Page 120 - DCAP601_SIMULATION_AND_MODELING

Simulation and Modelling

Notes Therefore x=–1/  ln u. x is a random number obeying negative index distribution.

With this method, as long as producing a random number obeying even distribution,
we could get a random number x obeying the negative index number distribution
with parameter .
(b) Creating the algorithm of obeying normal distribution with discarding-selecting
method
(i) Create two random number R and R in (0, 1)
1 2
(ii) With R , create a random number in [a,b]: x=a+(b – a)R , and calculate the
1 1
value of f(x)
(iii) when R <=f(x)/M, select x as, and M is the max value of f(X)
2
Simulating the model with event step-length method. In some degree, the process of the
simulation is considered as a series of event point. In terms of the sequence of event, the
system arranges the sequence of event executing with a table called “event table”. Event
table has three properties, ID, event style and time.

The simulation algorithm as below:
Step 1: Initiation (clear simulation clock
Configuring the state of the system

Clear accumulation statistic
creating initiating event table)
Step 2: Do
{
Find most recent event from event table
Simulation clock increase
If (Customers arrive)
Add the time of next customer arriving into event table
If (cashier is busy/ S=1)
LQ++ //queue increment
Else
S=1 //cashier turn to busy
Add the time of the customer finishing into event
Table
Else
Delete the customer from event table //service ends
If (the queue is not empty/ LQ>0)
LQ— //the length of queue decrease
Add the time of the customer finishing into event table
Else
S=0 // cashier is idle
} While (event table is not null)
Output result

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