See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/332801468
How to use Erlang B to determine the blocking probability of packet loss in a
wireless communication
Presentation · December 2018
CITATIONS
READS
2
178
2 authors:
Wasswa Shafik
Mojtaba Matinkhah
Yazd University
Yazd University
39 PUBLICATIONS 157 CITATIONS
21 PUBLICATIONS 96 CITATIONS
SEE PROFILE
Some of the authors of this publication are also working on these related projects:
Fog-Mobile Edge Performance Evaluation View project
Internet of Wearable Things (IoWT) View project
All content following this page was uploaded by Wasswa Shafik on 27 May 2019.
The user has requested enhancement of the downloaded file.
SEE PROFILE
How to use Erlang B to determine the blocking probability of
packet loss in a wireless communication
Wasswa Shafik1, S. Mojtaba Matinkhah2
Computer Department, Yazd University, Yazd, Iran1, 2
wasswashafik@gmail.com1
matinkhah@yazd.ac.ir2
Abstract
Being in a digitally advancing era where wireless communication has been simplified due
to plentiful radio technologies, traffic delay has increased during data transmission
between these devices. Erlang B is an entity that is mainly used in a call center in
measuring offered load like in switching materials. This article determines the rate of
blocking during the communication process which is when a circuit group is fully
occupied and cannot accept any more calls referred to as congestion, so they are either
queued or lost. Impact of grade of Service for computer networks with benefits and
drawbacks of each of this quality of service models in relation to the grade of services,
illustrating basic approaches to Erlang B formula in an attempt to calculate blocking
probabilities of packet loss for a group of identical parallel element. Our Calculations and
results were tested and proofed with MATLAB.
Keywords: Wireless communication, Performance Evaluation, Blocking probability,
Erlang B, Grade of Service
1. Introduction
The network Grade of Service (GoS) is defined as: “the measure of traffic congestion in
receiver network” the probability of a call in a circuit group being blocked or delayed for
more than a specified period cooperatively within wireless communication. Load
balancing modes have been attempted[1] with reliability awareness in chaining with
strong wireless energy, coverage with multi-hocs transfer [2] where device communicate
wirelessly on removing routing protocols in the next generation at possible
connectivity[3]. Basing on the effective wireless algorithm basing on met heuristic
methods[4] put in place articulated as a decimal or vulgar fraction in an attempt
approaching quality and efficiency as in [5]. The busy hour leads to the evaluation as
shown when setting up measures and improvement. It leads to the quality of routing
predictable through certain prospective of call blocking. Perhaps, in[6] different ideas are
shown in relation to local terrain shows best frequencies in [7] focuses on probabilistic
model experimented on the quality of services(QoS) in the measure of blocking traffics to
validate adherence to conditions to measure the success of clientele served as well as
efficiency radio resource allocation in [8]. A lot of efforts have been done in research to
improve on grade and quality of wireless communication services as addressed mostly
without addressing most aspects that causes low grade of services this article, therefore
comes to attempt on big issues that challenge grade of services during communication, to
determine the delay of GoS in wireless network through the use of Erlang B formula.
Focal inherence to all communication is in the formation of communicative motivation or
reasons aggressive Style; this style is about captivating frequently at someone else's
expense. All styles of communication are illustrated in Fig 1.An aggressive person
behaves as if their needs are the most important, as though they have more rights, and
have more to throw in than other people have.
Fig 1: illustration of communication styles
Passive-Aggressive Style; This is a style in which people emerge passive on the outside,
but are actually acting out their anger in indirect or behind-the-scenes conducted. For
instance, people in war habitually act in passive-aggressive ways in order to deal with an
overwhelming lack of power. Submissive Style; this approach is concerned agreeable
other people and avoiding inconsistency. A submissive person behaves as if other peoples'
needs are more important and other people have supplementary privileges and more to
contribute. Manipulative Style; this mode is underhanded, shrewd and calculating.
Manipulative communicators are accomplished at influencing others to their own benefit.
Their spoken words hide an underlying message, of which the other person may be
unconscious. Assertive Style; Assertive communication is instinctive and of high selfesteem. It is the healthiest and most effective style of communication due to act that a
sweet spot between being too passive and aggressive. Notably, when we are assertive and
we have the self-reliance to communicate without resorting to an operation. In this mode,
we know our confines and do not allow ourselves to be pushed beyond them just because
someone else wants or needs something from us. More surprisingly, assertive is the style
most people use the slightest.
In this paper, a new analysis for blocking probability of wireless communication is
conceived, and the efficient performance of the wireless algorithm concerning GoS is
designed specifically to determine structures that are needed throughout the network. We
confirm that the results are validated using MATLAB with the different assumptions for
accurate results as illustrated.
The structure of the paper follows as; in the section 2. Providing the model of wireless
performance analysis with notation conventions, in the section 3, finally, in the section 4
the numerical examples with concluding discussion is offered.
1. The model of wireless performance analysis
Different phenomenal like possible arrival rates, traffics, blocks of different occasions,
holding duration and many more are represented, ways of finding out the GoS of any data
transmission like for example calls, and the formula, provides the GoS which is the
probability (Pb) that a new call arriving at the resource group is rejected because all
resources needed like (lines, servers, circuits among others) are busy or used-up.
1.1 .
Mu (µ). This is mainly used to represent any rate of the service as predetermined.
For example, the figure of events may be handled in a unit of time. In case we are to
use arrival time or duration divided by the predetermined service rate gives the
utilization.
2.2. Utilization (ρ). This is worthy to note that the number of events may be handled in a
unit of time if the use arrival time or duration divided by the service rate gives the
utilization and its referred to us rho.
(Eq 1)
Where is total system utilization, λ is the arrival rate per unit time or period, µ becomes
the service rate per unit time or period as regards (Eq 1)
2.3.
Sigma ( ∑ ). It's mostly used to illustrate the summation of any given equation
from the valve under the symbol of the above value of the sigma (the symbol).
Assuming our formula is given by W.
∑
0
0
1
2
2.4.
(Eq 2)
Standard deviation (s). This is one of the tools used to show or determine the size
of the figure or valve of mean in its spread capacities.
Let us use this standard layout with 9, 8,5, 4, assign 6.5 to you.
Where N is the total number of values.
)2
∑(
√
√
(9
6 5 )2
(Eq 3)
(8
6 5 )2
(5
6 5 )2
(4
6 5 )2
4
√
(6 25 )
(2 25 )
(2 25 )
(6 25 )
4
17
4
√
2 06
2.5.
Mean (x). To have the average of a given collection of figures may be
arithmetically be illustrated as taking for example 8, 5,4,4 as our values
∑
(Eq 4)
0
(8 0 25 )
(5 025 )
(4 0 25 )
(4 0 25 )
6 05
In an attempt to determine the probability of queueing approach in stochastic producers
since its depth of deductive reasoning and in its diversity of application.
*
1 2
+ shows dependency on the resource and obtained from
12
In simplification, B (E, m) below where E is the total offered traffic in Erlang, offered
to m identical parallel resources like (servers, traffic lanes, communication channels).
(
)
(Eq 5)
∑ 0
is the probability of blocking, m is the number of identical parallel resources
Where:
such as servers, telephone lines, E = λh is the normalized ingress.
Let us illustrate the possibilities of loss of system if so during communication, assume the
rate λ is applied to Poisson processing, exponential distribution with defined mean be 1/ µ
infinite state.
Let us take the Pb to be probability where b represent calls within the system, s that is the
model is a loss system at the arbitrary time, like b =0,1,2, s. In order to have the equation
balancing
1
0
1
Then it follows
(
(Eq 7)
1)
1
(
)
(Eq 8)
1
1 is obtained
(Eq 9)
(Eq 10)
1
may be worked up and this produces a balanced equation *
above.
0
+ as calculated
Take the equation to be the
1
1
is given by (Eq 10)
where λ /µ (Eq11) becomes the traffic given by r since
2
1
1
(
(Eq 11)
2
1) 2
2
( )
(Eq 12)
0
In the case of normal situations, obtaining the probability distribution for the number of
calls within the system is easily got where 0 is obtained.
∑
1
0
(Eq 13)
Thus
0
∑
(Eq 14)
0
This is simply shown in the equation as
0
(Eq 15)
The probability of blocking is illustrated in truncated Poisson distribution where b in the
system immediately before the arrival period in arbitrary time as
(
⁄
)
∑
(Eq 14)
⁄ )
0(
Assuming that the s =1,2 where
(
) the relationship is simple to derive from the above equation like
(0 )
1
Basing on the above equation
1
This is because
(
)
(
(
1 )
1 )
(Eq 15)
This may possibly be expressed recursively as follows, in a form that is used to simplify
the calculation of tables of the Erlang B formula:
(
0)
1
(Eq 16)
(
1)
(
)
12
1)
(
(Eq 17)
Characteristically, instead of B (E, m) (E30), the inverse 1/B (E, m) (E31) is calculated in
numerical computation in order to ensure numerical stability.
1
1
( 0)
1
(
(Eq 18)
1
1
)
1)
(
12
(Eq 19)
Poisson processing requires call arrivals maybe modeled, but it is legitimate for any
statistical circulation of call holding times with finite mean. Using the possible approach
to determine the possibilities of blocking during the communication, let us assume the
following.
z- The average of time needed for a service
Sv- The servers to be used during communication
λ - The requests that come in a certain interval
To make ease in order for us to understand this model, lets begin in the condition of 0, 1,
2 , or any which represents the number of calls at the moment in a system .Once the first
customer arrives, the system jumps to state 1, it will stay there a while, until either that
request completes or another request arrives. In case another call arrives before the first
one completes, then the system jumps to position 2, and stays there a while. In other
words, dividing the number jumps up with the total amount of time we obtain the rate up,
and by dividing the number of jumps down by the total amount of time results in the rate
down for example.
Considering the rate from
0
1
1
In the same way
1
is
2
0
At the beginning
(Eq 19)
1
when the situation is for rate down of position 2 and in this
1
case, the probability of resources holders in this case servers are in a busy situation. By the
use of mathematical notation of
since each is independent variables.
1
0
0
and verse visa applies to obtain the like
2
2
1
0
2
2
(Eq 20)
Modern artworks compare to Plain Old Telephone Service (POTS) is still applicable to
optical burst switching and several current approaches to optical packet switching.
3
3
2
3
0
(Eq 21)
Therefore, it applies those traffic transmission systems that do not buffer traffic
automatically. To illustrate the proof set of the above three equations is given as
1
2
1
0
1
1
3
(Eq 22)
2
0
2
0
0
1
(Eq 23)
From (E10) to address the situation with computational results
We take E to be a busy situation during communication without any possibility of queues
and m is the total arriving traffic, µ becomes the termination possibilities, λ average
connection request period, chance of the communication possibilities be q the probability
of b connection arrivals in K duration is easily illustrated as below when K is the average
period for the connection to be possible.
(
(Eq 24)
)
From E39, there are possibilities finding out the probabilities of connection hold period µq
( )
1
(Eq 23)
In finding out the possibilities of servers from Erlang given that sv is number of services
[∑
0
1
1
]
1
(Eq 23)
And from above it is possible to determine the possibilities of all servers to be given by
0
1
(Eq 24)
4. Numerical Results and Analysis
From same equations mainly (Eq 7) above, were used in traffic measurement intensity,
probabilities, channels in MATLAB as results are graphically displayed below.
Fig 2: Erlang B and its inversion in blocking
From the above illustration, it shows that the blocking probability of the network(wireless
communication) decreases with the increasing number of wavelengths, the increase of
wavelength will not increase traffic intensity per wavelength. Erlangs of traffic are taken
to be the product of connection arrivals per second and the mean duration of connection
requests. Erlang B formula packet loss model used to calculate blocking probability with
the available traffic load within a different wireless situation. Possibilities of GoS can be is
measured with the rate blocking probabilities when applied mathematically identical
parallel element as shown.
4. Discussion and Conclusions
This paper concludes that new communication styles will be conceived, and our lives will
further be changed, the functionality and efficient performance any wireless algorithm
concerning GoS should be designed specifically to determine structures that are needed
throughout the network. These results are to benefit mainly the operators in an attempt to
ensure a raised GoS of their wireless networks. We confirm that the results are validated
through the use of MATLAB with the different assumptions for accurate results as
illustrated. In appreciation for the present, for our future work, a quantity of routing
algorithms will be proposed with the focal intention of behavior in the intrinsic
imprecision and lessening its effect. More importantly, we are working on a denial of
service, and security of the Internet of things within a fog, edge and could computing.
References
[1] Bitton, S., Cohen, I., & Cohen, M. A. (2018). Joint Repair Sourcing and Stocking
Policies for Repairables Using Erlang-A and Erlang-B Queueing Models.
[2] Chan, Y. C., & Wong, E. W. (2018). Blocking Probability Evaluation for NonHierarchical Overflow Loss Systems. IEEE Transactions on Communications, 66(5),
2022-2036.
[3] Tang, F., Mao, B., Fadlullah, Z. M., Kato, N., Akashi, O., Inoue, T., & Mizutani, K.
(2018). On removing routing protocol from future wireless networks: A real-time deep
learning approach for intelligent traffic control. IEEE Wireless Communications, 25(1),
154-160.
[4] Gerasimou, S., Calinescu, R., & Tamburrelli, G. (2018). Synthesis of probabilistic
models for quality-of-service software engineering. Automated Software Engineering, 147.
[5] Nyangaresi, V. O., Abeka, S. O., & Rodrigues, A. (2018). Multivariate probabilistic
synthesis of cellular networks teletraffic blocking with poissonian distribution arrival
rates.
Yue, Y. G., & He, P. (2018). A comprehensive survey on the reliability of mobile wireless
sensor networks: Taxonomy, challenges, and future directions. Information Fusion, 44,
188-204.
[6] Qu, L., Khabbaz, M., & Assi, C. (2018). Reliability-Aware Service Chaining In
Carrier-Grade Softwarized Networks. IEEE Journal on Selected Areas in
Communications, 36(3), 558-573.
[7] Sagkriotis, S. G., Pantelis, S. K., Moscholios, I. D., & Vassilakis, V. G. (2018). Call
blocking probabilities in a two-link multirate loss system for Poisson traffic. IET
Networks, 7(4), 233-241.
[8] Soo, W. K., Ling, T. C., Maw, A. H., & Win, S. T. (2018). Survey on Load-Balancing
Methods in 802.11 Infrastructure Mode Wireless Networks for Improving Quality of
Service. ACM Computing Surveys (CSUR), 51(2), 34.
View publication stats