Hospital Simulation with SimPy: Modelling Patient Flow

Published on February 14, 2026

Hospitals are complex systems. Patients arrive unpredictably. Resources are constrained. Lives depend on getting it right. Simulation helps. <h2 id="the-hospital-model">The Hospital Model</h2> Key elements: - Patients - Arrive with varying urgency - Staff - Doctors, nurses, technicians - Beds - Limited and precious - Departments - A&E, wards, theatres - Pathways - Patient journeys through the system <h2 id="emergency-department-simulation">Emergency Department Simulation</h2> <div class="code-block"><pre><code>import simpy import random class EmergencyDepartment: def __init__(self, env, config): self.env = env self.triage_nurses = simpy.Resource(env, config['triage_nurses']) self.doctors = simpy.PriorityResource(env, config['doctors']) self.beds = simpy.Resource(env, config['beds']) self.stats = { 'patients': [], 'wait_times': [], 'length_of_stay': [] } def patient_pathway(self, patient_id, severity): arrival = self.env.now # Priority: 1 = critical, 5 = minor priority_map = {'critical': 1, 'urgent': 2, 'standard': 3, 'minor': 4} priority = priority_map.get(severity, 3) # Triage with self.triage_nurses.request() as req: yield req yield self.env.timeout(random.uniform(3, 8)) triage_complete = self.env.now # Wait for doctor (priority queue) with self.doctors.request(priority=priority) as req: yield req wait_for_doctor = self.env.now - triage_complete self.stats['wait_times'].append({ 'patient': patient_id, 'severity': severity, 'wait': wait_for_doctor }) # Treatment time varies by severity treatment_times = { 'critical': (30, 60), 'urgent': (20, 45), 'standard': (15, 30), 'minor': (10, 20) } min_t, max_t = treatment_times.get(severity, (15, 30)) yield self.env.timeout(random.uniform(min_t, max_t)) # Some patients need admission admission_rates = {'critical': 0.8, 'urgent': 0.5, 'standard': 0.2, 'minor': 0.05} if random.random() < admission_rates.get(severity, 0.2): with self.beds.request() as req: yield req yield self.env.timeout(random.uniform(60, 240)) # Ward stay departure = self.env.now self.stats['length_of_stay'].append(departure - arrival) self.stats['patients'].append({ 'id': patient_id, 'severity': severity, 'arrival': arrival, 'departure': departure, 'los': departure - arrival }) def patient_arrivals(env, ed, arrival_rate): patient_id = 0 severity_probs = [0.05, 0.15, 0.40, 0.40] # critical, urgent, standard, minor severities = ['critical', 'urgent', 'standard', 'minor'] while True: yield env.timeout(random.expovariate(arrival_rate)) severity = random.choices(severities, weights=severity_probs)[0] env.process(ed.patient_pathway(patient_id, severity)) patient_id += 1 # Run simulation env = simpy.Environment() ed = EmergencyDepartment(env, { 'triage_nurses': 2, 'doctors': 3, 'beds': 20 }) env.process(patient_arrivals(env, ed, arrival_rate=1/10)) # ~6 per hour env.run(until=480) # 8-hour shift </code></pre></div> <h2 id="ward-model">Ward Model</h2> <div class="code-block"><pre><code>class HospitalWard: def __init__(self, env, name, beds, nurses_per_shift): self.env = env self.name = name self.beds = simpy.Resource(env, capacity=beds) self.nurses = simpy.Resource(env, capacity=nurses_per_shift) self.patients_discharged = 0 def admit_patient(self, patient_id, expected_los): """Admit patient, occupy bed for length of stay.""" with self.beds.request() as bed: yield bed print(f"Patient {patient_id} admitted to {self.name} at {self.env.now}") # Daily care rounds while self.env.now < expected_los: with self.nurses.request() as nurse: yield nurse yield self.env.timeout(random.uniform(10, 30)) # Care time yield self.env.timeout(random.uniform(60, 120)) # Time between rounds print(f"Patient {patient_id} discharged from {self.name} at {self.env.now}") self.patients_discharged += 1 </code></pre></div> <h2 id="operating-theatre">Operating Theatre</h2> <div class="code-block"><pre><code>class OperatingTheatre: def __init__(self, env, num_theatres): self.env = env self.theatres = simpy.Resource(env, capacity=num_theatres) self.surgeons = simpy.Resource(env, capacity=num_theatres) self.anaesthetists = simpy.Resource(env, capacity=num_theatres) self.surgeries_completed = 0 def surgery(self, patient_id, surgery_type): """Perform surgery requiring theatre, surgeon, and anaesthetist.""" surgery_times = { 'minor': (30, 60), 'major': (120, 240), 'emergency': (60, 180) } min_t, max_t = surgery_times.get(surgery_type, (60, 120)) # Need all three resources with self.theatres.request() as theatre: yield theatre with self.surgeons.request() as surgeon: yield surgeon with self.anaesthetists.request() as anaes: yield anaes # Pre-op yield self.env.timeout(15) # Surgery yield self.env.timeout(random.uniform(min_t, max_t)) # Recovery (still in theatre) yield self.env.timeout(30) self.surgeries_completed += 1 print(f"Surgery for patient {patient_id} completed at {self.env.now}") </code></pre></div> <h2 id="clinic-appointments">Clinic Appointments</h2> <div class="code-block"><pre><code>class OutpatientClinic: def __init__(self, env, num_consultants, appointment_slots_per_hour): self.env = env self.consultants = simpy.Resource(env, capacity=num_consultants) self.scheduled_appointments = simpy.Store(env) self.patients_seen = 0 self.no_shows = 0 def schedule_appointment(self, patient_id, appointment_time): """Schedule an appointment.""" yield self.scheduled_appointments.put({ 'patient_id': patient_id, 'time': appointment_time }) def run_clinic(self, start_time, end_time): """Run clinic for a session.""" yield self.env.timeout(start_time - self.env.now) while self.env.now < end_time: try: appt = yield self.scheduled_appointments.get() # No-show probability if random.random() < 0.1: self.no_shows += 1 continue with self.consultants.request() as req: yield req yield self.env.timeout(random.uniform(10, 25)) self.patients_seen += 1 except simpy.Interrupt: break </code></pre></div> <h2 id="ambulance-and-ae-integration">Ambulance and A&E Integration</h2> <div class="code-block"><pre><code>class AmbulanceService: def __init__(self, env, num_ambulances, hospital_ed): self.env = env self.ambulances = simpy.Resource(env, capacity=num_ambulances) self.hospital_ed = hospital_ed self.calls_responded = 0 def respond_to_call(self, call_id, location_distance): with self.ambulances.request() as req: yield req # Travel to scene travel_time = location_distance / 30 # 30 km/h average yield self.env.timeout(travel_time) # On-scene time yield self.env.timeout(random.uniform(10, 30)) # Travel to hospital yield self.env.timeout(travel_time) # Handover to ED severity = random.choice(['critical', 'urgent', 'standard']) self.env.process( self.hospital_ed.patient_pathway(f"amb_{call_id}", severity) ) # Turnaround time yield self.env.timeout(15) self.calls_responded += 1 </code></pre></div> <h2 id="complete-hospital-simulation">Complete Hospital Simulation</h2> <div class="code-block"><pre><code>import simpy import random import pandas as pd class Hospital: def __init__(self, env, config): self.env = env self.config = config # Resources self.ed_doctors = simpy.PriorityResource(env, config['ed_doctors']) self.ed_nurses = simpy.Resource(env, config['ed_nurses']) self.ed_beds = simpy.Resource(env, config['ed_beds']) self.ward_beds = simpy.Resource(env, config['ward_beds']) # Statistics self.patient_records = [] def ed_patient(self, patient_id, severity, arrival_time): record = { 'id': patient_id, 'severity': severity, 'arrival': arrival_time } # Triage with self.ed_nurses.request() as req: yield req yield self.env.timeout(random.uniform(5, 10)) record['triage_complete'] = self.env.now # Doctor priority = {'critical': 1, 'urgent': 2, 'standard': 3, 'minor': 4}[severity] with self.ed_doctors.request(priority=priority) as req: yield req treatment = random.uniform(15, 60) yield self.env.timeout(treatment) record['treatment_complete'] = self.env.now # Admission decision admission_prob = {'critical': 0.7, 'urgent': 0.4, 'standard': 0.15, 'minor': 0.05} if random.random() < admission_prob[severity]: with self.ward_beds.request() as req: yield req los = random.uniform(24*60, 72*60) # 1-3 days in minutes yield self.env.timeout(los) record['admitted'] = True record['ward_discharge'] = self.env.now else: record['admitted'] = False record['departure'] = self.env.now self.patient_records.append(record) def arrivals(self): patient_id = 0 severities = ['critical', 'urgent', 'standard', 'minor'] probs = [0.05, 0.20, 0.35, 0.40] while True: # Time-varying arrival rate hour = (self.env.now / 60) % 24 if 8 <= hour <= 20: rate = 1/8 # Busier during day else: rate = 1/15 # Quieter at night yield self.env.timeout(random.expovariate(rate)) severity = random.choices(severities, weights=probs)[0] self.env.process(self.ed_patient(patient_id, severity, self.env.now)) patient_id += 1 def run(self, duration): self.env.process(self.arrivals()) self.env.run(until=duration) def analyse(self): df = pd.DataFrame(self.patient_records) df['wait_for_doctor'] = df['treatment_complete'] - df['triage_complete'] df['ed_los'] = df['treatment_complete'] - df['arrival'] print("\n=== Hospital Simulation Results ===") print(f"Total patients: {len(df)}") print(f"Admissions: {df['admitted'].sum()}") print("\nWait for doctor (minutes):") print(df.groupby('severity')['wait_for_doctor'].describe()) return df # Run random.seed(42) env = simpy.Environment() hospital = Hospital(env, { 'ed_doctors': 3, 'ed_nurses': 4, 'ed_beds': 15, 'ward_beds': 50 }) hospital.run(duration=24*60) # 24 hours results = hospital.analyse() </code></pre></div> <h2 id="summary">Summary</h2> Hospital simulation models: - Patient pathways through departments - Resource constraints (staff, beds, equipment) - Priority-based treatment (triage) - Admission and discharge dynamics - Time-varying demand patterns Simulate to save lives. Optimise to save more. <h2 id="next-steps">Next Steps</h2> <ul> <li><a href="/blog_posts/simpy-call-center-simulation.html">Call Centre Simulation</a></li> <li><a href="/blog_posts/simpy-priorityresource-explained.html">SimPy PriorityResource</a></li> <li><a href="/blog_posts/simpy-queue-model.html">Queue Modelling</a></li> </ul>

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