Part A: Multiple Choice and True/False

Question 1

Suppose we run simulation experiments to estimate some network metric of interest (say, delay). From a large number N of samples, we are able to calculate the average and 90% confidence interval. How should we interpret these results?

(Hint: Check Credibility of simulation results in Module 2

a)All the options are correct.

b)If we calculate 90% confidence interval from independently obtained sets of N samples, we should expect 90% of those intervals to contain the true mean delay.

c)If N is large enough, we expect the collected samples to follow a Gaussian distribution.

d)If we repeat the experiment and collect an additional M samples, we should expect 90% of those M samples to fall into the calculated confidence interval.

e)If we repeat the experiment once and measure delay, the measured value has a 0.9 probability of falling in the calculated confidence interval.

Question 2

The picture shows a Linksys WiFi access point being sold at Amazon.com.

Two antennas are used:

a)To have a backup antenna in case one fails

b)For allowing dual frequency operation

c)To connect to two different wireless LANs

d)For frequency hopping

e)For spatial diversity

Question 3

Which of the following is true regarding fixed TDM (time division multiplex) wireless networks?

a)It is an efficient technique for handling bursty traffic

b)Delays can be infinite due to the rigid, slotted nature of communication

c)All the options are correct.

d)Synchronization is not an issue because nodes will defer transmission if they sense another node transmitting

e)Bandwidth is generally fixed because nodes can usually only transmit during their timeslot

Question 4

Which of the following components of delay is typically probabilistic and depends on the packet arrival process?

a)Queuing delay

b)Propagation delay

c)Processing delay

d)Transmission delay

e)Packetization delay

Question 5

Due to obstacles and reflectors in the wireless propagation channel, a transmitted signal may arrive at the receiver from various directions. This comprises an unpredictable set of reflections and/or direct waves, each with its own degree of attenuation and delay. This phenomenon, which can cause distortions to the received signal, is known as

a)Collision

b)Path loss

c)Multipath fading

d)Shadowing

e)Interference

Question 6

If a random variable describing wait time has a exponential distribution (aka, follows a Poisson process), which of the following is true?

a)Wait time is fixed, so you would know exactly how much longer you must wait

b)Wait time is independent of the time you have already waited

c)The longer you have waited, the sooner you would expect to be done

d)The longer you have waited, the longer you expected future waiting time will be

Question 7

The session initiation protocol (SIP) ...

a)Is adopted by several voice of IP applications

b)Is an example of mobility support at the application layer

c)All the options are correct.

d)Defines mechanisms for communication between end systems and proxy servers

Question 8

When analyzing packet sizes in observed Internet traffic, which of the following is true?

a)Packet size is bursty, making Internet traffic extremely hard to analyze mathematically

b)Packet size follows a uniform distribution

c)Packet size is mutli-modal, with a high percentage of header-only packets and large packets bounded by the maximum transmission unit of the network link

d)Packet size follows a light-tailed, Pareto distribution

Part B: Numerical Questions

Question 9

Requests arrive at a Domain Name Server at a rate of 3,600 requests per hour. The average response time is one half of a second. Requests are queued upon arrival and the buffer is long enough that no requests are lost (effectively, an infinite buffer).

Assume Poisson arrivals and exponentially distributed service times. Using Kendalls notation used in the lectures, what is the appropriate queuing model to be used in the analysis of this system?

Question 10

(1) For the queuing system in Question 9, load ) =

(2) Is the system stable? (yes/no) . Why?

Question 11

For the queuing system in Question 9, What is the average number of requests in the system? (i.e., the total, including in the queue and in service)?

Question 12

A large hotel maintains a customer service number staffed by 3 operators. If you call and all 3 operators are currently busy, you get disconnected. Assume that arrivals are Poisson and arrive at an average rate of 12 per hour. The average length of a call is 3 minutes and service times are exponentially distributed. For simplicity, do not consider call retry in case you get disconnected.

What formula is used to calculate blocking probability for this system (either name the formula or write it out)?

Question 13

For the queuing system in Question 12, assume that the blocking probability (P₃) = 0.02. On average, how many calls would be served per hour by this call center (specify to 2 decimal places)?

Question 14

Consider a finite buffer single server queuing system with arrival and service rate such that the equilibrium state probabilities are:

N: number of customers in the system	0	1	2	3	>=4
p(N): equilibrium state probability	0.415	0.277	0.185	0.123	0

Note: the state of the system is defined by the number of customers in the system.

Assume the service rate = 10.0. Calculate the mean number of customers in the queuing system with an accuracy of two digits after the decimal point.

Question 15

For question 14, compute the mean throughput of the queuing system with an accuracy of two digits after the decimal point.

Question 16

For question 14, compute the mean delay of the system with an accuracy of two digits after the decimal point.