Simulation in Waiting Lines

Simulation Advantages and Disadvantages

• Simulation can be used when an analytical solution is possible or preferable, especially in cases where closed-form queueing models are available.
• Four disadvantages of simulation can be offset by:
  • Using simulation software with pre-built models that require only input data.
  • Utilizing output analysis capabilities within simulation software for thorough analysis.
  • Taking advantage of advances in hardware and software that enable faster simulation.
  • Recognizing that closed-form models are not able to analyze complex systems that are often encountered in practice.

Areas of Application

• The applications of simulation are vast and can be explored through the Winter Simulation Conference (WSC) and its tutorials.
• Policy makers and analysts often identify problems before understanding their nature, and simulation can help answer questions and set objectives.

Simulation Process

• Setting objectives and overall project plan:
  • Determine if simulation is the appropriate methodology for the problem.
  • Define the alternative systems to be considered and a method for evaluating their effectiveness.
  • Plan the study, including the number of people involved, cost, and timeline.
• Model conceptualization:
  • Building a model of a system is both an art and a science.
  • Start with a simple model and build towards complexity.
  • Involve the model user in the conceptualization process.
• Experimental design:
  • Determine the alternatives to be simulated.
  • Decide on the length of the initialization period, simulation runs, and number of replications.
• Production runs and analysis:
  • Use simulation runs to estimate measures of performance for system designs.
  • Analyze the results to determine if additional runs are needed.
• Documentation and reporting:
  • Document the program and progress to facilitate understanding and modification.
  • Evaluate the distribution of results using the standard normal distribution.

Normal Distribution

• The normal distribution is important because it is the most commonly used distribution in data analysis.
• The sum of n independent normal variates is a normal variate.
• The sum of a large number of independent observations from any distribution has a normal distribution.

Example: Normal Distribution

• The time required to load an ocean-going vessel is distributed as N(12, 4).
• The probability that the vessel is loaded in less than 10 hours can be calculated using the standard normal distribution.

Poisson Process

• A Poisson process is a counting process that satisfies certain conditions:
  • Arrivals occur one at a time.
  • The process has stationary increments.
  • The process has independent increments.
• Properties of the Poisson process:
  • Equal mean and variance.
  • Stationary increment: The number of arrivals in time s to t is also Poisson distributed with mean λ(t-s).

Example: Poisson Process

• The time to pass through a queue to begin self-service at a cafeteria is found to be N(15, 9).
• The Poisson process is used to model arrivals in various contexts, such as arrival of jobs, e-mails to a server, boats to a dock, and calls to a call center.