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For the cross point 2560, the number of k matrices is calculated from Nx = k (2N + (N/n)2]

N 2560

P = np/k = 8 x 0.15/5 = 0.24 The probability that k links are busy is B = [1 - (1 - P)2]k B = [1 - (1 - 0.24)2]5 = 1.34%

5.5.2. Blocking Probability Evaluation Techniques

All the switching systems are designed to provide a certain maximum probability of blocking for the busiest hour of the day. It is one of the aspects of the grade of service of the telephone company. There are variety of techniques to evaluate the blocking probability of a switching matrix. Depends on the accuracy, required availability, geographical area, priority, complexity and applicability of different network structures, the techniques are varying. Here, two techniques are described.

1. Lee graphs. It was proposed by C.Y. Lee. It is a most versatile and straight forward approaches of calculating probabilities with the use of probability graphs.

2. Jacobaeus method. It was presented in 1950 by C. Jacobaeus. It is more accurate than Lee graph method.

Lee graphics. C.Y. Lee's approach of determing the blocking probabilities of various switching system is based on the use of utilization percentage or loadings of individual links.

Let p be the probability that a link is busy. The probability that a link is idle is denoted by q = 1 - p. When any one of n parallel links can be used to complete a connection, the blocking probability B is the probability that all links are busy is given by

when a series of n links are all needed to complete a connection,

For a probability graph of three stage network, shown in Fig. 5.12, the probability of blocking is given by

B = (1 - q2)k where q = probability that an interstage link is idle = 1 - p p = probability that any particular intersatge link is busy k = number of centre stage arrays.

If p is known, the probability that an interstage link is busy is given by p = p where P = k/n

P is the factor by which the percentage of interstage links that are busy is reduced.

Fig. 5.12. Probability graph of three stage network.

Fig. 5.12. Probability graph of three stage network.

Substituting in (5.19) in (5.18) , we set q = 1 - —

Substituting (5.21) in (5.17) we get complete expression for the blocking probability of a three stage switch interms p as

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