Simulation with Simpy

Summary

In this post, I'll be using the Simpy Python framework to create a simulation model.  I'll cover the base case here of generating requests to a finite set of resources.  I'll compare the simulation results to the expected/theoretical results for an Erlang B model. 

Architecture

The diagram below depicts the base simulation model.  A Request Generator sends a stream of requests at an interval corresponding to a Poisson process.  An intermediary process, the Regulator, makes a decision based on resource availability of where to route the request.  If all resources are busy, the request is blocked.  Otherwise, the resource assumes a position in the queue and is subsequently serviced by a worker for a period of time representing a Normal distribution on the average handle time.

Code Snippet

def scenario_one():
    rand: Random = Random()
    rand.seed(RANDOM_SEED)
    env: Environment = Environment()
    distributor: Distributor = Distributor(rand, env, POSITIONS, 0, HANDLE_TIME_MEAN, 0, QUEUE_COST, HANDLE_COST)
    regulator: Regulator = Regulator(env, distributor)
    requestGenerator: RequestGenerator = RequestGenerator(rand, env, regulator, 0, 0, STEADY_RATE)
    env.run(until=TOTAL_DURATION)
    print(f'***  Scenario 1: ErlangB Sanity Check.  Partial simulation: no workers, no surge, no deflection ***')
    print(f'Total Requests: {requestGenerator.total_requests}')
    print(f'Total Queued Requests: {distributor.total_queued}')
    print(f'Total Serviced Requests: {distributor.total_serviced}')
    print(f'Total Deflected Requests: {regulator.total_deflected}')
    print(f'Total Blocked Requests: {regulator.total_blocked}')
    print(f'Max Queue Depth: {distributor.max_positions_depth}')
    print(f'Max Resources Consumed: {distributor.max_resources}')
    print(f'Probability of Blockage: {regulator.total_blocked/requestGenerator.total_requests}')
    print(f'')

Results

Below are the results with 20 requests/sec rate and 15 minute average handle time.  The Erlang B blocking calculation for those parameters = 0.666694

***  Scenario 1: ErlangB Sanity Check.  Partial simulation: no workers, no surge, no deflection ***
Total Requests: 864377
Total Queued Requests: 288000
Total Serviced Requests: 0
Total Deflected Requests: 0
Total Blocked Requests: 576376
Max Queue Depth: 6000
Max Resources Consumed: 6000
Probability of Blockage: 0.666810893857657

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