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.