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# Exercise: Single Server Simulation

## Example 1:

In a single-server queueing system the time of the arrival and departure of the customers are given below. The simulation clock starts at 0 & ends at 12.

|                 |                                              |
| --------------- | -------------------------------------------- |
| Arrival times   | 0.4, 1.2, 2.2, 3.8, 4, 8.4, 9.8, 10.2, 11    |
| Departure times | 2.4, 3.1, 4.4, 4.9, 8.6, 9.6, 10, 10.5, 11.8 |

## Example 2:

In a single-server queueing system the time of the arrival and departure of the customers are given below. The simulation clock starts at 0 & ends at 10.

|                 |                                                          |
| --------------- | -------------------------------------------------------- |
| Arrival times   | 0.3, 1.2, 1.9, 3.1, 3.7, 4.5, 5.7, 6.1, 6.6, 7.3, 9, 9.2 |
| Departure times | 2.2, 3.3, 3.5, 4.7, 5.9, 6, 6.3, 6.8, 7, 8, 9.1, 9.6     |

## Example 3:

In a single-server queueing system the time of the arrival and departure of the customers are given below.

|                 |                                        |
| --------------- | -------------------------------------- |
| Arrival times   | 0.6, 1.2, 2.2, 3.7, 4, 9, 9.3, 10.1    |
| Departure times | 2.4, 3.5, 4.4, 4.9, 8.2, 9.8, 10, 10.5 |

## Example 4:

In a single-server queueing system the time of the arrival and departure of the customers are given below.

|                 |                                         |
| --------------- | --------------------------------------- |
| Arrival times   | 0.4, 1.6, 2.1, 3.8, 4.0, 5.6, 5.8, 7.2  |
| Departure times | 2.4, 3.1, 3.3, 4.9, 8.6, 9.2, 9.8, 10.5 |

## Example 5:

In a single-server queueing system the time of the inter-arrival of customer and service time of the customers are given below.

|                    |                        |
| ------------------ | ---------------------- |
| Inter arrival time | 1, 3, 4, 7, 4, 4, 3    |
| Service time       | 4, 2, 5, 4, 1, 5, 2, 3 |

## Example 6:

In a single-server queueing system the time of the inter-arrival of customer and service time of the customers are given below.

|                    |                                      |
| ------------------ | ------------------------------------ |
| Inter arrival time | 1.2, 0.5, 1.7, 0.2, 1.6, 0.2, 1.4    |
| Service time       | 2, 0.7, 0.2, 1.1, 3.7, 0.6, 0.6, 0.7 |

## Example 7:

In a single-server queueing system the time of the inter-arrival of customer and service time of the customers are given below.

|                    |                        |
| ------------------ | ---------------------- |
| Inter arrival time | 2, 4, 1, 2, 6, 3, 5    |
| Service time       | 2, 1, 3, 2, 1, 4, 5, 3 |

## Example 8:

In a single-server queueing system the time of the inter-arrival of customer and service time of the customers are given below.

|                    |                        |
| ------------------ | ---------------------- |
| Inter arrival time | 6, 1, 4, 3, 6, 5, 4    |
| Service time       | 2, 3, 5, 2, 1, 3, 2, 4 |

## Example 9:

In a single-server queueing system the time of the arrival and service of the customers are given below.

|               |                              |
| ------------- | ---------------------------- |
| Arrival times | 0.4, 1.6, 2.1, 3.8, 4.0, 5.6 |
| Service time  | 2.0, 0.7, 0.2, 1.1, 3.7, 0.6 |

## Example 10:

In a single-server queueing system the time of the arrival and service time of the customers are given below. the simulation clock starts at 0 & ends at 12.5

|               |                                         |
| ------------- | --------------------------------------- |
| Arrival times | 0.3, 1.8, 2.5, 3.9, 4.6, 5.8, 7.4, 10.5 |
| Service time  | 1.6, 1.2, 0.6, 0.5, 2.9, 2.1, 1.6, 0.9  |

## Example 11:

In a single-server queueing system the time of the arrival and service of the customers are given below.

|               |                                     |
| ------------- | ----------------------------------- |
| Arrival times | 4, 6, 8, 10, 16, 24, 29, 31, 38, 41 |
| Service time  | 2, 4, 5, 2, 5, 5, 3, 6, 6, 4        |

## Example 12:

In a single-server queueing system the time of the arrival and service of the customers are given below.

|               |                                     |
| ------------- | ----------------------------------- |
| Arrival times | 2, 4, 5, 13, 14, 18, 25, 31, 37, 43 |
| Service time  | 6, 3, 3, 1, 2, 4, 5, 5, 4, 3        |

## Example 13:

• Customers arrive at the server at random from 1 to 8 minutes apart. Each possible value of inter-arrival time has the same probability of occurrence.

• The service time vary from 1 to 6 minutes with the probability of 0.10, 0.20, 0.30, 0.25, 0.10, 0.05 respectably.

• The problem is to analyze the system by simulating the arrival and service time of 20 customers. 

• Random value for time between arrivals - 913, 727, 015, 948, 309, 922, 753, 235, 302, 109, 093, 607, 738, 359, 888, 106, 212, 493, 535.

• Random value for Service time - 84, 10, 74, 53, 17, 79, 91, 67, 89, 38, 32, 94, 79, 05, 79, 84, 52, 55, 30, 50.