Mathematical Modeling Problems and Solutions

Discrete Two-Dimensional Random Variable

Example output

1. Probability matrices

2. Confidence intervals and random variables histograms

Queueing System Simulation

Example 1

• Total servers: 2
• Total customers: 10000
• Arrival time mean: 0.5
• Arrival time order: 1
• Service time mean: 0.35
• Service time order: 1
• Queue delay time mean: 1
• Queue delay time order: 1
• Max customer queue size: 3

1. Simulation output

2. Simulation probabilities

3. Theoretical probabilities

4. Stationary mode set-up

Example 2

• Total servers: 5
• Total customers: 8000
• Arrival time mean: 1
• Arrival time order: 1
• Service time mean: 1
• Service time order: 1
• Queue delay time mean: 1
• Queue delay time order: 1
• Max customer queue size: 5

1. Simulation output

2. Simulation probabilities

3. Theoretical probabilities

4. Stationary mode set-up

Example 3

• Total servers: 4
• Total customers: 11000
• Arrival time mean: 7.5
• Arrival time order: 3
• Service time mean: 17
• Service time order: 2
• Queue delay time: unlimited
• Max customer queue size: 10

1. Simulation output

2. Simulation probabilities

3. Stationary mode set-up

Example 4

• Total servers: 3
• Total customers: 10000
• Arrival time mean: 0.5
• Arrival time order: 1
• Service time mean: 0.35
• Service time order: 1
• Queue delay time mean: 1
• Queue delay time order: 1
• Max customer queue size: 0

1. Simulation output

2. Simulation probabilities

3. Theoretical probabilities

4. Stationary mode set-up

Example 5

• Total servers: 1
• Total customers: 14000
• Arrival time mean: 10
• Arrival time order: 1
• Service time mean: 8
• Service time order: 3
• Queue delay time: unlimited
• Customer queue size: unlimited

1. Simulation output