DETALLE DE LAS MACRODIMENSIONES DEL MODELO DE BALANCE

Control of flow is of great interest in communication and production network application. Many researchers have examined this topic in context of queuing system and wealth of results has been published. Due to unpredictable nature of work demands placed on the resources (transmission lines) congestion occurs (depending upon workload level) in communication system, queues will be formed and delays introduced at critical resources. Hence, while evaluating the performance analysis of a communication system these queues are necessary to take into consideration. Of course, performance not the only measure technical issues in design of communication system but other issues such as routing and flow control, link capacity assignment, concentrator placement, allocation and distribution of data base are of great importance and can’t be separated from performance analysis. In order to support efficient and flexible sharing of these resources, good techniques as message switching and packets switching multiplexing have been introduced, at the expense of additional complexity of system structure.

How to schedule and allocate resources effectively among competing requests is certainly in realm of congestion or queuing theory in a broader outlook. Queue Models have led to accurate analysis of Modern communication system. These models play significant role in modeling voice calls. The satellite communication system has been designed for voice traffic. With the advent of faxes and internet, the nature of traffic has changed dramatically. As a result, packet switched networks have gained importance over circuit switching networks. In all packet node communication system, network resources are managed by statistical multiplexing or dynamic memory allocation in which a communication channel is effectively divided into an arbitrary number of logical bit rate channels or data streams. The delay in packet switching can be reduced by utilizing the statistical multiplexing in

Arti Tyagi, T.P. Singh 

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communication system. The term multiplexing is used in connection with computer communication networks which employ some variant of time division multiplexing to share communication channels.

Various researchers studied the communication network as interconnected queues assuming arrivals and service patterns independent (Jenq (1984), Hoshida (1993), Srinivason Rao etal. (2000, 2006). But in many practical situations such as in computer communication applications the massage are transmitted between nodes in a networks, the service time depends upon (i) the length of message (ii) the line speed. Hence the service time of the same message at different nodes is dependent. Indeed not only the service time dependent but inter arrival time between two consecutive messages are also dependent. Srinivason Rao etal (2006) & Singh T.P. (2011) developed a queue model to interdependent communication system assuming arrival and transmission process at the node are correlated.

Since in communication system there is unpredictable and uncertain nature of demand at transmission lines, the fuzzy logic suites better comparative to random process. In the literature, customers inter arrival time and their service times are required to follow certain probability distributions with fixed parameters. However, in many real applications the parametric distribution may only be characterized subjectively in linguistic form i.e. the arrival and service are typically observed in everyday language, slow, average, fast, very fast etc. that can be best described by fuzzy set & logic. In this paper the arrival massages as well as the concerned activity in transmission and covariance between composite arrival and transmission completion have been assumed fuzzy in nature differs with the work done by Srinivason etal. The fuzzy concept in communication system was first introduced by T.P. Singh (see Singh T.P. & Kusum (2012)). The study was extended by Arti Tyagi & Singh T.P. (2012, 2013).

The present study is further an extended work of Arti Tyagi & Singh T.P. (2013) in which the trapezoidal fuzzy nature has been considered for interdependence communication system and a relation is derived between optimal vocational time & cost ration of system characteristic. The model is more significant and is relevant in real world situations. The model mechanism not only reduce the idle time of transmitter but enhance the capacity of channel utilization by approximating the arrival, packets transmission & covariance all considered fuzzy in nature under a bi-variate Poisson process and the various system characteristics are derived & analyzed for the model using fuzzy arithmetic. The main objective is to find out how the behavior of the buffer is characterized in terms of fuzzy process and buffer capacity.

4. Fuzzy Set:

Fuzzy logic extends Boolean logic to handle the expression of vague concepts. To express impression quantitatively a set membership function maps elements to real values between 0 & 1. The value indicates the degree to which an element belongs to a set. The degree is not describing probabilities that the item is in the set, but instead describes to what extent the item is in the set.

In the universe of discourse X, a fuzzy subset A on X is defined by the membership function μ_A(X)Which maps

each element x into Xto a real number in the interval [0,1]. μ_A (X)Denotes the grade or degree of membership and it is usually denoted by μ_A(X) : X→[0,1].

4.1 TRAPEZOIDAL FUZZY NUMBER:

, x , = 1 x , , x , 0 , otherwise

Optimal Vacation Period With Cost Analysis of An Interdependence Fuzzy Queue Model To A Communication System

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4.2 TRAPEZOIDAL FUZZY NUMBER OPERATION:

Let = (a1,a2,a3, a4) and = (b1,b2,b3, b4) be two trapezoidal fuzzy number, then the arithmetic operation on and are given as follows :

Addition = [a1+b1, a2+b2, a3+b3, a4+b4] Subtraction = [a1-b4, a2-b3, a3-b2, a4- b1] Multiplication = [a1b2, a2b2, a3b3, a4b4] Division / = [a1/b4, a2/b3, a3/b2, a4/ b1] Provided are all non-zero positive numbers.