Background: To determine whether current deterministic models of mass prophylaxis underestimate staffing requirements by ignoring stochastic queuing effects, we built a model that addresses these effects using standard operations research techniques.

Methods: Queuing theory equations allow the estimation of long-run (steady-state) performance measures while accounting for variable arrival and service rates. We first modeled patient flow through a four-station mass prophylaxis site as an Open Jackson Network of M/M/s queuing processes, calculating per-station expected number in queue (Lq) and arrival rates (λ) and deriving average waiting time in queue (Wq, using Little's law) and staff utilization. These performance measures are subject to both user-defined limits (on Lq and Wq) as well as standard limits (<100% utilization), and are used to estimate a minimal acceptable staffing arrangement. Each resulting clinic set-up is then subjected to a discrete event simulation for the expected duration of clinic operation, yielding, in addition to the aforementioned parameters, data on maximal queue length. The model was created in Microsoft Excel with a Visual Basic macro running the simulation. Comparison is to the Weill Cornell BERM model, previously presented at SMDM.

Results: Running a hypothetical clinic set-up with processing times and arrival rates based on recent bioterrorism response exercises, staffing estimates generated by the stochastic/queuing theory model were larger than ones generated by the deterministic model (See Table), with “queue-less” clinics requiring approximately 1/3 more staff than anticipated by deterministic calculations. However, values began to converge at queue lengths of approximately 10 people on average waiting for service at each station. A 30-run simulation with average Lq≤10 yielded maximum queues of 23 (+/- 95% Confidence Interval=1), 70 (+/-6), 27 (+/-4), and 44 (+/-3) for the stations listed.

	Deterministic		Queuing Theory, average queue length =
	FTEs	Rounded	10.0	3.0	1.0	0.5	0.1
Greeting/Entry	2.1	3	3	3	4	4	5
Triage	29.9	30	32	34	37	38	41
Medical Evaluation	10.2	11	12	12	14	15	17
Drug Dispensing	10.4	11	12	13	14	15	17
Total	52.6	55	59	62	69	72	80

Conclusion: Deterministic models of mass prophylaxis clinic design underestimate the number of staff needed for efficient patient processing, but offer reasonable approximations of stochastic queuing models at average queue lengths of > 10.