16:330:543            Communication Networks I


Homework 2 (due November 11, 2003)

[50 points]   Consider the following protocol, a modified version of Stop-and-Wait which was already defined in Homework #1. Assume that there are three hosts, two of which are senders and one is receiver, sharing the same transmission medium. All hosts can listen to the medium and do so before transmitting any packet. Of course, we assume that all packets are of finite length. Assume an integer number CW, such that:
0 < CWmin £ CW £ CWmax < ¥

NOTE: This is a simplified version of the CSMA/CA protocol used in IEEE 802.11 wireless LANs.

Each sender follows these steps for all packets that it has to transmit until all of its packets are successfully transmitted:

  1. When busy medium is detected, wait with transmission until the medium becomes silent.
  2. When idle medium is detected, select a random number rn Î {0, 1, ..., CW-1} of time units. Decrement rn until it becomes 0. Listen again. If busy, go to 1; if idle, transmit one packet immediately. Wait for an acknowledgement.
  3. If an acknowledgement is not received within a timeout time, double the CW
    CW Ü 2 ´ CW
    If CW > CWmax, set CW Ü CWmax
  4. If an acknowledgement is received, set CW Ü CWmin
  5. Go to Step 1.
Assume that each sender has packet arrivals modeled a Poisson processes, and packets are transmitted in frames that are one unit long. Derive the average queuing and servicing delays for packets of one sender.

NOTE: If something is not clear about the problem statement you can either send me an email and request explanation or you can make your own reasonable assumptions which will help you solve the problem. In the latter case, make sure you clearly state and explain the assumptions in your solution.

HINT: Use the same methodology as in the textbook, Example 3.15, page 190, but for each sender consider the time when the other sender is transmitting as if the server (i.e., receiver) is on vacation. M/G/1 queues with vacations are covered in Section 3.5.1.

NOTE: According to the above algorithm, when a transmission is unsuccessful the sender has to re-contend for the medium. The other sender may win contention, which means that "vacations" are possible between successive retransmissions of the same packet.

Submission

Only electronic submission will be accepted. The file (Microsoft Word or Adobe PDF must be submitted by 4 p.m. on the due date. The cover page should contain the title: "Communication Networks I -- Homework #2" along with the student's full name and email address. Do not put the social security numbers.

Ivan Marsic
Sat Oct 18 18:52:24 EDT 2003