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branch D

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Tel G mote is a low rate wireless sensor mote that has limited storage (Queue A). An additional SD card (Queue B) is connected to the mote to help buffer any big files that has to wait before being transmitted to the next hop. Assume the probability of packet arrival to queue A is 0.6, and probability of packet departure from queue A is 0.8. Packets from queue A will only go to queue be when the queue is B1-1. Probability of arrival to queue B is 0.3 and probability of packet departure from queue B is 0.5. The buffer size for the mote storage, B1=4 and the buffer size, for the SD card, B2 is 3. Assume  that all packets the goes to queue A will go into queue B. Any overflow from queue B will go back to queue A.
a) Sketch the state transition diagram for the above scenario. Provide all the necessary probabilities in the diagram.
b) Construct the transition matrix (write the top left 3x3 and the bottom right 3x3 of the matrix ).
c) Calculate the probability that queue A is empty.
d) Determine the probability of loss in SD card.
e) Steady state distribution for both queues.
f) Elaborate comments of the performance of the TelG Mote in worst case scenario. Provide suggestions.

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1)  Define probability Distribution vector
Answer: A vector with non-negative entries that add up to 1. It is defined as the probability of the system being in each state at time step n.
2)Define the term steady state in Markov Chain
Answer: Steady states means the probability of being in any state will not change with time. S(n) = S(n-1)
3) Elaborate on initial distribution vector
Answer: The initial distribution vector S(0) that describes the distribution of load among state in the beginning of Markov Chain

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1)    Consider M/M/1/B queue with arrival probability a = 0.5 and departure probability c = 0.6 and B=4
a. Find the probability when the queue is empty
b. Calculate the distribution vector of this queue.
c. Determine the efficiency of the queue
d. Construct the transition probability matrix

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1)    Consider M/M/1 queue with arrival probability a = 0.5 and departure probability c = 0.6

a.     Construct the first four rows and column of the transition matrix P

b.     Find the values of the first five components of the equilibrium distribution vector (note: keep it to 4 decimal points)

2)    In an M/M/1 queue, it was found out that the average queue size Qa = 5 packets and the average waiting time is W = 20 time steps. Calculate the queue arrival and departure probabilities and find the first five entries of the distribution vector.

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1. why traffic conservation is needed in queueing analysis?
A:we're not living in an ideal world, so there has to be some lost, error or delayed packets for any reason. the traffic conversation helps us find the lost packets probability and its relation with the efficiency of the queuing system.

2. Explain the difference between throughput & good put?
Answer: In this book, throughput and goodput are the same. However, they may differ in other references. The throughput can mean all output packets ( in one time step) regardless whether the packets are corrupted or not. whereas the goodput refers to the output packets that got through without being corrupted.

3. elaborate the importance of the queuing system analysis.
Answer: Queuing analysis is used to predict the system performance. The capacity of the system can be estimate, hence can balance the cost of increased capacity against the gains of increased productivity and service. Such as the buffer size can be estimated through queuing system analysis.

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1.Elaborate the difference between Access probability and efficiency.
n = used for queues and switches
Pa = used for interconnection network
Both actually measure the effectiveness of the queue at processing data present at the input

2. Explain throughput.
Throuput of a queue is the estimating rate of coutomers leaving the queue. The throughput is given by Th= output data rate=Na(out)
the unit is packet/time step
3. Why efficiency should be less than 1.
Since the efficiency is the ratio of the average
output traffic relative to the average input traffic.
The average output traffic cannot be more than the average input traffic.

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si - prob that i packets are in    the buffer
a - prob that packet arrive in a system
b -prob that packet does not arrive
c- prob that packet depart
d- prob that packet does not depart

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For each group create three (3) Questions Regarding RM6 (until sec 7.4) that starts with the following keyword
*Explain...
*Elaborate...
*Why....