A stochastic service network model with application to hospital facilities

Area of Science:

• Operations Research
• Healthcare Management
• Stochastic Modeling

Background:

• Service network facilities often face capacity constraints in stochastic environments.
• Accurate estimation of utilization and service levels is crucial for efficient resource allocation.
• Modeling patient flow in healthcare systems requires accounting for finite capacities and no-queueing policies.

Purpose of the Study:

• To develop a methodology for estimating expected utilization and service levels in capacity-constrained service networks.
• To model customer (patient) flow through a network with a finite capacity unit where no queues form.
• To provide a computationally efficient approach for analyzing such systems.

Main Methods:

• Utilized a semi-Markov process to model customer flow through the service network.
• Developed a linear relationship for computing expected utilization and service levels.
• Employed Erlang's loss formula to calculate the probability of the finite capacity unit being at full capacity.

Main Results:

• The expected utilization and service level can be calculated using equilibrium arrival rates, mean holding times, and the probability of the finite capacity unit being full.
• Erlang's loss formula provides an exact calculation for the probability of full capacity in specific cases and a good approximation in general.
• The methodology's accuracy was validated using published data.

Conclusions:

• The proposed methodology offers an effective way to estimate key performance metrics in capacity-constrained service networks.
• The use of Erlang's loss formula as an approximation is recommended for practical applications.
• The study presents a technique for analyzing patient flow data based on the developed methodology.