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Please write clearly. Make your answers concise, but complete.
- (10 points) Packet classification. The table below shows a set of packet filters with three fields. The values in the range field can be divided into the five primitive ranges r 0 =0-1, r 1 =2-3, r 2 =4-6, r 3 =7-9, r 4 =10-15. Show how each of the ranges can be expressed in terms of the indexes of the primitive ranges.
The Karnaugh map below has a label for each of the primitive ranges. Use this to construct a bit vector for each range (with wild cards at selected bit positions). In your bit vectors, assume that the bits on the left side come before the bits on the top (so, 3 is represented by the bit vector 0111).
00 01 11 10 (^00 0 1 ) (^01 ) (^11 4 ) 10
CS 577 – Design and Analysis of Switching Systems
Exam 2
Jonathan Turner 11/10 /
- (14 points) Consider a variation of the basic queueing model (discrete time version), in which the arriving packets consist of high priority packets and low priority packets. An arriving high priority packet is added to the queue, if there room in the queue, but a low priority packet is added only if the number of packets currently in the queue is less than or equal to a threshold value. Draw a finite state model for such a queue, assuming the queue has space for a total of four packets and that the threshold is two. Label all the edges with the appropriate transition probabilities. Let the total arrival probability be λ=λ 0 +λ 1 , where λ 0 is the arrival probability for the high priority packets and λ 1 is the arrival probability for the low priority packets (at most one packet arrives during each time step) and let the departure probability be μ.
Write down any two of the steady-state balance equations for your finite state model.
- (16 points) In the analysis of NVF, we defined three quantities, pij , q (^) j and slackij. State the definitions of these terms.
The figure below shows the state of a crossbar for the NVF crossbar scheduler. Give the values of p 4,2 , q 2 and slack 4,.
Consider the following situation in a crossbar with speedup 2 that uses an NVF scheduler. At time t a cell arrives and is placed in Vij , making it active. In the next k time steps, cells arrive at input i for other active VOQs. Explain why after the input phase at time t + k , slackij ≥ k –1.
output queues
VOQ lists VOQs
1, 2 3, 2, 3,1,
0 1 2 3 4
0 1 2 3 4
- (9 points) Consider an adaptive resequencer with a window size W =50 and a delay difference bound Δ=50. Assume that the window boundaries occur on multiples of W. Suppose that after time step 94, the maximum delays seen in the current and previous windows are d 0 =20 and d −1= 35. What is age threshold T , at this point?
If cell A is received at time 95 with a timestamp of 55, what are the values of d 0 , d − and T.
Suppose that a cell B is received at time 120 with a timestamp of 60 and that no other cells are received. At what time are A and B forwarded?
