# Population Dynamics Simulation

Do the following dynamic simulation problem:

1. The following model is proposed to describe population growth in a confined space. The excess of births over natural deaths causes a growth rate of a times the current number of individuals N. Competition for food causes deaths from starvation at a rate of bN^2 . Simulate the population growth assuming:

a. a = 0.05

b. b = 0.00001

c. N = 500 at time t=0

2. Assume in problem 1 that a second species exists in the same space subject to a1=0.04, b1=0.000015, and N1=1,000 at time t=0. However interspecies fighting causes deaths to both species at a rate that is 0.000001 times the product of their numbers (0.000001N(N1) ). Extend the model to plot the population dynamics for both species.

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#### Solution Preview

Please see attachment.

In brief about the solution:

Sheet 1: Q1: Solution to first part.

dN/dt == delta(N)/delta_t = a*N(t) - b*N(t)^2

=> delta(N) == N(t+delta_t) - N(t) = delta_t * (a*N(t) - ...

#### Solution Summary

A simulation which estimates growth of the population of a species.

Project Management, Queuing, and Simulation

1. The use of simulation to examine corporate operations (industrial dynamics), national economies

(econometric models), and urban governments is known as

A. Monte Carlo Methods

B. Operational Gaming

C. System Simulation

D. Queuing Methods

2. PERT

A. Is a network technique that uses three time estimates for each activity

B. Assumes we do not know ahead of time what activities must be completed

C. Allows computation of the program's evaluation

D. Is a deterministic network technique that allows for project crashing

3. The following is NOT a characteristic of Monte Carol simulation:

A. It uses random numbers

B. It uses random sampling of a probabilitiy distribution

C. It deals with the dynamics of large organitional systems

D. It evaluates system reponses to various policies

4. In queuing problems, the size of the calling population is important because

A. We have models only for problems with infinite calling populations

B. We have models only for problems with finite calling populations

C. The size of the calling population determines whether or not the arrival of one

customer influences the probability of arrival of the next customer

D. We will have to consider the amount of space available for the queue

5. Which of the following is NOT true about arrivals?

A. Arrivals that are independent of each other are random

B. Random arrivals cannot be predicted exactly

C. The Poisson distribution is often used to represent arrival pattern

D. The exponential distribution is often used to represent arrival patterns

6. On a PERT network, the earliest (activity) start time is the

A. Earliest time activity can be finished without delaying the entire project

B. Latest time an activity can be started without delaying the entire project

C. Earliest time an activity can start without violation of precedence requirements

D. Latest time an activity can be finished without delaying the entire project

7. In assigning random numbers in a Monte Carlo simulation,

A. It is important to use a normal distribution for all variables simulated

B. It is important to develop a cumulative probability distribution

C. It is not important to assign probabilities to an exact range of random number

intervals

D. It is important to ensure all variables are positive

8. The most appropriate cost to consider in making a waiting line decision is the

A. Expected service cost

B. Expected waiting cost

C. Total expected cost

D. Expected balking cost

This must be simulation.

9. Solution can be effectively used in problems of all theses types EXCEPT:

A. Inventory problems

B. Transportation problems

C. Maintenance policy problems

D. Poorlly defined problems

10. The use of simulation in competitive situations such as military games and business games

is known as

A. Monte Carlo methods

B. Operational gaming

C. System simulation

D. Queuing methods

11. The following is NOT an advantage of simulation:

A. IT allows for the study of what-if questions

B. Each simulation model is unique

C. It allows the study of interaction of components or variables to determine which

are important

D. It allows time compression

12. Arriving at a convention, a person must first line up to register at a table, then proceed to a

table to gather information, then pay at another single table. This is an example of a

A. Single-channel, multiphase system

B. Single-channel, single-phase system

C. Multichannel, multiphase system

D. Multichannel, single-phase system

13. Slack time in a network is the

A. Time consuming job or task that is a key subpart of the total project

B. Shortest amount of time that could be required to complete the activity

C. Amount of time you would expect it would take to complete the activity

D. Amount of time an activity can be delayed without delaying the entire project

14. CPM

A. Is a network technique that allows three time estimates for each activity

B. Is a deterministic network technique that allows for project crashing

C. Assumes we do not know ahead of time what actvities must be completed

D. Is opposite to that of PERT, as it does not consider the network activities

15. An arrival in a queue that reneges is one who

A. After joining the queue, becaomes impatient and leaves

B. Refuses to join the queue because it is too long

C. Goes through the queue, but never returns

D. Jumps from one queue to another, trying to get through as quickly as possible

16. The expected time in PERT is

A. A weighted average of the most optimistic time, most pessimistic time, and four

times the most likely time

B. A simple average of the most optimistic, most likely, and most pessimistic times

C. The modal time of a beta distribution

D. The square root of the sume of the variance of the actvities on the critical path

17. Given the following small project, the critical path is _____________ days. Activity Immediate Time

A. 10 Predecessor (days)

B. 14 A - 10

C. 16 B - 4

D. 20 C A, B 6

18. Assume that we are using a waiting line model to analyze the number of service technicians

required to maintain machines in a factory. Our goal should be to

A. Minimize the total cost (cost of maintenance plus cost of downtime)

B. Maximize productivity of the technicians

C. Minimize the downtime for individual machines

D. Minimize the percent of idle time of the technicians

19. The critical path of a network is the

A. Shortest time path through the network

B. Path with the fewest activities

C. Path with the most activities

D. Longest time path through the network

20. A vendor selling newspapers on a street corner is an example of a

A. Single-channel, multiphase system

B. Single-channel, single-phase system

C. Multichannel, multiphase system

D. Multichannel, single-phase system