An Exploration Of Calculating The Packet Loss Rate 
State Key Laboratory of Networking and Switching Technology Beijing University of Posts and Telecommunications 
Corresponding author 
method  for  link  packet  loss  rate  .An  intermediate  quantity  is  
deduced from the block rate, Through this intermediate quantity 
to further solve the packet loss rate.
Keywords—network; links; WDM; packet loss rate 
At  the  same  time,  network  traffic  has  increased  
network   performance   becomes   more   and   more   important.
probability of such instability, which is called the packet loss rate.
Packet Loss Rate refers to the ratio of the number of packets lost 
required that we can successfully estimate the packet loss rate by 
packet loss rate of the entire network.
the blocking rate may be compared with the measurement of the 
loss rate, so this paper tries to propose a new method to estimate 
multicast address and the receiver only needs to tell the network 
transmission information of multicast network can be considered 
the packet loss rate is considered as unicast model in this paper.
B. Considering the Situation of link Network 
In the process of measuring the packet loss rate, The basis is 
to consider the current link network situation.
The link network 
follows, Any two nodes are connected by a link that determines 
converter that can be applied between partial wavelengths is set 
analyzing the converter with wavelength conversion, Therefore, 
this paper adopts the method of analyzing the condition without 
The probability of k paths where the wavelength is a certain 
value (λ) and between two certain nodes (i, j) all being blocked 
Calculate the value of the auxiliary variables use the method 
which  is  in  the  link  without  wavelength  converter,  solve  the  
block rate by two methods.
block rate is.
The probability that use the determined wavelength 
is  the  probability  of  k  paths  where  the  wavelength  is  a  
H+1 represents the number of nodes that need to pass 
So  the  probability  that  a  single  wavelength  cannot  be  
transmitted  successfully  is  called  the  blocking  rate  can  be  
So the probability that all wavelengths cannot be transmitted 
successfully is called the blocking rate can be solved .Results are 
w represents the number of wavelength categories contained 
Let's solve the block rate the other way, We break up the 
whole  link  network  into  countless  point-to-point  connections.
In this way, we first need to consider: network load on certain 
represent  all  links  in  the  total  arrival  rate.
number of links between two nodes.
using  some  certain  wavelength,  he  probability  of  successful  
probability that the optical path is successfully established when 
also is the probability of blocking is: 
So we can then figure out what the block rate is: 
OLVE THE PACKET LOSS RATE IN LINKS WITHOUT 
WAVELENGTH CONVERTER  
transmission efficiency of the link.
packet    loss    rate    of    each    wavelength    was    recorded    
In a network without wavelength converters, Information is 
transmitted  at  a  certain  wavelength.
wavelength selection algorithm.
at the same time, we are forced to use links with higher packet 
loss  rates,  as  the  higher  ranked  wavelengths  may  have  been  
content  of  this  algorithm  is  to  select  the  wavelength  with  the  
lowest packet loss rate from the current available wavelength to 
In  this  algorithm,  we  first  analyze  the  probability  of  each  
transmission  channels  of  other  wavelengths  prior  to  the    ߣ
wavelength between the two nodes are occupied is: 
The probability that the transmission channel which precedes 
the other wavelength of wave length ߣ
Therefore,    we    can    obtain    the    probability    that    the    
transmission  channel  of  all  the  nodes  is  occupied  before  the  
wavelength of ߣ
Therefore, the packet loss rate is: 
OLVE THE PACKET LOSS RATE WITH WAVELENGTH 
CONVERTER LINK 
When  we  analyze  the  packet  loss  rate,  we  can  convert  the  
calculation  of  the  packet  loss  rate  in  the  whole  transmission  
process into partial packet loss rate.
wavelength converter in between so that each small segment can 
be  processed  into  a  simple  part  without  wavelength  converter.
So the number of nodes that have each segment going through is 
can  obtain  the  packet  loss  rate  of  the  whole  link.
probability      that      the      wavelength      occupied      before      
Therefore, the packet loss rate of each small segment is: 
The packet loss rate can be obtained as follows: 
The calculated results obtained by the algorithm in this paper 
transmission capacity of complex network,9787512124745.
Lun  ,Introduction  to  network  
An Exploration Of Calculating The Packet Loss Rate 
By Using The Block Rate  
Fan Bu
*
 
School of Software Engineering 
State Key Laboratory of Networking and Switching Technology Beijing University of Posts and Telecommunications 
*
Corresponding author 
 
Abstract—This electronic document is about New estimation 
method  for  link  packet  loss  rate  .An  intermediate  quantity  is  
deduced from the block rate, Through this intermediate quantity 
to further solve the packet loss rate. 
Keywords—network; links; WDM; packet loss rate 
I. INTRODUCTION  
In  recent  years,  with  the  increasing  expansion  of  computer  
network scale, the unstable factors in the network are increasing 
under   the   influence   of   equipment   diversity   and   network   
complexity.  At  the  same  time,  network  traffic  has  increased  
sharply, and various new businesses, such as video conference, 
video   on   demand,   P2P,   etc.,   are   also   devouring   network   
resources  at  an  extremely  fast  speed.  The  measurement  of  
network   performance   becomes   more   and   more   important.   
	
ሾଵሿ
Therefore,  it  is  necessary  to  estimate  the  probability  of  
information    transmission    instability    before    infrastructure    
construction.   
Therefore,   we   introduce   a   new   variable   to   reflect   the   
probability of such instability, which is called the packet loss rate. 
Packet Loss Rate refers to the ratio of the number of packets lost 
in  the  test  to  the  data  group  sent.  The  calculation  method  is:  
[(incoming      message      -      output      message)/      incoming      
message]*100%.	
ሾଶሿ
 
However,  in  practical  applications,  such  estimation  usually  
takes place before the construction of the entire network, so it is 
required that we can successfully estimate the packet loss rate by 
relying  on  some  parameters  in  the  network.  In  the  usual  
calculation,  direct  logical  calculation  is  used  to  estimate  the  
packet loss rate of the entire network. 
In some cases in our usual application, the measurement of 
the blocking rate may be compared with the measurement of the 
loss rate, so this paper tries to propose a new method to estimate 
the loss rate using the reverse blocking rate. 
II. M
ODEL ANALYSIS  
A. Selecting a Template 
A key feature of the multicast communication model is the 
multicast  group  that  provides  indirect  identification.  Neither  
sender  nor  receiver  needs  to  know  the  other  party's  specific  
conditions.  The  sender  only  needs  to  send  the  packet  to  a  
multicast address and the receiver only needs to tell the network 
that  it  wants  to  receive  the  packet  that  sent  it.  Therefore,  the  
transmission information of multicast network can be considered 
as  the  transmission  of  two  unicast  model  segments.  Therefore,  
the packet loss rate is considered as unicast model in this paper. 
B. Considering the Situation of link Network 
In the process of measuring the packet loss rate, The basis is 
to consider the current link network situation. The link network 
model analyzed in this paper is WDM model. We abstract it as 
follows, Any two nodes are connected by a link that determines 
the  number  of  bars  (k  bars).  Each  of  these  links  has  a  certain  
number  of  (w  kinds)  wavelengths  to  transmit,  A  wavelength  
converter that can be applied between partial wavelengths is set 
up  at  some  of  the  nodes.  Because  of  the  difficulty  of  directly  
analyzing the converter with wavelength conversion, Therefore, 
this paper adopts the method of analyzing the condition without 
wavelength converter first. 
C. Reference Auxiliary Variables 
The probability of k paths where the wavelength is a certain 
value (λ) and between two certain nodes (i, j) all being blocked 
(This variable are recorded as C
୩
). 
III. S
OLVE THE UXILIARY VARIABLES BY THE BLOCK 
RATE 
Calculate the value of the auxiliary variables use the method 
which  is  in  the  link  without  wavelength  converter,  solve  the  
block rate by two methods. 
A. Solution Method 1 
So,  first  of  all,  we're  going  to  use  C
୩
to  figure  out  what  the  
block rate is. The probability that use the determined wavelength 
passes smoothly between all nodes can be solved. Results are as 
follows. 
					ܲ
λ
ൌሺ1െܥ
௞
ሻ
ு
                                   (1) 
  is  the  probability  of  k  paths  where  the  wavelength  is  a  
certain value (λ) and between two certain nodes(i ,j) all being 
blocked. H+1 represents the number of nodes that need to pass 
through for transmission. 
So  the  probability  that  a  single  wavelength  cannot  be  
transmitted  successfully  is  called  the  blocking  rate  can  be  
solved .Results are as follows: 
ܥ
଴
ൌ1െܲ
λ	
ൌ1െሺ1െܥ
௞
ሻ
ு
                     (2) 
3rd International Conference on Communications, Information Management and Network Security (CIMNS 2018)
Copyright © 2018, the Authors. Published by Atlantis Press. 
This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/). 
Advances in Computer Science Research, volume 65
147

So the probability that all wavelengths cannot be transmitted 
successfully is called the blocking rate can be solved .Results are 
as follows: 
ܥ
ଵ
ൌሺ1ܲ	—
λ
ሻ	
௪
ൌሺ1െሺ1െܥ
௞
ሻ
ு
ሻ	
௪
             (3) 
w represents the number of wavelength categories contained 
in each link 
B. Solution Method 2 
Let's solve the block rate the other way, We break up the 
whole  link  network  into  countless  point-to-point  connections.  
In this way, we first need to consider: network load on certain 
connection ( denote asL
୧୨
) : 
   	
ܮ
௜௝
ൌ
∑
ோ
ೞ೏ೞ，೏సబ
௞
                                   (4) 
{}  is  represented  call  arrival  rate  per  unit  time  from  
node  s  to  node  d,  When  s  is  equal  to  d  ܴ
௦ௗ
ൌ0,therefore 
∑
ܴ
௦ௗ௦，ௗୀ଴
represent  all  links  in  the  total  arrival  rate.  k  is  the  
number of links between two nodes. 
We can derive from these inferences that in the case of just 
using  some  certain  wavelength,  he  probability  of  successful  
response  to  the  call  isܮ		
పఫ
തതതത
.  In  turn,  we  can  obtain  that  the  
probability that the optical path is successfully established when 
a signal is applied to transmit from i to j is: 
 f
ሺ
i,j
ሻ
ൌ1െሺ1െ
∑
ܮ
పఫ
തതതത
௪
௜,௝ୀଵ
ሻ
௞
                       (5) 
Then the light path cannot be successfully established, that 
also is the probability of blocking is: 
ܥ
௜௝
ൌ1െ݂
ሺ
݆,݅
ሻ
                                    (6) 
So we can then figure out what the block rate is: 
ܥ
ଵ
ൌ
∑
ோ
ೞ೏
஼
೔ೕ
ೞ
，೏సభ
∑
ோ
ೞ೏ೞ，೏సబ
                                   (7) 
C. Simultaneous Exploration 
Simultaneous equation: 
∑
ோ
ೞ೏
஼
೔ೕ
ೞ
，೏సభ
∑
ோ
ೞ೏ೞ，೏సబ
ܥൌ
ଵ
ൌሺ1—	ܲ
ఒ
ሻ	
௪
ൌሺ1െሺ1െܥ
௞
ሻ
ு
ሻ	
௪
 (8) 
Therefore, we can calculate the expression of: 
ܥ
௞
ൌ1െ
ඨ
ሺ1െ ට
∑
ோ
ೞ೏
஼
೔ೕ
ೞ
，೏సభ
∑
ோ
ೞ೏ೞ，೏సబ
ೢ
ሻ
ಹ
                     (9) 
IV. S
OLVE THE PACKET LOSS RATE IN LINKS WITHOUT 
WAVELENGTH CONVERTER  
After  Before  starting,  we  should  first  test  the  specific  
transmission efficiency of the link. The performance of multiple 
optical  fibers  is  measured  and  averaged  to  obtain  data.  The  
packet    loss    rate    of    each    wavelength    was    recorded    
asܲሼ
ଵ
ܲ,
ଶ
ܲ,
ଷ
ܲ
ସ
ܲ,
ହ
.......ܲ
௪
ሽ.         To         correspond         
{ߣ
ଵ
ߣ,
ଶ
ߣ,
ଷ
ߣ	
ସ
,........ߣ
௪
}    these  several  wave  length.  And  to  
make it easier to write, we're going to rearrange the probabilities 
of these packets in order from small to large. Get a new set of 
data {ܲ
ଵ
ܲ,
ଶ
ܲ,
ଷ
ܲ
ସ
ܲ,
ହ
.......ܲ
௪
}.and{ߣ
ଵ
ߣ,
ଶ
ߣ,
ଷ
ߣ	
ସ
,........ߣ
௪
} . 
A. Allocation Algorithm Analysis 
In a network without wavelength converters, Information is 
transmitted  at  a  certain  wavelength.  on  this  occasion,  It  is  
necessary  that  we  first  define  the  most  reasonable  method  of  
wavelength assignment. We analyze the implementation of the 
wavelength selection algorithm. First, the packet loss rate of this 
wavelength must be the lowest under the current situation. But 
at the same time, we are forced to use links with higher packet 
loss  rates,  as  the  higher  ranked  wavelengths  may  have  been  
consumed   by   previous   transmissions.   Therefore,   the   main   
content  of  this  algorithm  is  to  select  the  wavelength  with  the  
lowest packet loss rate from the current available wavelength to 
complete the transmission	
ሾଷሿ
. 
B. The Specific Calculation 
In  this  algorithm,  we  first  analyze  the  probability  of  each  
wavelength   being   enabled.   The   probability   that   all   the   
transmission  channels  of  other  wavelengths  prior  to  the    ߣ
௜
 
wavelength between the two nodes are occupied is: 
ܥ
௜
ܥൌሺ
௞
ሻ
௜ିଵ
ሺ1െܥ
௞
ሻ                            (10) 
The probability that the transmission channel which precedes 
the other wavelength of wave length ߣ
௜
 between two nodes is not 
occupied is: 
ܥ
௜
ൌ1െሺܥ
௞
ሻ
௜ିଵ
ሺ1െܥ
௞
ሻ                       (11) 
Therefore,    we    can    obtain    the    probability    that    the    
transmission  channel  of  all  the  nodes  is  occupied  before  the  
wavelength of ߣ
௜
 : 
ܥ
௜
ൌ
∑
		
ሺ
ܥሺ
௞
ሻ
௜ିଵ
ሺ1െܥ
௞
ሻሻ
௝
ሺ
1െሺܥ
௞
ሻ
௜ିଵ
ሺ1െܥ
௞
ሻሻ
ுି௝
				
ுିଵ
௝ୀଵ
 
(12) 
ܥ
௜
ൌ		ሾ
ሺ
ܥሺ
௞
ሻ
௜ିଵ
ሺ1െܥ
௞
ሻሻ൅1െሺܥ
௞
ሻ
௜ିଵ
ሺ1െ	ܥ
௞
ሻሿ
ு
െ
ሺ
1െሺܥ
௞
ሻ
௜ିଵ
ሺ1െܥ
௞
ሻሻ
ு
                          (13) 
Transformation from (12) to (13) use knowledge of  binomial 
theorem.
	 
Therefore, the packet loss rate is: 
ܦ
௥
ൌ
∑
ܥ
௜
ܲ∗
௜
௪
௜ୀଵ
                              (14) 
V. S
OLVE THE PACKET LOSS RATE WITH WAVELENGTH 
CONVERTER LINK 
When  we  analyze  the  packet  loss  rate,  we  can  convert  the  
calculation  of  the  packet  loss  rate  in  the  whole  transmission  
process into partial packet loss rate. Separate by the wavelength 
converter  in  the  link,  ensuring  that  each  separate  part  has  no  
Advances in Computer Science Research, volume 65
148

wavelength converter in between so that each small segment can 
be  processed  into  a  simple  part  without  wavelength  converter.  
So the number of nodes that have each segment going through is 
{ܪ
ଵ
൅1,ܪ
ଶ
൅1,ܪ
ଷ
൅1,ܪ
ସ
൅1..................ܪ
௠
൅1}(  The  
number  of  segments  divided  is  denoted  as  m)  In  this  way,  we  
can  obtain  the  packet  loss  rate  of  the  whole  link.  Then  the  
probability      that      the      wavelength      occupied      before      
λ
୧
		in	the	j	segment	is: 
ܥ
௜
௝
ൌ		ሾ
ሺ
ܥሺ
௞
ሻ
௜ିଵ
ሺ1െܥ
௞
ሻሻ൅1െሺܥ
௞
ሻ
௜ିଵ
ሺ1െܥ
௞
ሻሿ
ு
ೕ
െ
ሺ
1െሺܥ
௞
ሻ
௜ିଵ
ሺ1െܥ
௞
ሻሻ
ு
ೕ
                      (15) 
Therefore, the packet loss rate of each small segment is: 
ܦ
௥
௝
ൌ
∑
ܥ
௜
௝
ܲ∗
௜
௪
௜ୀଵ
                            (16) 
The packet loss rate can be obtained as follows: 
ܦ
௥
ൌ
∏
ܦ
௥
௝
௠
௝ୀଵ
                                 (17) 
VI. T
EST THE RESULTS 
The calculated results obtained by the algorithm in this paper 
are compared with the actual results to solve the variance. The 
results are as figure I: 
 
 
 
 
FIGURE I.  RESULTS OF TWO SIMULATION EXPERIMENTS. 
REFERENCES 
[1]  [US] James F. Kurose  [US]Keith W. Ross  ,Computer network (edition 
5), China Machine Press 
[2] Zhongyuan   Jiang,   Mangui   Liang,   analysis   and   optimization   of   
transmission capacity of complex network,9787512124745. 
[3] [Singapore]Tracey  Ho    [Aus]Desmond  S.  Lun  ,Introduction  to  network  
coding China Machine Press 
[4]  Department  of  mathematics,  tongji  university,  Advanced  mathematics  
(7th edition),Higher Education Press 
Advances in Computer Science Research, volume 65
149