ECE 358 MAC Examples. Xuemin (Sherman) Shen Office: EIT 4155 Phone: x
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1 ECE 358 MAC Examples Xuemin (Sherman) Shen Office: EIT 4155 Phone: x xshen@bbcr.uwaterloo.ca
2 Problem 1. Consider the following Aloha systems. (a) A group of N users share a 56 kbps pure Aloha channel. Each user generates at a Passion rate of one 1000 bit packet every 100 sec, even if the previous one has not yet been sent. What is the maximum value of N? (b) Ten thousand airline reservation stations are competing for the use of a single slotted Aloha channel. The average station makes 18 requests/hour. A slot is 125. What is the approximate total channel load? (a) With pure ALOHA the maximum usable bandwidth is Each user requires 1000/100= 10 bps, so N=10300/10 = 1030 users. kbps. (b)the average station makes 18/3600=1/200 requests/sec. The total channel load is requests/sec. Using slot as the time unit, the total channel load is requests/slot.
3 Problem 2 A large population of Aloha users manages to generate 50 requests/sec, including both new requests and retransmissions. Time is slotted in units of 40 msec. (a) What is the chance of success on the first attempt? (b) What is the probability of exactly k collisions and then a success? (c) What is the expected number of transmission attempts needed? The channel traffic load rate requests/slot. In one slot, k requests happ en with the probability. (a) First attempt succeed with the probability Pr[no other request (new or retransmission) occurs within the first slot ] (b) If assuming that things happening in different slots are independent, the probability is (c) The expected number of transmission needed
4 Problem 3 A small slotted Aloha system has only k customers, each of whom has a probability 1/k of transmitting during any slot (both new and retransmission). What is the channel throughput as a function of k? Evaluate this expression numerically for k= 2, 3, 4, 5, 10; and. A packet transmission succeed in a slot when only one customer attempt to use it and the others not. The pr obability is, just meaning the channel throughput is packets/slot. When k =2, 3, 4, 5, 10, the throughput S are respectively , ,0.4219, , Considering the situation Note: Here we can see, the average load in this system is requests/slot. When the population number goes to, the throughput can be calculated by Poisson approximati on.
5 Problem 4. Assume that the number of packets n in a slotted Aloha system at a given time is a Poisson random variable with mean. Suppose each packet is independently transmitted in the next slot with probability. (a) Find the probability that the slot is idle. (b) Show that the posterior probability that there were n packets in the system, given an idle slot, is Poisson with mean. (c) Find the probability that the slot is successful. (a) Given k packets in the system, with each packet independently transmitted in a slot with probability, the probability of an idle slot,. The joint probability of an idle slot and k packets in the system is then The probability that the slot is idle.
6 Problem 4. (b) Using the result above, we can find, the posteriori probability that there were n packets in the system, given an idle slot. Thus, this probability is Poisson with mean. Note: Posterior probability is the conditional probability that is assigned after the relevant evidence is taken account. (c) Similarly as part (a), we can first find the joint probability of success and k in the system, namely, then calculate the successful probability.
7 CSMA CSMA/CA (Carrier Sense Multiple Access/Collision Avoidance) is the channel access mechanism used by most wireless LANs in the ISM bands. A channel access mechanism is the part of the protocol which specifies how the node uses the medium: when to listen, when to transmit. CSMA/CA is derived from CSMA/CD (Collision Detection), which is the base of Ethernet. The main difference is the collision avoidance: on a wire, the transceiver has the ability to listen while transmitting and so to detect collisions (with a wire all transmissions have approximately the same strength). But, even if a radio node could listen on the channel while transmitting, the strength of its own transmissions would mask all other signals on the air. So, the protocol can t directly detect collisions like with Ethernet and only tries to avoid them.
8 CSMA Under CSMA/CD, when a station has data to send, it first listens to determine whether any other station on the network is occupying the medium. If the channel is busy, the station will wait until it becomes idle before transmitting data. Since it is possible for two stations to listen at the same time and discover an idle channel, it is also possible that two stations could then transmit at the same time. When this occurs a collision will take place, and then a jamming signal is sent throughout the network in order to notify all stations of the collision. The stations will then wait for a random period of time before retransmitting their respective frames.
9 CSMA Currently the DCF resolves collision through multiple levels of CWs and backoff stages. In the initial backoff stage (stage 0), the value of CW has the minimal value CWmin. After each collision, the CW will be doubled until reaching the maximum CWmax. After each successful transmission, the backoff will resume with initial stage (0) and the CW will be reset to CWmin regardless the network condition or the number of competing nodes. By resetting the CW to CWmin, DCF increases the probability of collision and frequent retransmissions remain high until the CW attains appropriate values. This is obviously no optimal since high collision rate in the network means poor network exploitation. On the other hand, the intrinsic backoff randomness makes it difficult to instantaneously absorb an increasing number of flows. The backoff process is basically intended to reduce the collision rate when using a higher contention stage.
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