average ip packet delay goay

7/28/2019 Average IP Packet Delay Goay

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Due to architectural reasons, all IP packets are queued at the

Logical Link Control (LLC) buffer and are send one by one

to the RLC. Such queuing occurs at the LLC when the packet

arrival rate is greater than the service rate. The delay sensitive

traffic considered here can only tolerate such a circumstance

for very short periods of time. So, the LLC queuing delay is

set to zero here.

The paper is organized as follows: in Section II the analysis

of the transmission of IP packets over a wireless network

together with the methodology of IP packet delay analysis is

presented, while in Section III the delay estimation algorithm is

proposed. Section IV presents the results, being a comparison

between the output from computer simulation and analytical

calculation. Finally in Section V the main conclusions are

expressed.

II. IP PACKET DELAY ANALYSIS METHODOLOGY [3]

In order to chose the methodology of analysis of IP packet

delay it is necessary to examine the nature of the process

being investigating. Having QoS issues in mind for traffic that

demands low delays, it seems that knowledge about an averagedelay of transported IP packets is the most important question

to be answered. Consequently, the analysis of the average delay

of an IP packet being transmitted by a cellular data network is

our main aim.

The process of transporting IP packets over the wireless part

of the cellular networks relies on the protocol stacks structure.

As shown on Figure 1, the wireless protocol stack consists of

the following parts: LLC, RLC, MAC and the Physical Layer

(PHY).

Firstly, every IP packet is mapped into an LLC frame - in the

case studies here, each packet fits into one LLC frame, hence,

the LLC layer influence is omitted from this study. Next, each

LLC frame is fragmented into a number of radio blocks. The

number of radio blocks required to transmit one LLC frame

depends on the Modulation and Coding Scheme (MCS) used

and the size of the particular packet.

At the next step, the radio blocks are queued at the MAC and

wait for access to the radio channel. In already deployed sys-

tems, GPRS has only one available MCS for data transmission,

while EGPRS uses the Incremental Redundancy (IR) technique,

which again uses only one MCS. In these cases the IP packet

delay in the radio part will be dominated by the number of

times that its constituent blocks need to be retransmitted before

decoding. Following that, a radio block is transmitted to a

receiver through the PHY layer.To separate the delay caused by the RLC from that caused by

the MAC, the MACs dynamical influence on the transmission

rate has been omitted from this study. Instead, it is assumed

that every user has a fixed policy of obtaining access to the

radio resources - in the case of GPRS it will be a fixed number

of time-slots shared fairly with other users. This approach

allows the RLC influence to be studied in isolation and allows

the possible future development of MAC strategies that can

compensate for these effects.

IP

LLC

RLC

MAC

PHY

Mapping IP packet into LLC frame(s)

Segmentation of LLC frame into a number of radio blocks

Assigning radio blocks to relevant frequency and timeslot

Sending a radio block, bit by bit ,over a radio channel

Introducing the coding (FEC) and ARQ (BEC) to the radio blocks

Tx

Rx

Fig. 1: Typical cellular networks protocol stack

The influence of the PHY layer on the transmission process is

a more complex problem and is normally focused on modeling

Bit Error Rates. However, due to the FEC mechanism imple-

mented in the RLC it seems that the PHY can be considered

here as an entity for transporting radio blocks and having its

own radio block error characteristic, dependent on the radio

channel condition and chosen MCS.

So, in summary:

1) LLC influence is omitted

2) RLC influence is analyzed and it is the main topic of this

methodology

3) MAC influence is neglected

4) PHY influence is considered at the radio block level

The SR-ARQ technique assures high reliability data trans-

mission over an errored channel by repeating the transmission

of radio blocks that have not successfully reached the receiver.

The transmitter sends a few radio blocks to the receiver and

after a period of time, determined by the transmission window

size, expects to get a report from the receiver telling which radio

blocks were successfully transmitted and which were not. The

size of the transmission window is denoted by NPoll. When

the report is received, the transmitter sends again those radioblocks that have been errored. This improves the reliability

of the connection, however, it introduces additional delay to

transmitted radio blocks. The delay associated with the first

retransmission does not have to be the same as the delay

associated with the second retransmission attempt. Therefore

instead of one number describing the delay, a vector of delays,

called , is introduced. This vector represents the additionalaverage delay associated with the first, second, third and error

transmission attempt, 1, 2, 3, e, respectively.


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=

123e

(1)

Selecting an appropriate level of modeling accuracy of the

PHY layer is crucial to this work as a bit based model is overly

cumbersome for our purposes. Even modelling the PHY as asimple Block Error Rate (BLER) is not a sufficient solution

if more advanced BEC, in the form of Hybrid Type-II or

Incremental Redundancy (IR), is deployed. In IR, the receiver

combines information from all transmission attempts, so that

the first transmission attempt has less chance of success than

the second and third one. Hence, the BLER is different for

each transmission attempt. Thus, we allow a different BLER

for first, second and third transmission attempt by counting the

number of radio blocks successfully received at the first, second

and third attempt. This data gives a statistical description of

the channel from a radio block perspective, which simplifies

and generalises the methodology. The probabilities vector is

denoted by P and has the following form:

P =

p1p2p3pe

(2)

Where its elements: p1, p2, p3, pe represent the probability

of successful transmission of a certain radio block at the first,

second, third attempt or unsuccessful transmission after the

third try, respectively.

The pe represents the probability of error after three trans-

mission attempts and e is the additional delay related to such

a scenario. However, this paper does not address the issue

of reliability, so it is assumed that pe is small enough to be

considered to be zero. Therefore, e is assumed to be zero

valued.

The methodology chosen then uses the following input

information:

Traffic is described by the size of a single IP packet, being

transported in the data stream, denoted by IPsize. The

stream contains packets with fixed size as a result of the

assumption that VoIP, as an example of Conversational

traffic, is the traffic source.

ARQ loop design is described by a vector of extra delay

associated with each transmission attempt, called . This

vector stores information about the extra delay experiencedby a radio block if retransmission is necessary. This time

covers the period between the recognition of a failed trans-

mission at the receiver and the subsequent retransmission

attempt at the transmitter.

Radio channel influence is represented by a vector of

probabilities of successful transmission at the first, second,

third time and probability of non-successful transmission,

named P. The number of transmission attempts is limited

to three, due to the assumption that conversational traffic is

being transported. This class of traffic is characterized by

strict delay limits. Therefore, further transmission attempts

would occupy radio resources without any additional ben-

efit, as the delay would be too large for a VoIP packet to

be played out by the application layer.

Having the problem defined in this way,a computer simula-

tion model has been built as shown in Figure 2. The simulations

generated a series of statistics that are used for comparisonpurposes to validate the results from the IP packet delay

estimation technique that will now be presented.

Y ... 2

1

Y ... 2 1

IP[x-4]

IP[x-3]

IP[x-2]

IP[x-1]

Point A

Point B

ARQ loop

IP[x+4]

IP[x+3]

IP[x+2]

IP[x+1]

Point CIP packet delay

Stream of IP packets

with equal size

Tx Rx

Transmission buffer Service queue

Y ... 2 1

ed

3d

2d

1d

sd

pe

p3 pe+p2 +

p3 pe+

p1 p2+ p3 pe++

Fig. 2: Methodology description model

III. PROPOSAL OF IP DELAY ESTIMATION TECHNIQUE

Considering the IP packet delay mechanisms presented

above, the process of transportation of an IP packet is asfollows. First an IP packet is mapped into a number of radio

blocks. The number of radio blocks, called Y, depends on the

relationship between the size of the packet, IPsize, and the

payload size of selected MCS, RBPayloadsize, as shown in

equation 3.

Y =

IPsize

RBPayloadsize

(3)

After mapping the packet into this number of radio blocks,

these blocks are sent to a receiver over the radio channel.

Some of them successfully reach the receiver at the first

transmission attempt, but a fraction of these Y radio blocks haveto be transmitted two or three times before being successfully

received. This creates the situation where 3Y different IP packettransmission scenarios exist. Consequently, the following ques-

tions come up:

1) How to mathematically describe all possible scenarios?

2) What is the probability of a particular scenario happen-

ing?

3) What IP packet delay is expected for a particular sce-

nario?


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A. The mathematical representation of all scenarios

The mathematical representation of all possible scenarios

chosen here is a matrix, named R. Each row, denoted by

i, represents one possible transmission scenario, the columns,

denoted j, show the order of radio blocks in the transmission

buffer. Each element takes the value of the number of trans-

mission attempts associated with the specific radio block within

each scenario. Hence the matrix has the following form:

R =

r1,1 r1,2 r1,Yr2,1 r2,2 r2,Y

......

. . ....

r3Y ,1 r3Y ,2 r3Y ,Y

(4)

Where:

ri,j represents the number of transmission attempts ex-

perienced by the jth radio block of the ith possible

transmission scenario. In the case of a retransmission free

scenario, all ri,j of a particular i will be equal to one.

i 1, 2, 3, , 3Y

represents one of the 3Y possible

scenarios of transporting an IP packet which has a size ofY radio blocks.

j {1, 2, 3, , Y} represents the position of the radioblock in the transmission queue, in the ith transporting

scenario.

B. Probability of different scenarios

Knowing all possible scenarios, we can now create a vector

of order 3Y , denoted by S, that stores the probabilities ofoccurrence for each scenario. The probability of the ith trans-

mission scenario occurring is the product of the probabilities

of successful transmission of all its constituent radio blocks.

The probabilities of successful transmission of a radio block

at a particular attempt is stored in the vector P, which is oneof the initial parameters. However, these probabilities have to

be linked appropriately with the status of a particular radio

block. Therefore, the matrix R, is used to determine the number

of transmission attempts associated with this particular radio

block. Consequently, each element of R is an index of an

element of vector P. Hence, S has the following form:

S=

s1s2...

s3Y

(5)

Where:

si =Yj=1

pri,j represents the probability that ith constel-

lation of radio blocks will occur during the transmission

of IP packet.

C. Delay associated with different scenarios

When the IP packet is fragmented into radio blocks, these

radio blocks are sent to the transmission buffer where they wait

for access to the radio channel. The scale of the associated

queuing delay depends on the position of a radio block in

the transmission buffer, as the last radio block has to wait

at least Y-1 time-slots to be transmitted while the first radio

block experiences zero delay. Secondly, the retransmission of

errored blocks will not be performed instantaneously and the

radio block will experience some additional delay related to this

phenomena. Finally, the radio block with a larger number of

transmission attempts has a higher priority to obtain access to

the radio resources, in comparison to a radio block with a lower

number of transmission attempts. This priority mechanism

prevents dead lock situations from happening, yet, it postpones

the transmission of all radio blocks queuing in the transmission

buffer. These three phenomena have different effects on the total

delay of transported IP packet.

Starting with the representation of the total delay. Since all

possible scenarios have to be considered, the natural represen-

tation of the total delay is a vector that stores delays for every

possible constellation of Y radio blocks. The vector size is 3Y

and the row index i indicates a particular scenario. Thus,

Total =

Total1

Total2

...

Total3Y

(6)

Where:

Totali represents the delay of an IP packet when its radio

blocks have experienced the transmission attempt scenario

stored the ith row of the R matrix.

The radio blocks queuing in the transmission buffer expe-

rience a delay that is determined by the place of a particular

block in the queue. Consequently, the delay associated with

this phenomena, denoted by si,j, is equal to the index of the

radio block decremented by 1, since the delay of the first radioblocks is zero. Hence, si,j = j 1.

The process of sending a request for the retransmission of

errored transmitted radio blocks takes time and this delay has

to be taken into the account as well. The data to model this

problem is stored in the vector . If a radio block is transmittedonce, then it experiences a delay of a

1= 1 + s, where s

represents the time necessary for the medium for a successful

transmission. This time is normalised to one, and any other

delay is expressed as a multiple of it. For higher number of the

transmission attempts the situation looks the following: a2 =

a1

+ 2 + s, a3

= a2

+ 3 + s, ae =

a3

+ e.

a =

a1a2

a3

ae

(7)

The vector a therefore represents the accumulated influenceof the retransmission delay on the radio blocks being transmit-

ted once, twice, etc..

Having this vector, it is easy to find the delay of radio blocks

caused by the non-instantaneous retransmission phenomena.


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For a particular transmission scenario, indicated by i, and a

particular radio block labeled by j, we can find the associated

number of transmission attempts, ri,j. Hence, by linking the

number of transmission attempts with the relevant delay asso-

ciated with it, we can obtain the retransmission influence on

the delay of the considered radio block. Thus, ri,j = ari,j

.

To combine the influence of these two phenomenon on the

total IP packet delay, lets create a matrix, denoted by Dt,

representing the sum of these delays. Accordingly, the element

of this matrix is ti,j = si,j +

ri,j.

Dt =

t1,1

t1,2

t1,Y

t2,1

t2,2

t2,Y

......

. . ....

t3Y ,1

t3Y ,2

t3Y ,Y

(8)

The last radio block to reach the receiver effectively deter-

mines the total delay of a particular IP packet. Thus, if each row

of the matrix Dt is searched for the largest element, then this

element represents the delay of the last radio block related to the

ith transmission scenario. Lets create a vector Maxrowtstoring these delays.

Maxrowt =

Maxrowt1

Maxrowt2

...

Maxrowt3Y

(9)

Where:

Maxrowti is the maximum value from the ith row of

the Dt matrix.

In the case where the retransmitted radio blocks compete

for access to the radio resources with the radio blocks in the

transmission buffer, they slow down other radio blocks.Retransmission of a radio block has priority access, and takes

one time-slot, thus, the entire IP packet is slowed by one time-

slot. Moreover, in the case of a radio block experiencing two

retransmission attempts, which is equal to three transmission

attempts, the IP packet is slowed by two time-slots. Hence,

knowing the number of transmission attempts of a particular

radio block, the influence of this radio block on the IP packet

transmission delay can be calculated.

Since every radio block causing the priority stop will slow

down the entire transmission of the packet, the influence of

all such radio blocks needs to be accumulated. Therefore, the

following vector, named Sumq, storing this accumulated

delay caused by priority retransmission is created:

Sumq =

Sumq1

Sumq2

...

Sumq

3Y

(10)

Where:

Sumqi =

Yj=1

(ri,j 1)

These different contributions can now be combined to find a

technique of calculating Total vector.Now, by adding the vector Maxrowt, to the vector

Sumq the total delay for each possible transmission caseis obtained.

Total = Sumq + Maxrowt (11)

D. Main formula

Since vectors S and Total are defined and can be calcu-lated, then the average delay of the transported IP packet can

be computed as well. It is done by calculation of the weighted

average of delays of all possible scenarios. Thus, the final

formula looks like:

delayIPpacket =

3Y

i=1

Totali si

(12)

IV. RESULTS

Since the formula allowing for analytical calculation of the

estimation of average IP packet delay is known, the comparisonof results obtained from simulation and calculation is required

for validation. Simulation results come from the system that

was built in a general purpose simulator environment, called

SES workbench, and is shown in Figure 2. The simulations are

made with the same values ofP, and IPsize as the relevantcalculation. For space reasons, all vectors in the result section

are expressed in the transposed form.

The results shown below represent simulations and calcula-

tions for the following settings:

IP packet size, IPsize, varying in the range of 1 to 12

radio blocks, with 10,000 transmissions performed for

each packet size.

The P vector is represented in five forms, and each ofthem represents a different radio channel condition. The

first case, called T0, represents a situation where only 10

percent of radio blocks have to be retransmitted, while

cases T1, T2, T3 and T4 represent worsening retransmis-

sion scenarios.

1) T0 - P = [0.9; 0.07;0.03;0.0]T

, which means that

we assume that 90 percent of radio blocks will

reach the receiver at the first transmission attempt,

7 percent at the second attempt, and 3 percent at

the third attempt. The last position is zero and it

indicates that in this scenario there are no errors

experienced by any of the radio blocks after thesecond retransmission. The other cases, T1 to T4,

can be interpreted in the same way.

2) T1 - P = [0.6; 0.3; 0.1; 0.0]T

3) T2 - P = [0.3; 0.4; 0.3; 0.0]T

4) T3 - P = [0.1; 0.3; 0.6; 0.0]T

5) T4 - P = [0.03;0.07;0.9; 0.0]T

Using a memoryless receiver, it is expected to see a

relation between the transmission attempts looking like:

p1, p2 = p1 p1 and p3 = p1 p1 p1. However, soft


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decoding, and Incremental Redundancy (IR) in particular,

breaks this relationship. Nevertheless, the case T4 may still

look unrealistic, but, it is expected that the progress in cod-

ing theory may cause very different relationship between

following transmission attempts. Thus, for underlining the

generality of our method, the different configurations of

the P vector have been investigated.

= [0; 8;13;0]T

, which means that it is assumed that the

delay is caused by the interaction between the ARQ system

and lower level transmission delays. This vector represents

the design of the SR-ARQ loop, and here it is assumed that

the Transmission Window Npoll, is set to 10 radio blocks.

The zero means that the first transmission of a radio block

experiences only the delay caused by queuing in the RLC

layer and the transmission delay is one block period. The

eight represents the time necessary for the ARQ feedback

for the first radio block retransmission and is composed

of one block period for reception and decoding, five block

periods as the average occupancy of the polling buffer

at the receiver, another block period is required for the

return of the ACK message and another block period forreception and processing at the transmitter. The thirteen

represents the time delay due to the feedback delay for the

second retransmission which is similar to that of the first

retransmission, except that this block was errored during

the last polling period so that it will have been inserted at

the head of the transmission queue. It will, therefore, be

the first errored block in the polling buffer at the receiver,

so that its polling buffer delay will be equal to the full

length of that queue, rather than its mean occupancy. Zero

in the last position indicates that in this scenario there is

no delay due to the error of radio block after the second

retransmission.

0

10

20

30

40

50

60

70

0 2 4 6 8 10 12

Delay[radioblockperiods]

IP packet size [radio blocks]

Sim for T0Calc for T0Sim for T1Calc for T1Sim for T2Calc for T2Sim for T3Calc for T3Sim for T4Calc for T4

Fig. 3: Simulated and calculated average IP packet delay vs its

size for five different settings of P vector.

The results, shown in Figure 3, indicate that the proposed

methodology performs very well in all cases. Interestingly, for

the cases representing high levels of retransmission, T3 and

T4, the proposed technique overestimates the average delay

of small IP packets, between one and four blocks long, while

for larger packets the technique underestimates the delay. This

phenomena distinguishes the last two cases from the first three,

where the error is an offset having a different value.

Since it is unlikely that the system will transport data under

heavy retransmission conditions, it seems likely that real-life

scenarios will be somewhere between case T0 and T3. Thus,

the general accuracy of the introduced method is good, as the

difference between simulation and calculation is less than 2

radio block periods for cases T0, T1, T2 and T3.

V. CONCLUSIONS

A novel technique for the statistical estimation of the average

delay of IP packets transported over a wireless channel with an

SR-ARQ loop is proposed. This method represents a practical

approach since the data required for the vectors and P maybe easily collected in real-time.

The accuracy of the technique is assessed by comparison

to a simulation with identical system architecture. The results

of this comparison are promising, as the differences between

simulation and calculation are marginal. The highest error is

experienced for an exceptionally high ratio of retransmissions,

case (T4), although for low and medium retransmission levels

the error introduced by the proposed technique is small.

Since the size of the matrices used here grow exponentially

with the size of the transported IP packet, the practical use

of the proposed technique is limited to small packets. Further

work will address the issue of large IP packet size.

The values of delay analyzed in this work represent the most

optimistic scenario, as, queuing at the LLC buffer and core IPnetwork delays are not considered. Additionally, each cellular

network has its own protocol mechanisms that may affect the

delay. For example, the time unit in GPRS/EGPRS is 20 ms,

while in UMTS it is 10 ms. That simple issue greatly affects

the delay of IP packets. If the RLC delay budget is 100ms, then

from case T0 in Figure 3, VoIP packets in GPRS/EGPRS must

have less than two radio blocks, while in UMTS the packets

can be greater than four radio blocks long. Thus, UMTS can

send higher quality VoIP than GPRS/EGPRS within the same

delay budget and independent of the higher bandwidth offered

by UMTS.

The knowledge about the RLC influence on the IP packet

can be passed into the MAC. It can enrich the performancedescription of a channel, since the MAC may have access to

the C/I and BLER statistics that represent a bit and radio block

level of performance description. Therefore, the MAC can have

a better radio channel description and may use more advanced

scheduling algorithms to deliver better Quality of Service. The

IP packet predicted delay performance may be passed as well

to higher protocol layers, and be used by the Radio Resource

Management unit (RRM) or even higher by some application

layer adaptation mechanisms.


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