How to use Erlang B to determine the blocking probability of packet loss in a wireless

communication

Author(s):

Wasswa Shafik1 Dr: S. Mojtaba Matinkhah2

wasswashafik@gmail.com matinkhah@yazd.ac.ir

1 2Computer Department, Yazd University, Yazd, Iran

• Abstract

Being in a digitally advancing era where wireless communication has beensimplified due to plentiful radio technologies, traffic delay has increasedduring data transmission between these devices. Erlang B is an entity that ismainly used in a call center in measuring offered load like in switchingmaterials. This article determines the rate of blocking during thecommunication process which is when a circuit group is fully occupied andcannot accept any more calls referred to as congestion, so they are eitherqueued or lost. Impact of grade of Service for computer networks withbenefits and drawbacks of each of this quality of service models in relationto the grade of services calculating blocking probabilities of packet loss for agroup of identical parallel element.

Keywords: Wireless communication, Performance Evaluation, Blockingprobability, Erlang B, Grade of Service

The network Grade of Service (GoS) is defined as: “the measure of traffic congestion in receiver network congestion in the network results in lost call scenario” the probability of a call in a circuit group being blocked or delayed for more than a specified period.

Common Communication Styles

Aggressive Style: This style is about captivating frequently at someone else's expense. It is an unproductive communication style as the contented of the message may get lost since people are too busy reacting to the way it's delivered.

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: A submissive person behaves like other peoples' needs are more important and other people have supplementary privileges and more to contribute.

Manipulative Style: 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 totally unconscious.

Assertive Style: 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 operation.

Fig 1: illustration of communication styles traits

Mathematical Representation

Mu (µ). Used to represent any rate of the service as predetermined.

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 bythe service rate gives the utilization.

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.

𝑠 = 𝑋−𝑌 2

𝑁

𝑠 =9 − 6.5 2 + 8 − 6.5 2 + 5 − 6.5 2 + 4 − 6.5 2

4

Where: { P_{b}} 𝑃𝑏 is the probability of blocking, m is the number of identical parallel resources 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.

µ𝑃1 = 𝜆𝑃0

µPb−1 + b + 1 µPb + 1 = λ + bµ Pb

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. For example

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

Considering the rate from 𝑃0 At the beginning

P0 = λP1 =1

zP1

In the same way 𝜆𝑃1 is 2

𝑧𝑃1 when the situation is for rate down of position 2 and in this case,

the probability of resources holders in this case servers are in a busy situation. By the use of mathematical notation of

𝜆𝑧 = 𝑟 since each is independent variables.

𝑃1 = 𝜆𝑧𝑃0 = 𝑟𝑃0 and verse visa applies to obtain the like 𝑃2

P2 = λzP1 =r2

2P0

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

𝑃𝑧 + 𝑃1 + 𝑃2 + 𝑃3… . . = 1

(P0 +r1

1!P0 +

r2

2!P0 +

rz

z!+.…P0 = 1

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.

𝑃 𝑏, 𝐾 =𝜆𝐾𝑏

𝑏!𝑒−𝜆𝐾

From E39, there are possibilities finding out the probabilities of connection hold period µq

𝑠 𝑞 = 1 − 𝑒−µ𝑞

In finding out the possibilities of servers from Erlang given that sv is number of services

𝑃𝑏 = 𝑖=0𝑠𝑣−1 𝜌

𝑖

𝑖!+

𝜌𝑠𝑣

𝑠𝑣1−𝜌

𝑠𝑣

−1

And from above it is possible to determine the possibilities of all servers to be given by

Pb =ρsvP0

sv1−ρ

sv

Numerical Results and Analysis:

From same equation 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

Result interpretationIt shows that the blocking probability of the network(wireless communication) decreases with theincreasing number of wavelengths, the increase of wavelength will not increase traffic intensityper wavelength.

Erlangs of traffic are taken to be the product of connection arrivals per second and the meanduration of connection requests. Erlang B formula packet loss model used to calculate blockingprobability with the available traffic load within a different wireless situation. Possibilities of GoScan be is measured with the rate blocking probabilities when applied mathematically identicalparallel element as shown.

Conclusions

This paper concludes that new communication styles will be conceived, and our lives will furtherbe changed, the functionality and efficient performance any wireless algorithm concerning GoSshould 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 theirwireless networks. We confirm that the results are validated through the use of MATLAB with thedifferent assumptions for accurate results as illustrated.

In appreciation for the present, for our future work, a quantity of routing algorithms will beproposed 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 thingswithin a fog, edge and could computing.