COMP9334 Revision Questions Week02B — Solution
Question 1
(a) The state transition diagram is:
0
l
μ
1
l
2μ
2
The state transition rate from S2 and S1 should be 2μ. Note that in order for the state to move from S2 to S1, any one of the calls in the call centre has to finish. Consider a
small
time interval δ,
Prob[Transiting from S2 to S1]
= Prob[Call at Operator 1 has finished OR Call at Operator 2 has finished ]
= Prob[Call at Operator 1 has finished] + Prob[Call at Operator 2 has finished ] − T1, 2019 COMP9334
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Prob[Call at Operator 1 has finished AND Call at Operator 2 has finished ] = μδ+μδ−(μδ)2
≈ 2μδ
(b) The state balance equations for States 1, 2 and 3 are respectively:
λP0 = μP1 μP1+λP1 = λP0+2μP2
λP1 = 2μP2
(1) (2) (3)
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