CS 118 Homework 1

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Problem 1
Suppose users share a 10 Mbps link. Also suppose each user requires 1 Mbps when transmitting, but each
user transmits only 20 percent of the time.
(a) When circuit switching is used, how many users can be supported?
(b) For the remainder of the problem, suppose packet switching is used. Find the probability that a given
user is transmitting.
(c) Suppose there are 100 users. Find the probability that at any given time, exactly n users are transmitting simultaneously. (Hint: Use the binomial distribution)
(d) Find the probability that there are 21 or more users transmitting simultaneously.
Write your solution to Problem 1 in this box
Problem 2
Queuing delay.
(a) Suppose N packets arrive simultaneously to a link at which no packets are currently being transmitted
or queued. Each packet is of length L and the link has transmission rate R. What is the average
queuing delay for the N packets?
(b) Now suppose that N such packets arrive to the link every LN
R
seconds. What is the average queuing
delay of a packet?
Write your solution to Problem 2 in this box
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CS 118 Spring 2018 : Homework 1
Problem 3
Review the car-caravan analogy in lecture #1 slides (for Chapter 1). Assume a propagation speed of
100 km/h.
(a) Suppose the caravan (10 cars) travels 150 km, beginning in front of one tollbooth, passing through a
second tollbooth, and finishing just after a third tollbooth. The distance between two tollbooths is
75 km. Each car takes 12 sec to serve. What is the end-to-end delay?
(b) Repeat (a), now assuming that there are 8 cars in the caravan instead of 10.
Write your solution to Problem 3 in this box
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Problem 4
In this problem, we consider sending real-time voice from Host A to Host B over a packet-switched network
(VoIP). Host A converts analog voice to a digital 64 Kbps bit stream on the fly. Host A then groups the
bits into 56-byte packets. There is one link between Hosts A and B; its transmission rate is 2 Mbps and its
propagation delay is 10 msec. As soon as Host A gathers a packet, it sends it to Host B. As soon as Host
B receives an entire packet, it converts the packet’s bits to an analog signal. How much time elapses from
the time a bit is created (from the original analog signal at Host A) until the bit is decoded (as part of the
analog signal at Host B)?
Write your solution to Problem 4 in this box
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Problem 5
Suppose you would like to urgently deliver 50 terabytes data from Boston to Los Angeles. You have available
a 1 Gbps dedicated link for date transfer. Would you prefer to transmit the data via this link or to use
FedEx overnight delivery instead? Explain your choice.
Write your solution to Problem 5 in this box
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