ELASTICITY OF INTERNET TRAFFIC DISTRIBUTION IN COMPUTER
NETWORK IN TWO MARKET ENVIRONMENT

Diwakar Shukla; Sharad Gangele; Kapil Verma; Pankaja Singh

ELASTICITY OF INTERNET TRAFFIC DISTRIBUTION IN COMPUTER NETWORK IN TWO MARKET ENVIRONMENT

Diwakar Shukla^*1, Sharad Gangele², Kapil Verma ³ and Pankaja Singh⁴

Deptt. of Mathematics and Statistics, Sagar University, Sagar M.P. 470003, India.
Deptt. of Computer Science, M. P. Bhoj (Open) university, Kolar Road, Bhopal, M.P, India.
Deptt. of Computer Science, M. P. Bhoj (Open) university, Kolar Road, Bhopal, M.P, India.
Deptt. of Physics & Computer Science, Govt. Motilal Vigyan Mahavidhyalaya Bhopal, M.P.

Corresponding Author: Diwakar Shukla, E-mail: diwakarshukla@rediffmail.com

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Abstract

The Internet service is managed by operators and each one tries to capture larger proportion of Internet traffic. This tendency causes inherent competition in the market. The location of the market in also an important factor. This paper assumes two different markets and two operators are in competition. It is found that elasticities value depend on market position. The priority position market has higher level. This paper present Elasticities analysis of traffic sharing pattern among operators. Simulation study is performing to analyze the Elasticities impact on traffic sharing

Keywords

Markov chain model, Transition probability, Initial preference, Blocking probability, Call-by-call basis, Internet service providers [operators or ISP], Quality of service (QOS), Transition probability matrix.

INTRODUCTION

We assume a situation that there are two markets situated at distant apart in a city. Both the markets have Internet café with connection of two operators, Ou (u=1,3) and Ov (v=2,4). A user has a choice to pickup one market based on his liking and then selected the favourate operators in the Internet café. Both operators are in competitions to occupy more and more proportion of internet users. The network of both operators is suffering from blocking. The matter of interest is to know how blocking probability affects the customer proportion in the setup of two markets. Elasticities means rate of change of one variable with respect to other when many other parameters are kept constant. The traffic sharing by two operators is a variable and needs to examine in the light of Elasticities. This paper presents Elasticities based analysis of internet traffic sharing in multi operator and multi markets environment.

A REVIEW

Shukla et al. (2007) discussed analysis of internet traffic distribution between two markets using Markov chain model in computer networks. This contribution has initiated the problem of traffic sharing in two-market environment. Shukla et al. (2009) has extended the above approach by incorporating the share loss analysis of internet traffic distribution. Medhi (1991) discussed the basic fundamentals of Markov chain model. Shukla et al. (2009 b) presented all comparison analysis of internet traffic sharing using Markov chain model which is an extension of Naldi (2002). Catledge and Pitkow (1995) discussed a contribution on characterization of browsing strategies. Pirolli and pitkow (1996) suggested usable structure for web in light of many users. A similar study performed by pitkow (1997) regarding search of reliable usage data on www. Naldi (2001) presented Markov chain model based study in a multioperator environment. The detail distribution of Markov chain model is in Medhi (1991) and web browsing details are in Han and Kamber (2001). Shukla et al. (2007) discussed stochastic model for space decision switches for computer network. Shukla et al. (2007 a, b, c) suggested the use of Markov chain model in networking and operating system analysis. Shukla and Jain (2007) used Markov chain model for the analysis of multilevel Queue Scheduler in the operating system. Shukla and Singhai (2010 a) discussed traffic share analysis of massage flow in three crossbar architecture space division switches. Deshpande & Karypis (2004) discussed selective Markov chain model for predicting webpage access. Shukla et al. (2010 a, b, c, d, e, f, g, h) discussed different aspects on Markov chain model in determining the system behavior. Shrivastava et al. (2000) presented a thought oriented contribution on web page mining discovery and application of usage patterns from web data.

MARKOV CHAIN MODEL

Let {Xn, n 0} be a Markov chain model. As per Fig 3.1, let O1, O2, O3 and O4 be operators (ISP) in the two competitive Market-I (M1) and Market-II (M2). User chooses a market first, and then enters into a cyber-café situated inside. Where computer terminals of different operators are available to access the Internet. Operators are grouped as Ou (u=1,3) and Ov (v=2,4) for market-I and market-II Let{X(n), n>0} be a Markov chain having transitions over the state space M1, M2 and {O1, O2 , O3 , O4, Z1, Z2, A}

State O1: First operator in market-I,

State O2: Second operator in market-I,

State O3: Third operator in market-II,

State O4: Fourth operator in market-II,

State Z1: Success (link) in market-I (M1)

State Z2: Success (link) in market- II (M2)

State A: Abandon the attempt process.

The X(n) stands for the state of random variable X at nth attempt of connectivity (n > 0) made by the user. Some underlying assumptions of the Markov chain model are:

(a) A User (or Customer or CU) first select the Market-I with probability q and Market-II with probability (1-q), (see Fig 3.1)

(b) After choosing a market, User enters in the cyber-café (shop), chooses the first operator Ou with probability p or to Ov with (1-p).

(d) The connectivity attempts by user between operators are on call-by-call basis, if the call for Ou is blocked in kth attempt (k >O) then in (k + 1)th attempt user shifts to Ov. If this also fails, user switches to Ou in (k+2)th.

(e) Whenever call connects through either of operators Ou or Ov, we say system reaches to the state of success in n attempts.

(f) User can terminate the attempt process which is marked as system to the abandon state Z at nth attempts with probability pA (either Ou or from Ov).

SOME USEFUL RESULTS FOR nth CONNECTIVITY ATTEMPTS

Theorem 1.0 : The odd and even nth step probability for O1 in Market –I is:

QUALITY OF SERVICE [QOS]

There are two types of users as:

Faithful User [FU]

A user who is faithful to an operator Ou only otherwise he goes to abandon state but does not attempt for Ov. The converse of it may as he attempts for OV only and goes to state A otherwise.

Impatient User [IU]

A user who attempts between the two Operators Ou and Ov only all the time until call complete or otherwise abandons the process.

ELASTICITY STUDIES OVER LARGE ATTEMPT

Let p1 be the traffic sharing by the first operator, p2 be the traffic sharing by the second operator using Markov chain model using Naldi (2002), Shukla et al. (2007) we can obtain the expressions of traffic sharing as:

If y=f (x, z) is function then elasticity of y with respect to z is

SIMULATION STUDY

In view to fig. 1.0 the elasticities of the traffic share of the first operator in the first market is going down with the increasing level blocking probability. However if opponent operator also bears the same in increasing patterns, then the elasticity curve is further lower down.

While to consider traffic sharing of second operator, the elasticities pattern is in upward trend as in case of first market. With the increase of opponent L2 this pattern remains the same but elasticity value is lower.

When pA probability is high (fig. 6.0) the more stable pattern is found. In this case elasticities are looking like independent to L1 variation.

Fig. (7.0, 8.0) are similar type but having L2 probability as variant. These graphs are similar to figure (5.0, 6.0) but differ for traffic share p2 of O2.

Fig. (9.0, 10.0) are showing elasticities pattern for third operator bearing the blocking probability L1. The trend is downward and sharper than earlier cases. For little high L2 level this goes further down.

Fig. (11.0-12.0) are similar but with respect to L2 probability for P3 of operator O3 is high in the second market. Both the curves are having increasing Elasticities over L2 and decreasing probability level over L1.

Fig. (13.0-14.0) are similar to fig. (11.0, 12.0) and showing the positive value of elasticity. When pA is high then value of positive elasticity is also high.

Fig. (15.0, 16.0) are matching to fig. (9.0, 10.0) and the pattern of elasticity is downward showing a sharp decrement in the tendency.

CONCLUDING REMARKS

The Elasticities of traffic share of operator depends on blocking probability. These are negative in trend but when opponent blocking is high the negativity becomes high. Elasticities value depends on market position. If a market is of high priority, it has higher elasticities level. The abandon probability affects the elasticity level. High abandon chance produces stable pattern of traffic share independent to the blocking probability.

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