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.
So  the  probability  that  a  single  wavelength  cannot  be  transmitted  successfully  is  called  the  blocking  rate  can  be  solved .Results are as follows: ܥ଴ൌ1െܲλ	ൌ1െሺ1െܥ௞ሻு                     (2) 3rd International Conference on Communications, Information Management and Network Security (CIMNS 2018)Copyright © 2018, the Authors.
Advances in Computer Science Research, volume 65147So the probability that all wavelengths cannot be transmitted successfully is called the blocking rate can be solved .Results are as follows: ܥଵൌሺ1ܲ	—λሻ	௪ൌሺ1െሺ1െܥ௞ሻுሻ	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.
SOLVE THE PACKET LOSS RATE IN LINKS WITHOUT WAVELENGTH CONVERTER  After  Before  starting,  we  should  first  test  the  specific  transmission efficiency of the link.
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.
SOLVE 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.
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.   	ሾଵሿTherefore,  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. MODEL 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 C୩). III. SOLVE 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  C୩to  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. 					ܲλൌሺ1െܥ௞ሻு                                   (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଴ൌ1െܲλ	ൌ1െሺ1െܥ௞ሻு                     (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 65147So the probability that all wavelengths cannot be transmitted successfully is called the blocking rate can be solved .Results are as follows: ܥଵൌሺ1ܲ	—λሻ	௪ൌሺ1െሺ1െܥ௞ሻுሻ	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 asL୧୨) :    	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  ܴ௦ௗൌ0,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		పఫതതതത.  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:  fሺi,jሻൌ1െሺ1െ∑ܮపఫതതതത௪௜,௝ୀଵሻ௞                       (5) Then the light path cannot be successfully established, that also is the probability of blocking is: ܥ௜௝ൌ1െ݂ሺ݆,݅ሻ                                    (6) So we can then figure out what the block rate is: ܥଵൌ∑ோೞ೏஼೔ೕೞ，೏సభ∑ோೞ೏ೞ，೏సబ                                   (7) C. Simultaneous Exploration Simultaneous equation: ∑ோೞ೏஼೔ೕೞ，೏సభ∑ோೞ೏ೞ，೏సబܥൌଵൌሺ1—	ܲఒሻ	௪ൌሺ1െሺ1െܥ௞ሻுሻ	௪ (8) Therefore, we can calculate the expression of: ܥ௞ൌ1െඨሺ1െ ට∑ோೞ೏஼೔ೕೞ，೏సభ∑ோೞ೏ೞ，೏సబೢሻಹ                     (9) IV. SOLVE 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    asܲሼଵܲ,ଶܲ,ଷܲସܲ,ହ.......ܲ௪ሽ.         To         correspond         {ߣଵߣ,ଶߣ,ଷߣ	ସ,........ߣ௪}    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 {ܲଵܲ,ଶܲ,ଷܲସܲ,ହ.......ܲ௪}.and{ߣଵߣ,ଶߣ,ଷߣ	ସ,........ߣ௪} . 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௜ିଵሺ1െܥ௞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௜ିଵሺ1െܥ௞ሻ                       (11) Therefore,    we    can    obtain    the    probability    that    the    transmission  channel  of  all  the  nodes  is  occupied  before  the  wavelength of ߣ௜ : ܥ௜ൌ∑		ሺܥሺ௞ሻ௜ିଵሺ1െܥ௞ሻሻ௝ሺ1െሺܥ௞ሻ௜ିଵሺ1െܥ௞ሻሻுି௝				ுିଵ௝ୀଵ (12) ܥ௜ൌ		ሾሺܥሺ௞ሻ௜ିଵሺ1െܥ௞ሻሻ൅1െሺܥ௞ሻ௜ିଵሺ1െ	ܥ௞ሻሿுെሺ1െሺܥ௞ሻ௜ିଵሺ1െܥ௞ሻሻு                          (13) Transformation from (12) to (13) use knowledge of  binomial theorem.	 Therefore, the packet loss rate is: ܦ௥ൌ∑ܥ௜ܲ∗௜௪௜ୀଵ                              (14) V. SOLVE 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 65148wavelength 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 {ܪଵ൅1,ܪଶ൅1,ܪଷ൅1,ܪସ൅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      λ୧		in	the	j	segment	is: ܥ௜௝ൌ		ሾሺܥሺ௞ሻ௜ିଵሺ1െܥ௞ሻሻ൅1െሺܥ௞ሻ௜ିଵሺ1െܥ௞ሻሿுೕെሺ1െሺܥ௞ሻ௜ିଵሺ1െܥ௞ሻሻுೕ                      (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. TEST 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 65149