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ECE 533: Advanced Computer Communication Networks (Fall ’21)

Take-Home Quiz #5 due on 10/29/2021 @ 1pm

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1) What are the components of a switch. Briefly explain. 2) What are the three types of switching fabrics? Briefly explain. 3) Consider that an 8×8 switch constructed by interconnecting 2×2 switches. Assuming that there is no buffering at the switches, calculate the throughput per output link. 4) What are the advantages and disadvantages of the switches with output buffer architecture? 5) Consider an NxN input queued switch. Assume that the external arrivals to each input are Poisson with average rate A, and there is no queuing inside the switch and at the output ports. (i) Calculate the average

number of head-of-line (HoL) packets (Zk) destined to output port k. (ii) What is ∑ 𝑍𝑘 𝑁 𝑘=1 ?

6) Consider a 2×2 switch and assume input queues are infinitely backlogged. The destinations (output ports) of packets are randomly and uniformly chosen from {1, 2}, where 1 represents output port 1 and 2 represents output port 2. The destinations are independent across packets. Let di(t) (i = 1, 2) denote the

destination of the head-of-line packet of input queue i at time t. When d1(t) ≠ d2(t), both head-of-line

packets can be transferred to corresponding output ports; otherwise, one of them is randomly selected and transferred to the corresponding output port. (a) Note that d(t) is a Markov chain with state space {11, 12, 21, 22}. Write down the transition matrix of this Markov chain and compute the stationary distribution of the Markov chain.

(b) Based on the stationary distribution, compute the average throughput of this 2×2 switch.

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