5040 [1 + 4 + 8 + 21.3 + 10.6 + 8.5 + 5.7 + 3.25] B = 0.052 = GOS. (b) The probability of only one trunk is busy
(c) The probability that only one trunk is free
(d) The probability that at least one trunk is free
P(k < 7) = 1 - P(7) = 1 - B = 1 - 0.052 = 0.948.
8.4.2. Lost Calls Returned (LCR) System
In LCC system, it is assumed that unserviceable requests leave the system and never return. This assumption is appropriate where traffic overflow occurs and the other routes are in other calls service. If the repeated calls not exist, LCC system is used. But in many cases, blocked calls return to the system in the form of retries. Some examples are subscriber concentrator systems, corporate tie lines and PBX trunks, calls to busy telephone numbers and access to WATS lines. Including the retried calls, the offered traffic now comprise two components viz., new traffic and retry traffic. The model used for this analysis is known as lost calls returned (LCR) model. The following assumptions are made to analyse the CLR model.
1. All blocked calls return to the system and eventually get serviced, even if multiple retries are required.
2. Time between call blocking and regeneration is random statistically independent of each other. This assumption avoid complications arrising when retries are correlated to each other and tend to cause recurring traffic peaks at a particular waiting time interval.
3. Time between call blocking and retry is somewhat longer than average holding time of a connection. If retries are immediate, congestion may occur or the network operation becomes delay system.
Consider a system with first attempt call arrival ratio of X (say 100). If a percentage B (say 8%) of the calls blocked, B times X retries (i.e. 8 calls retries). Of these retries, however a percentage B will be blocked again.
Hence by infinite series, total arrival rate X' is given as
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