INST 346
Technologies, Infrastructure and Applications
Fall 2017
Assignment H1

1. Suppose users share a 3 Mbps link and each user requires 150 kbps when transmitting. Each user, however, only transmits with probability p=0.1 (i.e., 10 percent of the time).
   1. If circuit switching is used, what is the maximum number of users the link can support?
   2. For the remainder of this problem, suppose packet switching is used and that the users are acting independently (in the statistical sense, so for example two users transmit at the same time with probability p*p). What is the probability that a given user is transmitting?
   3. Suppose the network contains 120 users. What is the probability that, at any given time, exactly N users are transmitting simultaneously? (Hint: Use the binomial distribution. If you need a reminder of the formula for the binomial distribution, Wikipedia might be helpful).
   4. The network would reach capacity if 20 (=3M/150k) users were to be sending at the same time. What is the probability that 21 or more users are transmitting simultaneously?
   5. Now consider a network of M users. Give a formula in terms of p, M, and N for the probability that N or more users are sending data at the same time.
2. Use these results and your understanding from the reading and our class discussion to help you answer the following questions.
   1. What are the advantages of circuit switched network over a packet switched network?
   2. What are the advantages of packet switched network over circuit switched network?
3. We saw in equation (1.1) in Section 1.3.1 that d = N*L/R is the formula for end-to-end delay for sending one packet of length L over N links, each with transmission rate R, when store-and-forward packet switches are used (ignoring queuing, propagation delay, and processing time). Generalize the formula for sending K such packets back-to-back over the N links. Explain.
4. Suppose there is exactly one packet switch between a sending host and a receiving host, the transmission rates between the sending host and the switch and between the switch and the receiving host are R1 and R2, respectively and that the switch uses store-and-forward packet switching. What is the total end-to-end delay to send a packet of length L? (Ignore queuing, propagation delay, and processing delay.) Explain.
5. Suppose you need to deliver a 40-terabyte dataset from Boston to Los Angeles. You have available a 100 Mbps dedicated link for data transfer. Would you prefer to transmit the data via this link or instead use FedEx over-night delivery to send a set of disk drives? Explain. Be careful with the difference between bytes (B) and bits (b) when answering questions involving transmission rates.