ECE 5101/CSE 5463, Spring 2023
Due: Apr. 8 11:59pm, 2023 on Carmen
Homework Assignment #4
Late Submission NOT Accepted
Homework Assignment #4
1. (20 points) In an unslotted ALOHA system, the packet arrival times of all users form a
Poisson process having a rate of 103 packets/sec. If the bit rate is 10 Mbps and there are
1000 bits/packet, find (a) the normalized throughput of the system, and (b) the number of
bits per packet that will maximize the throughput.
2. (20 points) Repeat Problem 1 for a slotted ALOHA system.
3. (20 points) (a) Assume a line-of-sight radio path exists for a user 10 km away from the
transmitter. Determine the propagation delay in packet transmission units if a 19.2 kbps
channel data rate is used and each packet contains 256 bits. (b) If slotted ALOHA is to be
used for this single-user system, what is the optimal total transmission rate in the unit of
packets/second for this system?
4. (20 points) Suppose that there are two Wi-Fi service providers in a shopping mall (e.g.,
Starbucks and McDonald’s), with each service provider operating its own AP. Further assume
that, by accident, each service provider has configured its AP to operate over the same
channel. Will the 802.11 protocol completely break down in this situation? Discuss what
happens when two stations, each associated with a different Wi-Fi service provider, attempt
to transmit at the same time.
5. (20 points) Suppose an 802.11 station is configured to always reserve the channel with the
RTS/CTS sequence. Suppose that this station suddenly wants to transmit n bytes of data,
and all other stations are idle at this time. Denote the delay of DIFS, SIFS, RTS, CTS,
and acknowledgement by dDIFS, dSIFS, dRTS, dCTS, and dACK, respectively. Let R denote
the transmission data rate, in the unit of bits/sec. Under the use of SIFS and DIFS, and
ignoring propagation delay and assuming no bit errors, derive the expression to calculate the
time required to transmit the n bytes of data and receive the acknowledgement according to
the 802.11 DCF protocol.
6. (Bonus: 40 points) Background of CSMA/CD: In class, we mentioned that CSMA/CA is
the default MAC protocol for 802.11, which uses mechanisms such as random backoff timer
and RTS/CTS to prevent collisions from happening. However, due to these extra overhead,
CSMA/CA is less efficient than another variant of CSMA called CSMA/CD (CSMA with
collision detection).
CSMA/CD works as the following: When a station has a packet to transmit, it first listens
to the channel. If the channel is occupied, it will wait until the channel is free; otherwise,
it will start transmit after sensing the channel being idle for a fixed amount of time (i.e.,
the CSMA part). If, however, two stations sense the channel being idle and start transmit
simultaneously, then a collision still happens even if they already follow the CSMA rule. Now,
suppose that if both stations can detect the collision once it happens, then they can suspend
their ongoing colliding transmissions immediately to reduce the collision duration and shorten
the time wasted in transmitting unfinished packets (i.e., the CD part). After that, these two
stations contend for the channel again with random backoff. Clearly, CSMA/CD is more
efficient than CSMA/CA thanks to lower overhead.
1
ECE 5101/CSE 5463, Spring 2023
Due: Apr. 8 11:59pm, 2023 on Carmen
Homework Assignment #4
Late Submission NOT Accepted
Historically, CSMA/CD is used in older generations of Ethernet (IEEE 802.3) that are based
on shared medium (e.g., 10BASE2, 10BASE5), but no longer needed in modern Ethernet with
sophisticated switches and full-duplex connections, where there is no collision possibility at
all. Meanwhile, CSMA/CD does NOT work for wireless LANs because wireless transceivers
are half-duplex in nature as a result of self-interference (i.e., the radio can either transmit
or receive, but cannot do both simultaneously). Therefore, when a wireless device starts
transmitting, it cannot listen to the channel at the same time to detect collision.
However, recent years have witnessed significant advances in wireless technologies and re searchers have made a significant progress in the areas of full-duplex wireless.
1 As a result,
CSMA/CD received renewed interests in wireless networking MAC protocol design, which
could improve the efficiency of the default CSMA/CA MAC protocol of IEEE 802.11.
Questions: With the above background story, now let us consider an unslotted CSMA/CD
system, where the propagation delay is negligible compared to the β time units required for
a node to detect that the channel is idle or busy. Assume that each packet requires one
time unit for transmission. Assume that β time units after either a successful transmission
or a collision ends, all backlogged nodes attempt transmission after a random delay and that
the composite process of initiation times is Poisson of rate G (up to time β after the first
initiation). For simplicity, assume that each collision lasts for β time units.
(a) (10 points) Find the probability that the first transmission initiation after a given idle
detection is successful.
(b) (10 points) Find the expected time from one idle detection to the next.
(c) (10 points) Find the throughput based on the above given assumption.
(d) (10 points) Optimize the throughput numerically over G.
1For example, see https://fullduplex.rice.edu/ for the full-duplex hardware designed by Prof. Ashu Sabharwal,
who is an OSU alum. Prof. Kannan Athreya’s group at OSU also work on full-duplex wireless networking.
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