isson distribution has at least k calls in it: (23.7) In the no-retry case shown in Fig. 23.2, there is no activity beyond state k, and the blocking probability is as in Eq. (23.8): P(blocking) = (23.8) This is called the Erlang-B model. Any time the system is in a state j < k, there is room for one more call, but when the system is in state k, there is no more room for another Superscript(3)The notation j! is j factorial, the product of all the whole numbers from 1 up to j. Figure 23.2 State diagram for k telephone channels. Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. Traffic Engineering for Voice and Data Traffic Engineering for Voice and Data call, and the system is in a blocked state. The probability of a new call being blocked is precisely the probability that the system is in state k. The difference between having blocked callers try again and having them go away quietly can be important in congested systems or systems with small numbers of chan- nels. For large values of k and for low blocking probabilities, it makes little difference whether or not blocked callers try again. 23.1.4 Blocking tables Table 23.1 shows Erlang-B capacity as a function of the number of channels (trunks) and the blocking probability. For example, 25 channels can support 16.1 erlangs at percent blocking and 20 erlangs at 5 percent blocking. Insisting on the higher standard of 1 percent blocking costs us 4 erlangs of capacity. Another way of looking at the same 20 erlangs is that 25 channels can serve that demand at 5 percent blocking, but it takes 30 channels to offer 1 percent blocking to the same user community. Let us look closely at the first, second, and last rows of Table 23.1 to help us under- stand what this table really means. Consider a single server, one telephone line, one Xerox copier, or one bank teller, and consider customers who refuse to w