bs3619s12.pdf bs3619r12.pdf

Section A
Answer 1. a) Simulation is a process of replicating real world scenarios on computer.
Analyst usually creates models for different issues and bottlenecks. Inputs for models are
revalue from real world situation with certain assumptions. Once model provides output for
the scenarios, analysts study them and try to find solution for the issues. Simulation allows
easy understanding of scenarios and provide testing environment where analysts capture
different outputs when inputs are influenced with different assumptions. This allows
understanding models responses under different strategies, policies, or customer demand.
One particular query which simulation provides answer is “what-if” question of existing or
proposed system. For instance simulation can be used in project management where project
completion time distribution can be studied when activities are uncertain or studying
economic order quantity under different demand requirement.
b) Five steps of Monte Carlo Simulation:
1. Monte Carlo simulation starts with deciding probability of important variables
(possible outcomes) for the stochastic process.
2. Prepare the cumulative probability from the step 1 process distributed for the each
variable
3. To generate a random number decide an interval of random numbers to setup a
correspondence between the outcomes of the experiment.
4. Generate the random number and conduct the experiment.
5. Repeat the experiment and compare the outcome in each and every case.
c) Random numbers are integral part of simulation as it allows verification of model based on
unbiased number generation. However there are multiple random number generation
techniques varying from simple to complex calculation. Every model can only respond to
particular set of random numbers only. Therefore it becomes quintessential to pin point
random number generation technique to be used for any specific model.
Multiplicative congruential random number generator technique is arithmetic process of
generating a finite number of random numbers. Where two randomly generated numbers are
congruent and their relationship can be explained through following equation:
Where a≥0 and m ≥ 0
In the information provided we have been following details:
Initial seed z0=1
With parameters m =23 and a =13 our first random number will be as:
So our three random numbers through multiplicative congruential random number generator
technique are 13,8,12.
d) Simulation model is a single server single waiting line model which demonstrates the
arrival of customer at the ticket booth of a music event. Here three hundred trials have been
presented with detailed performance has been shown through the inter arrival time, arrival
time, service time and system time. Exponential distribution has been exhaustively used to
calculate the arrival time of customer and based on the same simulation model calculates all
the other performance values. Exponential distribution has also been used in the service time
calculation as there is no fixed time service provided to the customer. So service time is
dependent on the customer behaviour and it has been handled through random number
generation based on the exponential distribution.
i) Second customer arrived at the ticket booth at 1.801 units where one unit is equivalent to 5
minutes. Hence second customer arrived at:
5 X 1.801 = 9 minutes.
As the ticketing booth opened at 9:00 AM, Second customer arrived at 9:09 AM.
ii) Fifth customer arrived at 3.278 units and he was provided service at 3.278 units or we can
say fifth customer did not spend any time in queue waiting for the service.
iii) Ticketing booth could be closed when they have served 300 customers. Simulation model
highlights that service ended for 300
th
customer at 65.300 units. It has been mentioned that
one unit is equivalent to 5 minutes. Thus 300 customers had been served in 5*65.3 minutes or
326.6 minutes or 5 hours 26.6 minutes. As the ticketing booth opened at 9:00 AM, booth had
been closed at 2:26 PM.
e) The construction of the probability of the n number of customers in the system is can be
generalized with 0 number of customer in the system. In case that no customer is waiting in
the system our generalized poisson distribution will be:




So when we calculate that n numbers of customer are waiting in the system can be written as:
(


)
f) As there are four servers in the system and...