CS 118 : Homework 1

CS 118 : Homework 1
Problem 1
Suppose users share a 100 Mbps link. Also suppose each user requires 10 Mbps when transmitting, but each
user transmits only 25% 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 (Hint: only the
formula is required).
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CS 118 Spring 2020 : Homework 1
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 N packets?
(b) Now suppose that a batch of packets arrives to the link every LN
R
seconds and each batch has N
packets. What is the average queuing delay of a packet?
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CS 118 Spring 2020 : 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 (5 cars) travels 100 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
50 km. Each car takes 12 sec to serve. The caravan can only dispatch a tollbooth after all cars in
the caravan are served. What is the end-to-end delay (from when the caravan is lined up before 1st
tollbooth till the caravan is served by the 3rd tollbooth)?
(b) Repeat (a), now assuming that there are 8 cars in the caravan instead of 5.
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CS 118 Spring 2020 : Homework 1
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, which means it take 1 second
to create 64K bits from the analog signal. 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 56-byte 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 the first bit of one
packet is created (from the original analog signal at Host A) until the packet is received at Host B)?
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CS 118 Spring 2020 : Homework 1
Problem 5
Suppose you would like to urgently deliver 50 terabytes data from Boston to Los Angeles. You have available
a 2 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.
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