arrival-and-service.ipynb

arrival-and-service.ipynb

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        "# Arrival and Service Rates in Queues\n",
        "In the context of queueing systems, the exponential distribution's memoryless property serves as the foundation for stochastic modeling. The interplay between arrival rate a and service rate b governs the system's equilibrium and transient states. When the arrival rate exceeds the service rate, the system becomes unstable, leading to infinite queues, while a higher service rate ensures stability and efficient performance. This forms the theoretical backbone for the analysis of networks and various service mechanisms."
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        "# Cumulative Distribution Function\n",
        "\n",
        "In probability theory, the cumulative distribution function (CDF) of a real-valued random variable $X$ is the function given by:\n",
        "\n",
        "$$ F(x) = P(X \\leq x) $$\n",
        "\n",
        "where the right-hand side represents the probability that the random variable $X$ takes on a value less than or equal to $x$.\n",
        "\n",
        "The CDF has the following properties:\n",
        "\n",
        "1. **Non-decreasing**: The CDF is a non-decreasing function of $x$:\n",
        "\n",
        "   $ F(x_1) \\leq F(x_2) \\text{ if } x_1 \\leq x_2 $\n",
        "\n",
        "2. **Normalized**: The CDF starts at 0 and goes up to 1:\n",
        "\n",
        "   $ \\lim_{x \\to -\\infty} F(x) = 0 $\n",
        "   $ \\lim_{x \\to \\infty} F(x) = 1 $\n",
        "\n",
        "3. **Right-Continuous**: For every $x$, the function $F(x)$ is right-continuous:\n",
        "\n",
        "   $ \\lim_{y \\to x^+} F(y) = F(x) $\n",
        "\n",
        "The CDF is related to the probability density function (PDF), denoted by $f(x)$, in the case of continuous random variables by:\n",
        "\n",
        "$$ f(x) = \\frac{d}{dx} F(x) $$\n",
        "\n",
        "That is, the PDF is the derivative of the CDF. The PDF gives the relative likelihood of the random variable taking on a particular value, while the CDF gives the cumulative probability up to a particular value.\n",
        "\n",
        "# Exponential Decay\n",
        "The exponential distribution is a continuous probability distribution used to model the time intervals between successive, independent events that occur at a constant average rate. Characterized by a single parameter, $ \\lambda $ (the rate), its probability density function is given by\n",
        "\n",
        "$$ f(t; \\lambda) = \\lambda e^{-\\lambda t} \\, \\text{for} \\, t \\geq 0 $$\n",
        "\n",
        "The distribution is memoryless, meaning the future event behavior is independent of past events, and its mean is $ \\frac{1}{\\lambda} $. Commonly, it's employed in reliability analysis and survival studies, representing situations like the time between arrivals of customers or the life span of a machine component.\n",
        "\n",
        "## Example: Customer Arrivals at a Coffee Shop\n",
        "\n",
        "Suppose you own a coffee shop, and on average, a customer enters your coffee shop every 10 minutes. We can model the time between customer arrivals using an exponential distribution. In this context:\n",
        "\n",
        "- The **rate parameter** $ \\lambda $ would be $ \\frac{1}{10} $ or 0.1, as on average there's one customer every 10 minutes.\n",
        "- The **expected time** between arrivals (or the mean of the distribution) is $ \\frac{1}{\\lambda} = 10 $ minutes.\n",
        "\n",
        "Now, let's address a few questions using this model:\n",
        "\n",
        "1. **What's the probability that the next customer will arrive within 5 minutes?**\n",
        "   \n",
        "   To answer this, we'll use the CDF:\n",
        "\n",
        "   $ F(5; 0.1) = 1 - e^{-0.1 \\times 5} $\n",
        "   \n",
        "   This computes to approximately 0.39, or 39%.\n",
        "\n",
        "2. **What's the probability that you'll have to wait more than 15 minutes for the next customer?**\n",
        "\n",
        "   This is 1 minus the probability that the next customer arrives within 15 minutes:\n",
        "\n",
        "   $ 1 - F(15; 0.1) = e^{-0.1 \\times 15} $\n",
        "   \n",
        "   This computes to approximately 0.22, or 22%.\n",
        "\n",
        "3. **Memoryless Property in Action**: If 10 minutes have passed without a customer, what's the probability the next customer will arrive within the next 5 minutes?\n",
        "\n",
        "   Using the memoryless property:\n",
        "\n",
        "   $ P(X > 10 + 5 | X > 10) = P(X > 5) $\n",
        "   \n",
        "   Which, as we computed above, is 39%. This means even after waiting for 10 minutes without a customer, the probability for the next customer to arrive in the subsequent 5 minutes remains the same.\n",
        "\n",
        "This example highlights how the exponential distribution can provide insights into real-world scenarios. It's especially useful for understanding \"average rates\" and the variability around them.\n",
        "\n",
        "\n",
        "## Exponential Decay Simulation\n",
        "Simulates the random decay of atoms based on the exponential distribution, a continuous probability distribution often used to model the time between independent events that happen at a constant average rate.\n",
        "\n",
        "An exponential Distribution describes the time intervals between successive, independent events that occur at a constant average rate. Its probability density function is given by:\n",
        "\n",
        "$$\n",
        "f(t; \\lambda) = \\lambda e^{-\\lambda t}\n",
        "$$\n",
        "\n",
        "where,\n",
        "\n",
        "+ $\\lambda$ is the Decay Constant. A higher $ \\lambda $ means atoms decay faster, and a lower $ \\lambda $ means they decay slower.\n",
        "+ $\\frac{1}{\\lambda}$ is the average number of events in a unit time interval.\n",
        "+ $t$ is time.\n",
        "\n",
        "For each atom, the simulation generates a random time drawn from the exponential distribution representing when that atom will decay. This is repeated for the specified number of atoms.\n",
        "\n"
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        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "def simulate_decay(num_atoms, decay_constant):\n",
        "    \"\"\"\n",
        "    Simulate the decay of atoms over time.\n",
        "\n",
        "    Parameters:\n",
        "    - num_atoms: Initial number of atoms.\n",
        "    - decay_constant: Decay constant (lambda) for the exponential distribution.\n",
        "\n",
        "    Returns:\n",
        "    - times: List of decay times for each atom.\n",
        "    \"\"\"\n",
        "    # Generate random decay times for each atom based on the exponential distribution\n",
        "    times = np.random.exponential(scale=1/decay_constant, size=num_atoms)\n",
        "    return sorted(times)\n",
        "\n",
        "def visualize_decay(times):\n",
        "    \"\"\"\n",
        "    Visualize the decay of atoms over time.\n",
        "\n",
        "    Parameters:\n",
        "    - times: List of decay times for each atom.\n",
        "    \"\"\"\n",
        "    # Generate histogram of decay times\n",
        "    bins = np.linspace(0, max(times), 100)\n",
        "    plt.hist(times, bins=bins, cumulative=-1, label='Decayed Atoms', histtype='step')\n",
        "\n",
        "    plt.xlabel('Time')\n",
        "    plt.ylabel('Number of Atoms Remaining')\n",
        "    plt.title('Decay of Atoms Over Time')\n",
        "    plt.legend()\n",
        "    plt.show()\n",
        "\n",
        "# Parameters\n",
        "num_atoms = 1000\n",
        "decay_constant = 0.1  # This can be adjusted based on the specific atom/material\n",
        "\n",
        "# Simulate and visualize\n",
        "decay_times = simulate_decay(num_atoms, decay_constant)\n",
        "visualize_decay(decay_times)\n"
      ],
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              "<Figure size 640x480 with 1 Axes>"
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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## CDF of an Exponential Distribution: An Example\n",
        "\n",
        "Let's consider a common example where the time a person waits for an elevator, denoted by the random variable $X$, follows an exponential distribution.\n",
        "\n",
        "The CDF represents the probability that the person will wait at most $x$ units of time for the elevator.\n",
        "\n",
        "Given:\n",
        "$$ f(t; \\lambda) = \\lambda e^{-\\lambda t} \\, \\text{for} \\, t \\geq 0 $$\n",
        "\n",
        "We want to find the CDF, so we'll calculate:\n",
        "$$ F(x) = \\int_0^x \\lambda e^{-\\lambda t} \\,dt = 1 - e^{-\\lambda x} \\text{ for } x \\geq 0 $$\n",
        "\n",
        "So if you want to find the probability that the person waits at most 2 units of time for the elevator, you would calculate:\n",
        "\n",
        "$$ F(2) = 1 - e^{-0.5 \\times 2} \\approx 0.632 $$\n",
        "\n",
        "This means there is approximately a 63.2% chance that the person will wait 2 or fewer units of time for the elevator to arrive.\n",
        "\n",
        "# Arrival and Service Rates: Queue Behavior\n",
        "The parameters $a$ and $b$, represent the arrival and service rates in a queueing system and fundamentally govern its behavior. The ratio $ \\frac{a}{b} $ delineates the system's stability region, with $ a > b $ leading to an unstable regime, and $ a < b $ ensuring stable and efficient operation. This elegant relationship serves as a critical analytical tool in network performance and optimization.\n",
        "\n",
        "The $ A(t) $ distribution represents the cumulative distribution function (CDF) of the inter-arrival times. It gives the probability that the time between two consecutive arrivals to the queue is less than or equal to $ t $. In essence, it describes how frequently new entities arrive.\n",
        "\n",
        "$$ A(t) = P[\\text{time between arrivals} \\le t] $$\n",
        "\n",
        "In simpler terms, if you pick a random point in time and measure the time until the next arrival, $ A(t) $ tells you the likelihood that this time is no more than $ t $. This function helps in understanding the distribution and frequency of arrivals over time.\n",
        "\n",
        "$ B(x) $ represents the cumulative distribution function (CDF) of the service times. It denotes the probability that a randomly chosen service (like processing a customer or job) will be completed in \\( x \\) time or less.\n",
        "\n",
        "$$ B(x) = P[\\text{service time} \\le x] $$\n",
        "\n",
        "This is crucial for determining how quickly tasks or customers are processed in the system and for understanding the distribution of service durations. It helps in estimating queue lengths, waiting times, and the overall efficiency of the service mechanism.\n",
        "\n",
        "Both distributions are pivotal for understanding the system's dynamics. For instance, if entities arrive faster than they're serviced, we'd expect queues to grow. Contrarily, if the service rate outpaces the arrival rate, queues would shrink or remain minimal.\n",
        "\n",
        "## An Example Simulation\n",
        "\n",
        "This program uses exponential distributions to generate inter-arrival and service times. Then it calculates the empirical CDFs $A(t)$ and $B(x)$ and overlays plots the probability density functions (PDFs) of the two distributions. Adjusting the parameters (`lambda_` and `mu`) or even using different distributions will allow you to see how these impact the plots."
      ],
      "metadata": {
        "id": "XDKTA1QCv3KH"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 564
        },
        "id": "BNf1ECF_uN2b",
        "outputId": "a69e6d22-70cc-4571-d902-49262381e66c"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "def simulate_queue(lambda_arrival, lambda_service, total_time, num_customers=100):\n",
        "    service_end_time = 0\n",
        "    records = []\n",
        "    inter_arrival_times = np.random.exponential(1 / lambda_arrival, size=num_customers)\n",
        "    arrival_times = np.cumsum(inter_arrival_times)\n",
        "\n",
        "    for arrival_time in arrival_times:\n",
        "        if arrival_time > service_end_time:\n",
        "            service_start_time = arrival_time\n",
        "        else:\n",
        "            service_start_time = service_end_time\n",
        "\n",
        "        service_time = np.random.exponential(1 / lambda_service)\n",
        "        service_end_time = service_start_time + service_time\n",
        "\n",
        "        if service_end_time > total_time:\n",
        "            break\n",
        "\n",
        "        record = [arrival_time, service_start_time, service_end_time]\n",
        "        records.append(record)\n",
        "\n",
        "    return zip(*records)\n",
        "\n",
        "def plot_gantt_chart(arrival_times, service_start_times, service_end_times):\n",
        "    num_customers = len(arrival_times)\n",
        "    plt.figure(figsize=(10, 6))\n",
        "\n",
        "    for i, (arrival, start, end) in enumerate(zip(arrival_times, service_start_times, service_end_times)):\n",
        "        plt.barh(i, start - arrival, left=arrival, color='blue', edgecolor='black')\n",
        "        plt.barh(i, end - start, left=start, color='green', edgecolor='black')\n",
        "\n",
        "    plt.xlabel('Time')\n",
        "    plt.ylabel('Customer Number')\n",
        "    plt.title('Queue Simulation')\n",
        "    plt.yticks(np.arange(num_customers), labels=[str(i + 1) for i in range(num_customers)])\n",
        "    plt.legend(['Waiting Time', 'Service Time'])\n",
        "    plt.grid(True, linestyle='--', alpha=0.6)\n",
        "    plt.gca().invert_yaxis() # Invert y-axis to have customer 1 at the top\n",
        "    plt.show()\n",
        "\n",
        "# Parameters\n",
        "lambda_arrival = 1\n",
        "lambda_service = 1.2\n",
        "total_time = 30\n",
        "\n",
        "# Simulate queue and get times\n",
        "arrival_times, service_start_times, service_end_times = simulate_queue(lambda_arrival, lambda_service, total_time)\n",
        "\n",
        "# Plot Gantt chart\n",
        "plot_gantt_chart(arrival_times, service_start_times, service_end_times)\n"
      ]
    }
  ]
}