Bank Queue Simulation with SimPy: The Classic Example

Published on February 16, 2026

The bank queue is the "Hello World" of simulation. It's simple enough to understand, complex enough to be interesting, and applicable to dozens of other scenarios. <h2 id="the-basic-bank-model">The Basic Bank Model</h2> <div class="code-block"><pre><code>import simpy import random def customer(env, name, tellers, stats): """Customer arrives, waits for teller, completes transaction.""" arrival = env.now with tellers.request() as req: yield req wait = env.now - arrival stats['waits'].append(wait) # Transaction time transaction = random.expovariate(1/5) yield env.timeout(transaction) stats['transactions'].append(transaction) stats['departures'].append(env.now) def arrivals(env, tellers, stats, arrival_rate): i = 0 while True: yield env.timeout(random.expovariate(arrival_rate)) env.process(customer(env, f"Customer {i}", tellers, stats)) i += 1 # Run simulation env = simpy.Environment() tellers = simpy.Resource(env, capacity=3) stats = {'waits': [], 'transactions': [], 'departures': []} env.process(arrivals(env, tellers, stats, arrival_rate=1/2)) env.run(until=480) # 8 hours print(f"Customers served: {len(stats['waits'])}") print(f"Average wait: {sum(stats['waits'])/len(stats['waits']):.2f} minutes") </code></pre></div> <h2 id="multiple-transaction-types">Multiple Transaction Types</h2> Different services take different times: <div class="code-block"><pre><code>class Bank: def __init__(self, env, num_tellers): self.env = env self.tellers = simpy.Resource(env, capacity=num_tellers) self.stats = [] def customer(self, customer_id, transaction_type): arrival = self.env.now transaction_times = { 'deposit': (2, 5), 'withdrawal': (1, 3), 'loan_inquiry': (10, 20), 'account_opening': (15, 30) } with self.tellers.request() as req: yield req wait = self.env.now - arrival min_t, max_t = transaction_times.get(transaction_type, (3, 7)) service = random.uniform(min_t, max_t) yield self.env.timeout(service) self.stats.append({ 'customer': customer_id, 'type': transaction_type, 'wait': wait, 'service': service }) def arrivals(env, bank): customer_id = 0 types = ['deposit', 'withdrawal', 'loan_inquiry', 'account_opening'] probs = [0.4, 0.35, 0.15, 0.1] while True: yield env.timeout(random.expovariate(1/3)) transaction_type = random.choices(types, weights=probs)[0] env.process(bank.customer(customer_id, transaction_type)) customer_id += 1 </code></pre></div> <h2 id="express-lane">Express Lane</h2> Separate queue for quick transactions: <div class="code-block"><pre><code>class BankWithExpressLane: def __init__(self, env, regular_tellers, express_tellers, express_threshold): self.env = env self.regular = simpy.Resource(env, capacity=regular_tellers) self.express = simpy.Resource(env, capacity=express_tellers) self.express_threshold = express_threshold # Max service time for express def customer(self, customer_id, expected_service): arrival = self.env.now # Choose lane if expected_service <= self.express_threshold: teller = self.express lane = "express" else: teller = self.regular lane = "regular" with teller.request() as req: yield req yield self.env.timeout(expected_service) print(f"Customer {customer_id} served at {lane} lane, waited {self.env.now - arrival - expected_service:.1f}") </code></pre></div> <h2 id="balking-and-reneging">Balking and Reneging</h2> Customers who leave: <div class="code-block"><pre><code>def impatient_customer(env, name, tellers, max_queue, patience): """Customer may balk or renege.""" arrival = env.now # Balking: refuse to join long queue if len(tellers.queue) >= max_queue: print(f"{name} balked at {arrival:.1f} (queue too long)") return "balked" with tellers.request() as req: # Reneging: leave after waiting too long result = yield req | env.timeout(patience) if req in result: # Got served yield env.timeout(random.expovariate(1/5)) return "served" else: # Ran out of patience print(f"{name} reneged at {env.now:.1f} (waited too long)") return "reneged" </code></pre></div> <h2 id="vip-customers">VIP Customers</h2> Priority service for special customers: <div class="code-block"><pre><code>def bank_with_vip(env, tellers): def vip_customer(customer_id): with tellers.request(priority=1) as req: # High priority yield req yield env.timeout(random.uniform(3, 8)) print(f"VIP {customer_id} served at {env.now:.1f}") def regular_customer(customer_id): with tellers.request(priority=5) as req: # Lower priority yield req yield env.timeout(random.uniform(2, 6)) print(f"Regular {customer_id} served at {env.now:.1f}") # VIP customers jump the queue tellers = simpy.PriorityResource(env, capacity=3) </code></pre></div> <h2 id="peak-hours-modelling">Peak Hours Modelling</h2> <div class="code-block"><pre><code>def time_varying_arrivals(env, bank): """Arrival rate varies by time of day.""" customer_id = 0 while True: hour = (env.now / 60) % 24 # Peak hours if 12 <= hour <= 14: # Lunch rush rate = 1/1 # 1 per minute elif 9 <= hour <= 11 or 15 <= hour <= 17: rate = 1/2 else: rate = 1/5 yield env.timeout(random.expovariate(rate)) env.process(bank.customer(customer_id)) customer_id += 1 </code></pre></div> <h2 id="queue-display-board">Queue Display Board</h2> Track and display queue status: <div class="code-block"><pre><code>class QueueDisplay: def __init__(self, env, tellers): self.env = env self.tellers = tellers self.log = [] def monitor(self, interval=1): while True: self.log.append({ 'time': self.env.now, 'waiting': len(self.tellers.queue), 'serving': self.tellers.count, 'available': self.tellers.capacity - self.tellers.count }) # Estimate wait time if self.tellers.count == self.tellers.capacity and self.tellers.queue: estimated_wait = len(self.tellers.queue) * 5 / self.tellers.capacity print(f"[{self.env.now:.0f}] Queue: {len(self.tellers.queue)}, Est. wait: {estimated_wait:.0f} min") yield self.env.timeout(interval) </code></pre></div> <h2 id="complete-bank-simulation">Complete Bank Simulation</h2> <div class="code-block"><pre><code>import simpy import random import numpy as np import pandas as pd class BankSimulation: def __init__(self, env, config): self.env = env self.config = config self.tellers = simpy.Resource(env, capacity=config['tellers']) self.customer_records = [] def customer(self, customer_id, transaction_type): arrival = self.env.now record = { 'id': customer_id, 'type': transaction_type, 'arrival': arrival } # Balking check if len(self.tellers.queue) > self.config['max_queue']: record['outcome'] = 'balked' self.customer_records.append(record) return patience = random.expovariate(1/self.config['mean_patience']) with self.tellers.request() as req: result = yield req | self.env.timeout(patience) if req in result: record['wait'] = self.env.now - arrival # Service time by type service_params = self.config['service_times'][transaction_type] service = random.uniform(*service_params) yield self.env.timeout(service) record['service'] = service record['outcome'] = 'served' record['departure'] = self.env.now else: record['wait'] = patience record['outcome'] = 'reneged' self.customer_records.append(record) def arrivals(self): customer_id = 0 types = list(self.config['service_times'].keys()) probs = self.config['type_probabilities'] while True: # Time-varying rate hour = (self.env.now / 60) % 24 rate = self.get_arrival_rate(hour) yield self.env.timeout(random.expovariate(rate)) transaction_type = random.choices(types, weights=probs)[0] self.env.process(self.customer(customer_id, transaction_type)) customer_id += 1 def get_arrival_rate(self, hour): if 12 <= hour <= 14: return self.config['peak_rate'] elif 9 <= hour <= 17: return self.config['normal_rate'] else: return self.config['off_peak_rate'] def monitor(self, interval=5): while True: yield self.env.timeout(interval) def run(self, duration): self.env.process(self.arrivals()) self.env.process(self.monitor()) self.env.run(until=duration) def report(self): df = pd.DataFrame(self.customer_records) served = df[df['outcome'] == 'served'] balked = df[df['outcome'] == 'balked'] reneged = df[df['outcome'] == 'reneged'] print("\n=== Bank Simulation Report ===") print(f"Total arrivals: {len(df)}") print(f"Served: {len(served)} ({len(served)/len(df):.1%})") print(f"Balked: {len(balked)} ({len(balked)/len(df):.1%})") print(f"Reneged: {len(reneged)} ({len(reneged)/len(df):.1%})") if len(served) > 0: print(f"\nWait time (served customers):") print(f" Mean: {served['wait'].mean():.2f} min") print(f" Max: {served['wait'].max():.2f} min") print(f" 90th pct: {served['wait'].quantile(0.9):.2f} min") print(f"\nBy transaction type:") print(served.groupby('type')['wait'].mean()) return df # Configuration config = { 'tellers': 4, 'max_queue': 10, 'mean_patience': 8, 'peak_rate': 1.0, 'normal_rate': 0.5, 'off_peak_rate': 0.2, 'service_times': { 'deposit': (2, 4), 'withdrawal': (1, 3), 'inquiry': (3, 8), 'complex': (10, 20) }, 'type_probabilities': [0.35, 0.35, 0.2, 0.1] } # Run random.seed(42) env = simpy.Environment() bank = BankSimulation(env, config) bank.run(duration=480) # 8 hours results = bank.report() </code></pre></div> <h2 id="summary">Summary</h2> The bank queue teaches: - Basic queue dynamics - Multiple service types - Customer behaviour (balking, reneging) - Priority handling - Time-varying demand Master the bank. Model anything. <h2 id="next-steps">Next Steps</h2> <ul> <li><a href="/blog_posts/simpy-queue-model.html">Queue Modelling</a></li> <li><a href="/blog_posts/simpy-call-center-simulation.html">Call Centre Simulation</a></li> <li><a href="/blog_posts/simpy-restaurant-simulation.html">Restaurant Simulation</a></li> </ul>

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