Simulation and modelling assignment | Mathematics homework help

a)      Suppose you are simulating a clinic with one doctor:

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                    i.            State the type of simulation model you will develop? Justify your answer                      (4 Marks)

                  ii.            List the state variables you will use to estimate the average delay time for the patients, hence examine the relationship between these variables                                                   (6 Marks)

                iii.            List and explain the two events for the system                                                     (4 Marks)

b)      Outline three attributes of Discrete-event simulation models                                                          (3 Marks)

c)      Describe the components of a single-server queuing system                                                        (4 Marks)

d)      State the time variables associated with a single-server queuing system, assuming that the queue discipline is FIFO, and, service is conservative and non-preemptive                                       (6 Marks)

e)       Describe the concept behind Monte Carlo Simulation                                                      (4 Marks)

f)       Discuss four steps that are performed for the Monte Carlo simulation of a physical process  (4 Marks)  

g)      Outline the well-accepted random number generation criteria                                                    (5 Marks)

h)      State Lehmer’s algorithm for random number generation                                                (5 Marks)

i)        Given a modulus, m = 13, multiplier, a = 6, and an initial seed x0 = 2, give the resulting full-period sequence of random numbers using Lehmer’s algorithm.                                                 (5 Marks)

a)      The data below shows the arrival time , service time , and delays  for 6 customers arriving at a Barbershop, which has one Barber, and service is offered on a first-come first-served basis.

     i

1

2

3

4

5

6

ai

15

47

71

111

123

152

di

0

11

23

17

35

44

si

43

36

34

30

38

40

                    i.            Calculate the average interarrival time and the arrival rate                                   (3 Marks)

                  ii.            Calculate the average service time and the service rate                                        (3 Marks)

                iii.            Calculate the average delay in the queue                                                             (2 Marks)

 

                iv.            Calculate the average wait in the service node                                                     (2 Marks)

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