ELEN7015 Module 7 Solutions

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Solutions

1. A system where there is congestion and callers do not have indefinite patience and reattempt calls and congestion leads to further congestion. The arrival distribution of incoming calls ceases to be a random poissonian process but becomes a function of blocking.

2. Erlang calculations make assumptions of poissonian arrival process, that blocked calls will leave the system and that callers have indefinite patience when they encounter congestion which is not true for high loss systems.

3. a. Call demand: This is an intention or desire to make a call and results in a call attempt.

b. Call attempt: The operation of attempting to make a connection to the intended party in a communication.

c. Rank of reattempt: The subsequent number of the reattempt after the first attempt.

d. Efficiency rate r: a ratio of the number of successful call attempts to the number of call attempts.

e. Coefficient of call repetition β: The average number of repeated calls after the call intention.

4. We use the relation λc =λ1(1-p) to find λ1 the total traffic. Making λ1 the subject of the formula, λ1= λc/ (1-p) =0.583/ (1-0.36) = 0.911 erl.

Blocked traffic is λ1x p = 0.911x0.36 = 0.328 erl

Alternativly Blocked traffic = total traffic - carried traffic = 0.911-0.583 = 0.328 erl