, which utilized data from the Indonesian Doctors Association (IDI), focused on key variables influencing queue length. These included the speed of service, measured as total patients per hour, and operational factors like when additional service points might open. By visualizing these variables as linear functions, the study aimed to identify the point at which queues begin to dissipate.

Drawing on principles from Queueing Theory, first introduced by A.K. Erlang in 1909 for telephone networks and now applied to various service sectors including healthcare, the simulation highlights the critical relationship between patient arrival rates (λ) and service rates (μ). The theory posits that if the rate at which patients arrive is greater than or equal to the rate at which they are served, the system becomes saturated, leading to accumulating queues.

Specifically testing scenarios based on IDI data for general practitioners (average consultation time 11.5 minutes) and specialists (average 12 minutes), the simulation revealed that an increase in doctors alone is insufficient. The core issue lies in ensuring the service rate consistently surpasses the patient arrival rate. Without this balance, adding more service points or personnel may not effectively untangle the waiting lines.