Advanced Teletraffic Project 1

7/28/2019 Advanced Teletraffic Project 1

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CPEN 447- Advanced Teletraffic Engineering

Project 1Queuing Disciplines

Submitted By:Abeer Abou HaitGrace YammineNicole TannousFarouk Jammal

Submitted To:

Professor J.Daba

24-04-2012

Introduction:

In this project, we will compute the latencies of all applications (services) for all queuing

disciplines using both GPRS and EDGE technologies. We will generate graphs of latencies versus

the various traffic classes. We will also discuss the Kleinrocks conservation law.

Any queue consists of three components: an arrival process which determines when

customers arrive at the queue and what there characteristics are; a buffer (also referred to as the

queue itself) where customers wait to be served and a service time requirement for each customer

at the server serving the queue.

By convention, the term queue length includes the customer currently being served, if any.

Thus for an empty queue, the server is idle. Customer's service time is determined by the demand


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of the customer expressed in units of work and the service rate of the server specified by work

units performed in unit time. Service time is then the demand divided by the rate.

Queues are classified according to Kendalls notation which in its original form defines the class

A/S/m as follows:

A describes the nature of the arrival process. If for example the arrival process is Poisson,A=Mfor

Markovian or memoryless. If the inter-arrival times are constant,A=D for deterministic. For a

general inter-arrival rateA=G. The arrival rate is conventionally denoted by which is the

reciprical of the mean inter-arrival time. In general may depend on the number of customers in

the queue

S' denotes the service time distribution. We could haveS=M

for Markovian service time, i.e. one

with exponential distribution, S=D for deterministic or constant service times.

m denotes the number of servers available to give service to the customers in the queue.

The Queueing discipline describes how the server decides which customer in the queue to pick

next for service. Common disciplines are:

First in first out FIFO in which customers are served in strict order of arrival.

Last in first out LIFO under which the most recent arrival is served first.

Kendall's notation has been extended to include two additional fields that define the capacity of the

buffer/waiting room, c, and the population of the customer pool, i.e. the maximum number of

customers, p. The queue is then specified as A?S/m/c/p. Ifc and p are unspecified they are

assumed to be infinite.

Now, The latency L is obtained by calculating the sum of the waiting time Tw and the servicetime Ts.

Ts= Average Frame Size / Channel Capacity.

The Channel Capacity is given in Kbps so we multiply it by 1000 to get it in bits per second.

The average frame size is given in bytes per frame, so we convert it to bits per frame by multiplying

the value by 8.

To compute the waiting time Tw we need to get the arrival rate, the variable service time, the

inter arrival time and the variable inter arrival time.

Arrival Rate = Mean bit arrival rate (Rb) / Average Frame Size.

The mean bit arrival rate was given in Kbps so we multiplied it by 1000 to get it in bits per

second and the average frame size was given in bytes per frame so we multiplied it by 8 to get it in

bits per frame.

varServiceTime = (64 * varFrameSize) / ( channelCapacity^2).

varInterArrivalTime = ((SAR)^2) * (interArrivalTime^2).


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For a D/D/1 and G/G/1 distribution, we compute the waiting time Tw using the following

formula:

Tw= (arrival Rate/2) * ((varServiceTime^2 + varInterArrivalTime^2) / (1 arrival

Rate*service Time))

For an exponential M/G/1 distribution, a Pollaczek-Khintchine formula is used:

Tw= ((arrivalRate^2 * ((service Time * (1 + SAR)) 2)) / (2 * (1 arrival Rate * service

Time)))/arrival rate.

I- Type of queuing dispatching : FIFO

A- GPRS technology:

1) CS-1 time slot 1: channel capacity 9.05 Kbps

a- Not peaky traffic: SAR=1

%FIF0 - GPRS - CS1 - 1 Time slotclear all;close all;classesNb = 6;waitingTime = zeros(1,6);i = 1;%%%%%%%%%%%%%%%%%%%%%%%%%%%% Traffic Classes %%%%%%%%%%%%%%%%%%%%%%%%%%%%% 1 Voice Messaging G/G/1 %

% 2 Telnet M/G/1 %% 3 Audio Streaming G/G/1 %% 4 Video Streaming G/G/1 %% 5 Email M/G/1 %% 6 FTP G/G/1 %%%%%%%%%%%%%%%%%%%%%%%%%%%%% CS1 - 1 TSchannelCapacity = 9.05 * 1000;% 1 Voice messaging%%%%%%%%%%%%%%%%%%%%%%%%%%%averageFrameSize = 31;

arrivalRate = (1000 * 10.7) / (8 * averageFrameSize);serviceTime = 8 * averageFrameSize / channelCapacity;varFrameSize = 4;varServiceTime = (64 * varFrameSize) / ( channelCapacity^2);SAR = 1;interArrivalTime = 0.02308;varInterArrivalTime = ((SAR)^2) * (interArrivalTime^2);ETwSup = (arrivalRate/2) * ((varServiceTime^2 + varInterArrivalTime^2) / (1 -arrivalRate*serviceTime));ETqSup = ETwSup + serviceTime;waitingTime(i) = ETqSup;i = i + 1;% 2 Telnet%%%%%%%%%%%%%%%%%%%%%%%%%%%averageFrameSize = 64;arrivalRate = (1000 * 0.512) / (8 * averageFrameSize);throughput = arrivalRate;


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serviceTime = 8 * averageFrameSize / channelCapacity;SAR = 1;ETs2 = (serviceTime * (1 + SAR))^2;%Mean buffer lengthENw = (arrivalRate^2 * ETs2) / (2 * (1 - arrivalRate * serviceTime));ETw = ENw / throughput;ETq = ETw + serviceTime;waitingTime(i) = ETq;i = i + 1;

% 3 Audio streaming%%%%%%%%%%%%%%%%%%%%%%%%%%%averageFrameSize = 200;arrivalRate = (1000 * 20) / (8 * averageFrameSize);serviceTime = 8 * averageFrameSize / channelCapacity;varFrameSize = 4;varServiceTime = (64 * varFrameSize) / ( channelCapacity^2);SAR = 1;interArrivalTime = 0.08;varInterArrivalTime = ((SAR)^2) * (interArrivalTime^2);ETwSup = (arrivalRate/2) * ((varServiceTime^2 + varInterArrivalTime^2) / (1 -arrivalRate*serviceTime));ETqSup = ETwSup + serviceTime;waitingTime(i) = ETqSup;i = i + 1;% 4 Video streaming%%%%%%%%%%%%%%%%%%%%%%%%%%%averageFrameSize = 320;arrivalRate = (1000 * 64) / (8 * averageFrameSize);serviceTime = 8 * averageFrameSize / channelCapacity;varFrameSize = 4;varServiceTime = (64 * varFrameSize) / ( channelCapacity^2);SAR = 1;

interArrivalTime = 0.04;varInterArrivalTime = ((SAR)^2) * (interArrivalTime^2);ETwSup = (arrivalRate/2) * ((varServiceTime^2 + varInterArrivalTime^2) / (1 -arrivalRate*serviceTime));ETqSup = ETwSup + serviceTime;waitingTime(i) = ETqSup;i = i + 1;% 5 Email%%%%%%%%%%%%%%%%%%%%%%%%%%%averageFrameSize = 500;arrivalRate = (1000 * 4) / (8 * averageFrameSize);throughput = arrivalRate;

serviceTime = 8 * averageFrameSize / channelCapacity;SAR = 1;ETs2 = (serviceTime * (1 + SAR))^2;%Mean buffer lengthENw = (arrivalRate^2 * ETs2) / (2 * (1 - arrivalRate * serviceTime));ETw = ENw / throughput;ETq = ETw + serviceTime;waitingTime(i) = ETq;i = i + 1;% 6 FTP%%%%%%%%%%%%%%%%%%%%%%%%%%%averageFrameSize = 500;

arrivalRate = (1000 * 55) / (8 * averageFrameSize);serviceTime = 8 * averageFrameSize / channelCapacity;varFrameSize = 4;varServiceTime = (64 * varFrameSize) / ( channelCapacity^2);SAR = 1;


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interArrivalTime = 0.5;varInterArrivalTime = ((SAR)^2) * (interArrivalTime^2);ETwSup = (arrivalRate/2) * ((varServiceTime^2 + varInterArrivalTime^2) / (1 -arrivalRate*serviceTime));ETqSup = ETwSup + serviceTime;waitingTime(i) = ETqSup;i = i + 1;stem(waitingTime);

grid onxlabel('Application Class Number')ylabel('Queueing Time')title('Latencies Versus Traffic Classes')

The following is the graph of the latencies versus the various traffic classes.

b- Very Peaky traffic SAR=10

We used the same Matlab code as before but we replaced the SAR value by 10 instead of 1.

The following is the obtained result.


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The Matlab code used is the same as the previous one with the difference that the channel

capacity is 171.2 Kbps now and the SAR value is 1.The following is the obtained result.



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capacity is 171.2 Kbps now and the SAR value is 10.


B- EDGE technology:

1) Time slot 1: channel capacity 69.2 Kbps






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capacity is 69.2 Kbps now and the SAR value is 10.The following is the obtained result.


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II- Type of queuing dispatching: Priority Resume

A- GPRS technology:


% Priority Resume - GPRS - CS1 - 1 TimeSlotclear all;close all;classesNb = 6;%%%%%%%%%%%%%%%%%%%%%% Traffic Classes %%%%%%%%%%%%%%%%%%%%%%% 1 Voice Messaging %% 2 Telnet %% 3 Audio Streaming %

% 4 Video Streaming %% 5 Email %% 6 FTP %%%%%%%%%%%%%%%%%%%%%%% CS1 - 1 TSchannelCapacity = 9.05 * 1000;% Ascending order = Shortest packet firstaverageFrameSize = [31, 64, 200, 320, 500, 500];arrivalRate = [10.7, 0.512, 20, 64, 4, 55];priorities = zeros(1,classesNb);

prioritizedArrivalRate = zeros(1,classesNb);prioritizedAverageFrameSize = zeros(1,classesNb);% Assigning priorities for traffic classesfor i=1:classesNb

priority = input ('Please assign class priority: ');prioritizedArrivalRate(i) = arrivalRate(priority);prioritizedAverageFrameSize(i) = averageFrameSize(priority);priorities(i) = priority;

end% Getting the arrival rate vector in packet/sec with respect to the% assigned priorities

for i=1:classesNb, arrivalRate(i) = 1000 * (prioritizedArrivalRate(i) / (8 *averageFrameSize(i))); endserviceTime = zeros(1, classesNb);% Computing the mean frame service timefor i=1:classesNb, serviceTime(i) = 8 * prioritizedAverageFrameSize(i) /channelCapacity; endvarFrameSize = zeros(1, classesNb);for i=1:classesNb, if(priorities(i)==1) varFrameSize(i)=0; elseif(priorities(i)==2) varFrameSize(i)=6; elseif(priorities(i)==3) varFrameSize(i)=0; elseif(priorities(i)==4) varFrameSize(i)=8; elseif(priorities(i)==5) varFrameSize(i)=8; elseif(priorities(i)==6) varFrameSize(i)=4; endend


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varServiceTime = zeros(1, classesNb);% Computing service time variancefor i=1:classesNb, varServiceTime(i) = (64 * varFrameSize(i) ) / ( channelCapacity^2);endETs2 = zeros(1, classesNb);% Computing service time second order statisticsfor i=1:classesNb, ETs2(i) = varServiceTime(i) + (serviceTime(i))^2; end

ro = zeros(1, classesNb);ETw = zeros(1, classesNb);% Computing mean waiting time per class kfor k=1:classesNb, ro(k) = arrivalRate(k) * serviceTime(k); endfor k=1:classesNb,

numerator = 0; denom1 = 0; denom2 = 0; for i=1:k, numerator = numerator + arrivalRate(i) * ETs2(i); end if(k==1) denom1 = 0;

elsefor i=1:k-1, denom1 = denom1 + ro(i); endend

for j=1:k, denom2 = denom2 + ro(j); enddenominator = 2 * (1 - denom1) * (1 - denom2);ETw(k) = numerator / denominator;

end% Computing mean queuing time (latency) per class kETqk = ETw + serviceTime;% Kleinrock's Conservation LawsumRo = sum(ro);r = 0;for i=1:classesNb, r = r + arrivalRate(i) * ETs2(i); endR = 0.5*r;p1 = zeros(1, classesNb);

for i=1:classesNb, p1(i) = ro(i) * ETw(i); endp2 = (( sumRo * R ) / (classesNb * ( 1 - sumRo)));e = zeros(1, classesNb);for i=1:classesNb, e(i) = p1(i) - p2; endsumE = sum(e);stem(ETqk);grid onxlabel('Application Class Number')ylabel('Queueing Time')title('Latencies Versus Traffic Classes')figurestem(p1,'b','LineWidth',3);

grid onxlabel('Application Class Number')ylabel('Sum (ro * ETw)')title('Kleinrock Conservation Law')hold onfor i=1:6, p2Line(i) = p2; endplot(p2Line,'r');

The following is a graph of latencies versus traffic classes and a graph showing if Kleinrock conservation

law applies.


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Note here that Kleinrock's conservation law does not apply



capacity is 171.2 Kbps now.


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The following is a graph of latencies versus traffic classes and a graph showing if Kleinrock

conservation law applies.


B- EDGE technology:



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III- Type of queuing dispatching : Priority Non Resume

A- GPRS technology:


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% Non Preemptive Resume - GPRS - CS1 - 1 TimeSlotclear all;close all;

classesNb = 6;%%%%%%%%%%%%%%%%%%%%%% Traffic Classes %%%%%%%%%%%%%%%%%%%%%%% 1 Voice Messaging %% 2 Telnet %% 3 Audio Streaming %% 4 Video Streaming %% 5 Email %% 6 FTP %%%%%%%%%%%%%%%%%%%%%%

% CS1 - 1 TSchannelCapacity = 9.05 * 1000;% Ascending order = Shortest packet firstaverageFrameSize = [31, 64, 200, 320, 500, 500];arrivalRate = [10.7, 0.512, 20, 64, 4, 55];priorities = zeros(1,classesNb);prioritizedArrivalRate = zeros(1,classesNb);prioritizedAverageFrameSize = zeros(1,classesNb);% Assigning priorities for traffic classesfor i=1:classesNb

priority = input ('Please assign class priority: ');prioritizedArrivalRate(i) = arrivalRate(priority);prioritizedAverageFrameSize(i) = averageFrameSize(priority);priorities(i) = priority;

end% Getting the arrival rate vector in packet/sec with respect to the% assigned prioritiesfor i=1:classesNb, arrivalRate(i) = 1000 * (prioritizedArrivalRate(i) / (8 *averageFrameSize(i))); endserviceTime = zeros(1, classesNb);

% Computing the mean frame service timefor i=1:classesNb, serviceTime(i) = 8 * prioritizedAverageFrameSize(i) /channelCapacity; endvarFrameSize = zeros(1, classesNb);for i=1:classesNb, if(priorities(i)==1) varFrameSize(i)=0; elseif(priorities(i)==2) varFrameSize(i)=6; elseif(priorities(i)==3) varFrameSize(i)=0; elseif(priorities(i)==4) varFrameSize(i)=8; elseif(priorities(i)==5) varFrameSize(i)=8; elseif(priorities(i)==6) varFrameSize(i)=4; end

endvarServiceTime = zeros(1, classesNb);% Computing service time variancefor i=1:classesNb, varServiceTime(i) = (64 * varFrameSize(i) ) / ( channelCapacity^2);


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endETs2 = zeros(1, classesNb);% Computing service time second order statisticsfor i=1:classesNb, ETs2(i) = varServiceTime(i) + (serviceTime(i))^2; endro = zeros(1, classesNb);ETw = zeros(1, classesNb);% Computing mean waiting time per class k

for k=1:classesNb, ro(k) = arrivalRate(k) * serviceTime(k); endfor k=1:classesNb,

numerator = 0; denom1 = 0; denom2 = 0; for i=1:classesNb, numerator = numerator + arrivalRate(i) * ETs2(i); end if(k==1) denom1 = 0;

elsefor i=1:k-1, denom1 = denom1 + ro(i); endend

for j=1:k, denom2 = denom2 + ro(j); enddenominator = 2 * (1 - denom1) * (1 - denom2);ETw(k) = numerator / denominator;

end% Computing mean queuing time (latency) per class kETqk = ETw + serviceTime;% Kleinrock's Conservation LawsumRo = sum(ro);r = 0;for i=1:classesNb, r = r + arrivalRate(i) * ETs2(i); endR = 0.5*r;p1 = zeros(1, classesNb);for i=1:classesNb, p1(i) = ro(i) * ETw(i); endp2 = (( sumRo * R ) / (classesNb * ( 1 - sumRo)));e = zeros(1, classesNb);for i=1:classesNb, e(i) = p1(i) - p2; end

sumE = sum(e);stem(ETqk);grid onxlabel('Application Class Number')ylabel('Queueing Time')title('Latencies Versus Traffic Classes')figurestem(p1,'b','LineWidth',3);grid onxlabel('Application Class Number')ylabel('Sum (ro * ETw)')title('Kleinrock Conservation Law')

hold onfor i=1:6, p2Line(i) = p2; endplot(p2Line,'r');


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conservation law applies

Note here that the Kleinrock's conservation law applies and sumE is equal to zero







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B- EDGE technology:



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The Matlab code used is the same as the previous one with the difference that the channel capacity is

69.2 Kbps now.





The Matlab code used is the same as the previous one with the difference that the channel capacity is

553.6 Kbps now.


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Discussion:


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As we saw from the graphs verifying the Kleinrock's conservation law which

states that The average waiting time for all classes weighted by the traffic (load) of

the mentioned class, is independent of the queue discipline.

We may thus give a small proportion of the traffic a very low waiting time, without

increasing the average waiting time of the remaining customers very much. By

various strategies we may allocate waiting times to individual customers according

to our preferences.

Advanced Teletraffic Project 1

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