# operating systems

**Question description**

- ( 10 points )

A ring network has 8 logical nodes. Six distinct computers (i.e. each computer has a unique ID ) are to be assigned to the nodes and each node can associate with at most one computer. How many different ways can we assign the 6 computers to the 8 nodes. - ( 20 points )

A DHT Chord network uses 4 bits (i.e.*m*= 4 ) to identify machines and keys of entities. At a certain time, machines with identifiers 2, 5, 9, and 11 are attached to and active in the network.- Draw a diagram to show the machine ids and keys of the network.
- Find the finger table of each of the machines.
- An application running in node 11 is looking for the entity with key value 7. Find the route the system takes to get to the node that has the entity. Show your steps clearly and draw the route on your diagram.

- ( 10 points )
- .
- Would you consider a URL such as
*http://www.acme.org/index.html*to be location independent? What about*http://www.acme.nl/index.html*? - Consider the behavior of two machines in a distributed system. Both have clocks that are supposed to tick 1000 times per millisecond. One of them actually does, but the other ticks only 990 times per millisecond. If UTC updates come in once a minute, what is the maximum clock skew that will occur?

- ( 10 points )

If each process uses a different value for d in the Lamport's clock and vector clock equations, will the logical clocks and vector clocks schemes satisfy the total order relation => and the relation:- a → b iff t

^{a}< t^{b}Explain your argument in detail. - ( 10 points )

Suppose Process P_{1}has eventse_{11}, e_{12}, e_{13}, e_{14}, e_{15}e_{16}e_{17}P_{2}has eventse_{21}, e_{22}, e_{23}, e_{24}, e_{25}, e_{26},P_{3}has eventse_{31}, e_{32}, e_{33}, e_{34}, e_{35}e_{36}There are message transits from e_{12}to e_{22}, e_{24}to e_{15}, e_{21}to e_{32}, e_{35}to e_{25}. Suppose the vector time clocks for e_{11}, e_{21}, and e_{31}are

respectively.1

0

0, 0

1

0, 0

0

1a) Draw a diagram to show all the transitions and events.

b) Find the vector clocks of all the events.

c) Give an example for each of the following:

i) a strongly consistent stateii) a consistent but not strongly consistent state

iii) an inconsistent state

Your global state should be consisted of the the events given ( e.g. e_{11}) but should**not**contain any event that is sending ( e.g. e_{12}) or receiving a message ( e.g. e_{22}).

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