Advanced Patterns and Techniques

Growth Modeling

Growth modeling helps predict long-term capacity needs based on business trajectories:

1. Linear Growth: Constant increase over time

   y(t) = a * t + b
   

2. Exponential Growth: Growth proportional to current size

   y(t) = a * e^(b*t)
   

3. Logistic Growth: S-shaped curve with saturation

   y(t) = L / (1 + e^(-k*(t-t0)))
   

4. Gompertz Growth: Asymmetric S-shaped growth

   y(t) = L * e^(-b*e^(-c*t))
   

Scenario-Based Forecasting

Scenario-based forecasting considers multiple possible futures:

1. Base Case: Expected growth under normal conditions
2. Best Case: Optimistic scenario (e.g., viral adoption)
3. Worst Case: Conservative scenario (e.g., market downturn)
4. Stress Case: Extreme but plausible scenario (e.g., 10x traffic spike)

Example Scenario Planning Table:

Resource Modeling

Resource modeling translates demand forecasts into specific infrastructure requirements.

Workload Characterization

Before modeling resources, characterize your workload:

1. Request Types: Different operations with varying resource needs
2. Request Distribution: How requests are distributed over time
3. Resource Consumption: CPU, memory, disk, network per request type
4. Dependencies: How services interact and depend on each other

Example Workload Profile:

{
  "service": "payment-processing",
  "request_types": {
    "create_payment": {
      "cpu_ms": 120,
      "memory_mb": 64,
      "disk_io_kb": 5,
      "network_io_kb": 2,
      "percentage": 60
    },
    "verify_payment": {
      "cpu_ms": 80,
      "memory_mb": 48,
      "disk_io_kb": 2,
      "network_io_kb": 1,
      "percentage": 30
    },
    "refund_payment": {
      "cpu_ms": 150,
      "memory_mb": 72,
      "disk_io_kb": 8,
      "network_io_kb": 2,
      "percentage": 10
    }
  },
  "peak_to_average_ratio": 2.5,
  "dependencies": [
    {"service": "user-service", "calls_per_request": 0.8},
    {"service": "inventory-service", "calls_per_request": 0.5},
    {"service": "notification-service", "calls_per_request": 1.0}
  ]
}

Resource Estimation Models

Several approaches can be used to estimate resource requirements:

1. Linear Scaling: Resources scale linearly with load

   Resources = Base resources + (Load * Scaling factor)
   

2. Queueing Theory: Models systems as networks of queues

   Utilization = Arrival rate / (Number of servers * Service rate)
   Average queue length = Utilization / (1 - Utilization)
   

3. Simulation: Mimics system behavior under various conditions

   def simulate_system(arrival_rate, service_rate, num_servers, duration):
       # Simplified simulation example
       servers = [0] * num_servers
       queue = []
       total_wait = 0
       served = 0
   
       for t in range(duration):
           # New arrivals
           new_arrivals = np.random.poisson(arrival_rate)
           queue.extend([t] * new_arrivals)
   
           # Service completions
           for i in range(num_servers):
               if servers[i] <= t and queue:
                   arrival_time = queue.pop(0)
                   wait_time = t - arrival_time
                   total_wait += wait_time
                   servers[i] = t + np.random.exponential(1/service_rate)
                   served += 1
   
       avg_wait = total_wait / served if served > 0 else 0
       return avg_wait, len(queue)
   

4. Load Testing: Empirical measurement of resource needs

   def analyze_load_test(results):
       cpu_per_rps = []
       memory_per_rps = []
   
       for test in results:
           cpu_per_rps.append(test['cpu_utilization'] / test['requests_per_second'])
           memory_per_rps.append(test['memory_utilization'] / test['requests_per_second'])
   
       return {
           'avg_cpu_per_rps': sum(cpu_per_rps) / len(cpu_per_rps),
           'avg_memory_per_rps': sum(memory_per_rps) / len(memory_per_rps)
       }
   

Capacity Models

Capacity models combine forecasts with resource estimates:

1. Static Capacity Model: Fixed resources based on peak demand

   def static_capacity_model(peak_rps, resources_per_rps, headroom_factor=1.5):
       return {
           'cpu': peak_rps * resources_per_rps['cpu'] * headroom_factor,
           'memory': peak_rps * resources_per_rps['memory'] * headroom_factor,
           'disk': peak_rps * resources_per_rps['disk'] * headroom_factor,
           'network': peak_rps * resources_per_rps['network'] * headroom_factor
       }
   

2. Dynamic Capacity Model: Adjusts resources based on actual demand

   def dynamic_capacity_model(current_rps, forecast_rps, resources_per_rps, 
                             min_headroom=1.2, max_headroom=2.0, 
                             scale_up_threshold=0.7, scale_down_threshold=0.3):
       # Calculate headroom based on forecast confidence
       forecast_confidence = calculate_forecast_confidence(current_rps, forecast_rps)
       headroom = min_headroom + (max_headroom - min_headroom) * (1 - forecast_confidence)
   
       # Calculate target capacity
       target_capacity = forecast_rps * resources_per_rps * headroom
   
       # Determine if scaling is needed
       current_utilization = current_rps / (target_capacity / resources_per_rps)
   
       if current_utilization > scale_up_threshold:
           action = "scale_up"
       elif current_utilization < scale_down_threshold:
           action = "scale_down"
       else:
           action = "maintain"
   
       return {
           'target_capacity': target_capacity,
           'action': action,
           'headroom': headroom
       }