Predictive Modeling for Optimal Bed Capacity in a Sleep Study Center: A Comprehensive Queueing Theory Approach

Background: Sleep study services are experiencing exponential demand growth due to rising awareness of sleep-disordered breathing.Limited polysomnography (PSG) capacity in Indian hospitals results in prolonged waiting times, delaying diagnosis and treatment for obstructive sleep apnea (OSA) and related disorders.Objective: To apply predictive queueing-modeling techniques to determine the optimal bed capacity for a hospital-based sleep study center, minimizing patient waiting times while maximizing resource utilization efficiency.Methods: An M/M/c queueing model (Erlang C) was applied to 12-month operational data from a tertiary care teaching hospital sleep center in Pune, India.The facility operated 305 nights annually with one bed.Key parameters included an arrival rate of λ = 1.1475 patients/night (annual demand of 350 studies/year, including a 45-patient backlog) and a service rate of μ = 1 study/bed/night.System utilization (ρ), average waiting time (W q ), queue length (L q ), and backlog clearance time were calculated for configurations ranging from 1 to 4 beds using standard queueing formulas and validated through discrete-event simulation.Results: A single-bed configuration demonstrated critical instability (ρ = 114.7%),explaining the persistent 45-day wait and growing backlog.The two-bed system achieved stability (ρ = 57.4%)with a 12-hour average wait and a 2.1-month backlog clearance.The three-bed configuration provided optimal performance: 38.2% utilization, a 2-hour average wait, 1-month backlog clearance, and 62% reserve capacity.The four-bed system showed diminishing returns (28.7% utilization).Sensitivity analysis confirmed robustness across ±20% demand variations.Conclusions: Queueing theory provides a rigorous, evidence-based framework for sleep laboratory capacity planning.For an annual demand of 350 studies with 305 operational nights, three beds represent the optimal configuration, balancing minimal patient wait times, rapid backlog clearance, operational resilience, and efficiency.This reproducible methodology applies broadly to diagnostic services facing capacity constraints.