Part 1: Theoretical Questions

ELT-53607, Network analysis and dimensioning Responsible person: Dmitri Moltchanov Return to: TG411 No calculators allowed! Please answer in the order of questions. Answer the following questions. 1. What are the time-advance methods in discrete-event simulation? 2. What is the event list? 3. What structures are used to organize event lists? 4. What methods of data collection exist? Why do we need them? 5. How to decrease the effect of transient periods? 6. How quickly confidence limits shorten increasing the number of experiments? 7. Explain the idea of the method of antithetic variables. 8. Give a definition of a memoryless property. 9. Which two distributions are memoryless? 10. How memoryless distributions are related to Markov chains? 11. Which quantities does Little’s law relate? 12. What is the difference between network analysis and network optimization? 13. Consider M/M/1 queue, λ ,  – arrival and service rates. I. How the system state is defined? Why is it possible? Explain. II. Draw state transition diagram of a Markov chain associated with system. III. Get differential equations describing time-dependent behavior. IV. Get linear equations describing the system at steady-state. V. Derive distribution of the number of customers in the system. VI. Derive an expression for mean number of customers in the system. Hint: it is not needed to determine the sum of series you may encounter. 14. Consider M/G/1 queuing system. Complete the following tasks. I. How the state of the system can be defined? Why is it possible? Explain. II. Draw state transition diagram of imbedded Markov chain. 15. What is the difference between capacitated and uncapacitated design problems? 16. Consider a simple network below

Fig. 1. A simple network. There are three bidirectional demands a. 1 and 2 of volume 1

b. 1 and 3 of volume 4

c. 2 and 3 of volume 12

Bidirectional links are between a. 1 and 2 with rate 4 units

b. 1 and 3 with rate 5 units

c. 2 and 3 with rate 8 units Write down capacity and demand constraints using the notation we used. 17. For Fig. 1 write down objective function for routing cost optimization a. cost of routing over a link between 1 and 2 is 1 b. cost of routing over a link between 1 and 3 is 1

c. cost of routing over a link between 2 and 3 is 4

18. Convert the problem to uncapacitated design one and solve.